,,the ,,telescope ,mc,graw-,hill ,book ,co4 ,inc4 ,,publishers ,,of ,,books ,,for ,coal ,age ,electric ,railway ,journal ,electrical ,world ,engineering ,news-,record ,american ,machinist ,ingeniera ,internacional ,engineering ,mining ,journal ,power ,chemical ,metallurgical ,engineering ,electrical ,merchandising ,illustration3 ,galileo's ,telescopes4 7,frontispiece7 7,bull4 de la ,soc4 ,astron4 de ,france47 ,,the ,,telescope ,,by ,,louis ,,bell1 ,,ph4,d4 ,,consulting ,,engineer2 ,,fellow1 ,,american ,,academy ,,of ,,arts ,,sciences2 ,,past-,,president1 ,,the ,,illuminating ,,engineering ,,society2 ,,member1 ,,american ,,astronomical ,,society ,,first ,,edition ,,mcgraw-,,hill ,,book ,,company1 ,,inc4 ,,new ,,york3 #cgj ,,seventh ,,avenue ,,london3 #f #h ,,bouverie ,,st41 ,e4 ,c4 #d #aibb ,,copyright1 #aibb1 ,,by ,,the ,,mcgraw-,,hill ,,book ,,company1 ,,inc4 ,,the ,,maple ,,press ,,york ,,pa ,,preface ,this book is written for the many observers1 who use telescopes for study or pleasure and desire more information about their construction and properties4 ,not being a 8handbook0 in two or more thick quartos1 it attempts neither exhaustive technicalities nor popular descriptions of great observatories and their work4 ,it deals primarily with principles and their application to such instruments as are likely to come into the possession1 or within reach1 of students and others for whom the ,heavens have a compelling call4 ,much has been written of telescopes1 first and last1 but it is for the most part scattered through papers in three or four languages1 and quite inaccessible to the ordinary reader4 ,for his benefit the references are1 so far as is practicable1 to ,english sources1 and dimensions are given1 regretfully1 in ,english units4 ,certain branches of the subject are not here discussed for lack of space or because there is recent literature at hand to which reference can be made4 ,such topics are telescopes notable chiefly for their dimensions1 and photographic apparatus on which special treatises are available4 ,celestial photography is a branch of astronomy which stands on its own feet1 and although many telescopes are successfully used for photography through the help of color screens1 the photographic telescope proper and its use belongs to a field somewhat apart1 requiring a technique quite its own4 ,it is many years1 however1 since any book has dealt with the telescope itself1 apart from the often repeated accounts of the marvels it discloses4 ,the present volume contains neither pictures of nebul nor speculations as to the habitibility of the planets2 it merely attempts to bring the facts regarding the astronomer's chief instrument of research somewhere within grasp and up to the present time4 ,the author cordially acknowledges his obligations to the important astronomical journals1 particularly the ,astro-physical ,journal1 and ,popular ,astronomy in this country2 ,the ,observatory1 and the publications of the ,royal ,astronomical ,society in ,england2 the ,bulletin de la ,socit ,astronomique de ,france2 and the ,astronomische ,nachrichten2 which1 with a few other journals and the official reports of observatories form the body of astronomical knowledge4 ,he also acknowledges the kindness of the various publishers who have extended the courtesy of illustrations1 especially ,macmillan ,co4 and the ,clarendon ,press1 and above all renders thanks to the many friends who have cordially lent a helping hand--the ,director and staff of the ,harvard ,observatory1 ,dr4 ,george ,e4 ,hale1 ,c4 ,a4 ,r4 ,lundin1 manager of the ,alvan ,clark ,corporation1 ,j4 ,b4 ,mc,dowell1 successor of the ,brashear ,company1 ,j4 ,e4 ,bennett1 the ,american representative of ,carl ,zeiss1 ,jena1 and not a few others4 ,,louis ,,bell4 ,,boston1 ,,mass41 ,february1 #aibb4 ,,contents ,,page ,,preface vii ,,chap4 ,i4 ,,the ,,evolution ,,of ,,the ,,telescope #a ,,ii4 ,,the ,,modern ,,telescope #ca ,,iii4 ,,optical ,,glass ,,and ,,its ,,working #eg ,,iv4 ,,the ,,properties ,,of ,,objectives ,,and ,,mirrors #gf ,v4 ,,mountings #ih ,,vi4 ,,eye-,,pieces #acd ,,vii4 ,,hand ,,telescopes ,,and ,,binoculars #aej ,,viii4 ,,accessories #afe ,,ix4 ,,the ,,testing ,,and ,,care ,,of ,,telescopes #bja ,x4 ,,setting ,,up ,,and ,,housing ,,the ,,telescope #bbh ,,xi4 ,,seeing ,,and ,,magnification #bec ,,appendix #bgi ,,index #bha ,,the ,,telescope ,,chapter ,i ,,the ,,evolution ,,of ,,the ,,telescope ,in the credulous twaddle of an essay on the ,lost ,arts one may generally find the telescope ascribed to far antiquity4 ,in place of evidence there is vague allusion of classical times or wild flights of fancy like one which argued from the ,scriptural statement that ,satan took up ,christ into a high mountain and showed him all the kingdoms of the earth1 that the ,devil had a telescope--bad optics and worse theology4 ,in point of fact there is not any indication that either in classical times1 or in the black thousand years of hopeless ignorance that followed the fall of ,roman civilization1 was there any knowledge of optical instruments worth mentioning4 ,the peoples that tended their flocks by night in the ,east alone kept alive the knowledge of astronomy1 and very gradually1 with the revival of learning1 came the spirit of experiment that led to the invention of aids to man's natural powers4 ,the lineage of the telescope runs unmistakably back to spectacles1 and these have an honorable history extending over more than six centuries to the early and fruitful days of the ,renaissance4 ,that their origin was in ,italy near the end of the thirteenth century admits of little doubt4 ,a ,florentine manuscript letter of #abhi refers to 8,those glasses they call spectacles1 lately invented1 to the great advantage of poor old men when their sight grows weak10 and in #acje ,giordano da ,rivalto refers to them as dating back about twenty years4 ,finally1 in the church of ,santa ,maria ,maggiore in ,florence lay buried ,salvino d',amarto degli ,armati1 7obiit #acag7 under an epitaph1 now disappeared1 ascribing to him the invention of spectacles4 ,w4 ,b4 ,carpenter1 ,f4 ,r4 ,s41 states that the inventor tried to keep the valuable secret to himself1 but it was discovered and published before his death4 ,at all events the discovery moved swiftly4 ,by the early fourteenth century it had spread to the ,low ,countries where it was destined to lead to great results1 and presently was common knowledge over all civilized ,europe4 ,it was three hundred years1 however1 between spectacles and the combination of spectacle lenses into a telescope1 a lapse of time which to some investigators has seemed altogether mysterious4 ,the ophthalmological facts lead to a simple explanation4 ,the first spectacles were for the relief of presbyopia1 the common and lamentable affection of advancing years1 and for this purpose convex lenses of very moderate power sufficed1 nor was material variation in power necessary4 ,glasses having a uniform focus of a foot and a half or thereabouts would serve every practical purpose1 but would be no material for telescopes4 ,myopia was little known1 its acquired form being rare in a period of general illiteracy1 and glasses for its correction1 especially as regards its higher degrees1 probably came slowly and were in very small demand1 so that the chance of an optical craftsman having in hand the ordinary convex lenses and those of strong negative curvature was altogether remote4 ,indeed it was only in #aege that ,maurolycus published a clear description of myopia and hypermetropia with the appropriate treatment by the use of concave and convex lenses4 ,until both of these1 in quite various powers1 were available1 there was small chance of hitting upon an instrument that required their use in a highly special combination4 ,at all events there is no definite trace of the discovery of telescopic vision until #afjh and the inventor of record is unquestionably one ,jan ,lippershey1 a spectacle maker of ,middelburg in ,zeeland1 a native of ,wesel4 ,on ,oct4 #b1 #afjh the ,states-,general took under consideration a petition which had been presented by ,lippershey for a #cj-year patent to the exclusive right of manufacture of an instrument for seeing at a distance1 or for a suitable pension1 under the condition that he should make the instrument only for his country's service4 ,the ,states ,general pricked up its ears and promptly appointed on ,oct4 #d a committee to test the new instrument from a tower of ,prince ,maurice's palace1 allotting #ijj florins for the purchase of the invention should it prove good4 ,on the #fth the committee reported favorably and the ,assembly agreed to give ,lippershey #ijj florins for his instrument1 but desired that it be arranged for use with both eyes4 ,lippershey therefore pushed forward to the binocular form and two months later1 ,dec4 #i1 he announced his success4 ,on the #aeth the new instrument was examined and pronounced good1 and the ,assembly ordered two more binoculars1 of rock crystal1 at the same price4 ,they denied a patent on the ground that the invention was known to others1 but paid ,lippershey liberally as a sort of retainer to secure his exclusive services to the ,state4 ,in fact even the ,french ,ambassador1 wishing to obtain an instrument from him for his ,king1 had to secure the necessary authorization from the ,states-,general4 ,illustration3 ,bull4 de la ,soc4 ,astron4 de ,france4 ,,fig4 #a4--;,jan ,lippershey1 ,inventor of the ,telescope4 ,it is here pertinent to enquire what manner of optic tube ,lippershey showed to back up his petition1 and how it had come to public knowledge4 ,as nearly as we may know these first telescopes were about a foot and a half long1 as noted by ,huygens1 and probably an inch and a half or less in aperture1 being constructed of an ordinary convex lens such as was used in spectacles for the aged1 and of a concave glass suitable for a bad case of short sightedness1 the only kind in that day likely to receive attention4 ,it probably magnified no more than three or four diameters and was most likely in a substantial tube of firmly rolled1 glued1 and varnished paper1 originally without provision for focussing1 since with an eye lens of rather low power the need of adjustment would not be acute4 ,as to the invention being generally known1 the only definite attempt to dispute priority was made by ,james ,metius of ,alkmaar1 who1 learning of ,lippershey's petition1 on ,oct4 #ag1 #afjh1 filed a similar one1 alleging that through study and labor extending over a couple of years he1 having accidentally hit upon the idea1 had so far carried it out that his instrument made distant objects as distinct as the one lately offered to the ,states by a citizen and spectacle maker of ,middelburg4 ,he apparently did not submit an instrument1 was politely told to perfect his invention before his petition was further considered1 and thereafter disappears from the scene1 whatever his merits4 ,if he had actually noted telescopic vision he had neither appreciated its enormous importance nor laid the facts before others who might have done so4 ,the only other contemporary for whom claims have been made is ,zacharius ,jansen1 also a spectacle maker of ,middelburg1 to whom ,pierre ,borel1 on entirely second hand information1 ascribed the discovery of the telescope4 ,but ,borel wrote nearly fifty years later1 after all the principals were dead1 and the evidence he collected from the precarious memories of venerable witnesses is very conflicting and points to about #afaj as the date when ,jansen was making telescopes--like many other spectacle makers4#a #a ,there is a very strong probability that ,jansen was the inventor of the compound microscope about the beginning of the seventeenth century4 ,borel also gave credence to a tale that ,metius1 seeking ,jansen1 strayed into ,lippershey's shop and by his inquiries gave the shrewd proprietor his first hint of the telescope1 but set the date at #afaj4 ,a variation of this tale of the mysterious stranger1 due to ,hieronymus ,sirturus1 contains the interesting intimation that he may have been of supernatural origin--not further specified4 ,there are also the reports1 common among the ignorant or envious1 that ,lippershey's discovery was accidental1 even perhaps made by his children or apprentice4 ,just how it actually was made we do not know1 but there is no reason to suppose that it was not in the commonplace way of experimenting with and testing lenses that he had produced1 perhaps those made to meet a vicious case of myopia in one of his patrons4 ,when the discovery was made is somewhat clearer4 ,plainly it antedated ,oct4 #b1 and in ,lippershey's petition is a definite statement that an instrument had already been tested by some1 at least1 of the members of the ,states-,general4 ,a somewhat vague and gossipy note in the ,mercure ,franaise intimates that one was presented to ,prince ,maurice 8about ,september of the past year0 7#afjh7 and that it was shown to the ,council of ,state and to others4 ,allowing a reasonable time between ,lippershey's discovery and the actual production of an example suitable for exhibition to the authorities1 it seems likely that the invention dates back certainly into the summer of #afjh1 perhaps even earlier4 ,at all events there is every indication that the news of it spread like wild-fire4 ,unless ,lippershey were unusually careful in keeping his secret1 and there are traditions that he was not1 the sensational discovery would have been quickly known in the little town and every spectacle maker whose ears it reached would have been busy with it4 ,if the dates given by ,simon ,marius in his ,mundus ,jovialis be correct1 a ,belgian with an air of mystery and a glass of which one of the lenses was cracked1 turned up at the ,frankfort fair in the autumn of #afjh and at last allowed ,fuchs1 a nobleman of ,bimbach1 to look through the instrument4 ,fuchs noted that it magnified 8several0 times1 but fell out with the ,belgian over the price1 and returning1 took up the matter with ,marius1 fathomed the construction1 tried it with glasses from spectacles1 attempted to get a convex lens of longer focus from a ,nuremburg maker1 who had no suitable tools1 and the following summer got a fairly good glass from ,belgium where such were already becoming common4 ,with this ,marius eventually picked up three satellites of ,jupiter--the fourth awaited the arrival of a superior telescope from ,venice4 ,early in #afji telescopes 8about a foot long0 were certainly for sale in ,paris1 a ,frenchman had offered one in ,milan by ,may of that year1 a couple of months later one was in use by ,harriot in ,england1 an example had reached ,cardinal ,borghese1 and specimens are said to have reached ,padua4 ,fig4 #b from the 8,mundus ,jovialis10 shows ,marius with his 8,perspicilium10 the first published picture of the new instrument4 ,early in #afaj telescopes were being made in ,england1 but if the few reports of performance1 even at this date1 are trustworthy1 the 8,dutch trunk0 of that period was of very indifferent quality and power1 far from being an astronomical instrument4 ,illustration3 ,the ,observatory4 ,,fig4 #b4--,simon ,marius and his ,telescope4 ,one cannot lay aside this preliminary phase of the evolution of the telescope without reference to the alleged descriptions of telescopic apparatus by ,roger ,bacon1 7c4 #abgj71 ,giambattista della ,porta 7#aeeh71 and ,leonard ,digges 7#aega71 details of which may be found in ,grant's ,history of ,physical ,astronomy and many other works4 ,of these the first on careful reading conveys strongly the conviction that the author had a pretty clear idea of refraction from the standpoint of visual angle1 yet without giving any evidence of practical acquaintance with actual apparatus for doing the things which he suggests4 ,given a suitable supply of lenses1 it is reasonably certain that ,bacon was clever enough to have devised both telescope and microscope1 but there is no evidence that he did so1 although his manifold activities kept him constantly in public view4 ,it does not seem unlikely1 however1 that his suggestions in manuscripts1 quite available at the time1 may have led to the contemporaneous invention of spectacles4 ,porta's comments sound like an echo of ,bacon's1 plus a rather muddled attempt to imagine the corresponding apparatus4 ,kepler1 certainly competent and familiar with the principles of the telescope1 found his description entirely unintelligible4 ,porta1 however1 was one of the earliest workers on the camera obscura and upon this some of his cryptic statements may have borne4 ,somewhat similar is the situation respecting ,digges4 ,his son makes reference to a ,ms4 of ,roger ,bacon as the source of the marvels he describes4 ,the whole account1 however1 strongly suggests experiments with the camera obscura rather than with the telescope4 ,the most that can be said with reference to any of the three is that1 if he by any chance fell upon the combination of lenses that gave telescopic vision1 he failed to set down the facts in any form that could be or was of use to others4 ,there is no reason to believe that the ,dutch discovery1 important as it was1 had gone beyond the empirical observation that a common convex spectacle lens and a concave one of relatively large curvature could be placed in a tube1 convex ahead1 at such a distance apart as to give a clear enlarged image of distant objects4 ,it remained for ,galileo 7#aefd-afdg7 to grasp the general principles involved and to apply them to a real instrument of research4 ,it was in ,may #afji that1 on a visit to ,venice1 he heard reports that a ,belgian had devised an instrument which made distant objects seem near1 and this being quickly confirmed by a letter from ,paris he awakened to the importance of the issue and1 returning to ,padua1 is said to have solved the problem the very night of his arrival4 ,next day he procured a plano-convex and a plano-concave lens1 fitted them to a lead tube and found that the combination magnified three diameters1 an observation which indicates about what it was possible to obtain from the stock of the contemporary spectacle maker4#b ,the relation between the power and the foci of the lenses he evidently quickly fathomed for his next recorded trial reached about eight diameters4 #b ,the statement by ,galileo that he 8fashioned0 these first lenses can hardly be taken literally if his very speedy construction is to be credited4 ,with this instrument he proceeded to ,venice and during a month's stay1 ,august1 #afji1 exhibited it to the senators of the republic and throngs of notables1 finally disclosing the secret of its construction and presenting the tube itself to the ,doge sitting in full council4 ,this particular telescope was about twenty inches long and one and five eighths inches in aperture1 showing plainly that ,galileo had by this time found1 or more likely made1 an eye lens of short focus1 about three inches1 quite probably using a well polished convex lens of the ordinary sort as objective4 ,illustration3 ,lodge 8,pioneers of ,science40 ,,fig4 #c4--;,galileo4 ,laden with honors he returned to ,padua and settled down to the hard work of development1 grinding many lenses with his own hands and finally producing the instrument magnifying some #cb times1 with which he began the notable succession of discoveries that laid the foundation of observational astronomy4 ,this with another of similar dimensions is still preserved at the ,galileo ,museum in ,florence1 and is shown in the ,frontispiece4 ,the larger instrument is forty-nine inches long and an inch and three quarters aperture1 the smaller about thirty-seven inches long and of an inch and five-eighths aperture4 ,the tubes are of paper1 the glasses still remain1 and these are in fact the first astronomical telescopes4 ,galileo made in ,padua1 and after his return to ,florence in the autumn of #afaj1 many telescopes which found their way over ,europe1 but quite certainly none of power equalling or exceeding these4 ,in this connection ,john ,greaves1 later ,savilian ,professor of ,astronomy at ,oxford1 writing from ,sienna in #afci1 says3 8,galileus never made but two good glasses1 and those were of old ,venice glass40 ,in these best telescopes1 however1 the great ,florentine had clearly accomplished a most workmanlike feat4 ,he had brought the focus of his eye lens down to that usual in modern opera glasses1 and has pushed his power about to the limit for simple lenses thus combined4 ,the lack of clear and homogeneous glass1 the great difficulty of forming true tools1 want of suitable commercial abrasives1 impossibility of buying sheet metals or tubing 7except lead71 and default of now familiar methods of centering and testing lenses1 made the production of respectably good instruments a task the difficulty of which it is hard now to appreciate4 ,the services of ,galileo to the art were of such profound importance1 that his form of instrument may well bear his name1 even though his eyes were not the first that had looked through it4 ,such1 too1 was the judgment of his contemporaries1 and it was by the act of his colleagues in the renowned ,acaddemia dei ,lincei1 through the learned ,damiscianus1 that the name 8,telescope0 was devised and has been handed down to us4 ,a serious fault of the ,galilean telescope was its very small field of view when of any considerable power4 ,galileo's largest instrument had a field of but #gae1 less than one quarter the moon's diameter4 ,the general reason is plain if one follows the rays through the lenses as in ,fig4 #d where ,,ab is the distant object1 o the objective1 e the eye lens1 ab the real image in the absence of e1 and ab the virtual magnified image due to e4 ,it will be at once seen that the axes of the pencils of rays from all parts of the object1 as shown by the heavy lines1 act as if they diverged from the optical center of the objective1 but diverging still more by refraction through the concave eye lens e1 fall mostly outside the pupil of the observer's eye4 ,in fact the field is approximately measured by the angle subtended by the pupil from the center of o4 ,to the credit of the ,galilean form may be set down the convenient erect image1 a sharp1 if small1 field somewhat bettered by a partial compensation of the aberrations of the objective by the concave eye lens1 and good illumination4 ,for a distant object the lenses were spaced at the difference of their focal lengths1 and the magnifying power was the ratio of these1 fo_/fe4 ,illustration3 ,,fig4 #d4--;,diagram of ,galileo's ,telescope4 ,but the difficulty of obtaining high power with a fairly sizeable field was ultimately fatal and the type now survives only in the form of opera and field glasses1 usually of #b to #e power1 and in an occasional negative eye lens for erecting the image in observatory work4 ,practically all the modern instruments have achromatic objectives and commonly achromatic oculars4 ,illustration3 ,,fig4 #e4--;,diagram of ,kepler's ,telescope4 ,the necessary step forward was made by ,johann ,kepler 7#aega-afcj71 the immortal discoverer of the laws of planetary motion4 ,in his ,dioptrice 7#afaa7 he set forth the astronomical telescope1 substantially1 save for the changes brought by achromatism1 as it has been used ever since4 ,his arrangement was that of ,fig4 #e in which the letters have the same significance as in ,fig4 #d4 ,there are here three striking differences from the ,galilean form4 ,there is a real image in the front focus of the eye lens e1 the rays passing it are refracted inwards instead of outwards1 to the great advantage of the field1 and any object placed in the image plane will be magnified together with the image4 ,the first two points ,kepler fully realized1 the third he probably did not1 though it is the basis of the micrometer4 ,the lenses o and e are obviously spaced at the sum of their focal lengths1 and as before the magnifying power is the ratio of these lengths1 the visible image being inverted4 ,kepler1 so far as known1 did not actually use the new telescope1 that honor falling about half a dozen years later1 to ,christopher ,scheiner1 a ,jesuit professor of mathematics at ,ingolstadt1 best known as a very early and most persistent1 not to say verbose1 observer of sun spots4 ,his ,rosa ,ursina 7#afcj7 indicates free use of ,kepler's telescope for some years previously1 in just what size and power is uncertain4#c ,fontana of ,naples also appears to have been early in the field4 #c ,scheiner also devised a crude parallactic mount which he used in his solar observations1 probably the first ,european to grasp the principle of the equatorial4 ,it was only near the end of the century that ,roemer followed his example1 and both had been anticipated by ,chinese instruments with sights4 ,but the new instrument despite its much larger field and far greater possibilities of power1 brought with it some very serious problems4 ,with increased power came greatly aggravated trouble from spherical aberration and chromatic aberration as well1 and the additive aberrations of the eye lens made matters still worse4 ,the earlier ,keplerian instruments were probably rather bad if the drawings of ,fontana from #afbi to #afcf fairly represent them4 ,if one may judge from the course of developments1 the first great impulse to improvement came with the publication of ,descartes' 7#aeif-afej7 study of dioptrics in #afcg4 ,therein was set forth much of the theory of spherical aberration and astronomers promptly followed the clues1 practical and impractical1 thus disclosed4 ,without going into the theory of aberrations the fact of importance to the improvement of the early telescope is that the longitudinal spherical aberration of any simple lens is directly proportional to its thickness due to curvature4 ,hence1 other things being equal1 the longer the focus for the same aperture the less the spherical aberration both absolutely and relatively to the image4 ,further1 although ,descartes knew nothing of chromatic aberration1 and the colored fringe about objects seen through the telescope must then have seemed altogether mysterious1 it1 also1 was greatly relieved by lengthening the focus4 ,for the chromatic circle produced by a simple lens of given diameter has a radial width substantially irrespective of the focal length4 ,but increasing the focal length increases in exact proportion the size of the image1 correspondingly decreasing the relative effect of the chromatic error4 ,descartes also suggested several designs of lenses which would be altogether free of spherical aberration1 formed with elliptical or hyperbolic curvature1 and for some time fruitless efforts were made to realize this in practice4 ,it was in fact to be near a century before anyone successfully figured non-spherical surfaces4 ,it was spherical quite as much as chromatic aberration that drove astronomers to long telescopes4 ,meanwhile the astronomical telescope fell into better hands than those of ,scheiner4 ,the first fully to grasp its possibilities was ,william ,gascoigne1 a gallant young gentleman of ,middleton1 ,yorkshire1 born about #afbj 7some say as early as #afab7 and who died fighting on the ,king's side at ,marston ,moor1 ,july #b1 #afdd4 ,to him came as early as #afch the inspiration of utilizing the real focus of the objective for establishing a telescopic sight4 ,illustration3 ,,fig4 #f4--;,diagram of ,terrestrial ,ocular4 ,this shortly took the form of a genuine micrometer consisting of a pair of parallel blades in the focus1 moved in opposite directions by a screw of duplex pitch1 with a scale for whole revolutions1 and a head divided into #ajj parts for partial revolutions4 ,with this he observed much from #afch to #afdc1 measured the diameters of sun1 moon and planets with a good degree of precision1 and laid the foundations of modern micrometry4 ,he was equipped by #afci with what was then called a large telescope4 ,his untimely death1 leaving behind an unpublished treatise on optics1 was a grave loss to science1 the more since the manuscript could not be found1 and1 swept away by the storms of war1 his brilliant work dropped out of sight for above a score of years4 ,meanwhile ,de ,rheita 7#aeig-affj71 a ,capuchin monk1 and an industrious and capable investigator1 had been busy with the telescope1 and in #afde published at ,antwerp a somewhat bizarre treatise1 dedicated to ,jesus ,christ1 and containing not a little practical information4 ,de ,rheita had early constructed binoculars1 probably quite independently1 had lately been diligently experimenting with ,descartes' hyperbolic lens1 it is needless to say without much success1 and was meditating work on a colossal scale--a glass to magnify #d1jjj times4 ,but his real contribution to optics was the terrestrial ocular4 ,this as he made it is shown in ,fig4 #f where a b is the image formed by the objective in front of the eye lens r1 s and t two equal lenses separated by their focal lengths and a b the resultant reinverted image4 ,this form remained in common use until improved by ,dolland more than a century later4 ,illustration3 ,,fig4 #g4--;,johannes ,hevelius4 ,a somewhat earlier form ascribed to ,father ,scheiner had merged the two lenses forming the inverting system of ,fig4 #f1 into a single lens used at its conjugate foci4 ,closely following ,de ,rheita came ,johannes ,hevelius 7#afaa-afhg7 of ,danzig1 one of the really important observers of the seventeenth century4 ,his great treatise ,selenographia published in #afdg gives us the first systematic study of the moon1 and a brief but illuminating account of the instruments of the time and their practical construction4 ,at this time the ,galilean and ,keplerian forms of telescope were in concurrent use and ,hevelius gives directions for designing and making both of them4 ,apparently the current instruments were not generally above five or six feet long and from ,hevelius' data would give not above #cj diameters in the ,galilean form4 ,there is mention1 however1 of tubes up to #ab feet in length1 and of the advantage in clearness and power of the longer focus plano-convex lens4 ,paper tubes1 evidently common1 are condemned1 also those of sheet iron on account of their weight1 and wood was to be preferred for the longer tubes4 ,evidently ,hevelius had at this time no notion of the effect of the plano-convex form of lens as such in lessening aberration1 but he mentions a curious form of telescope1 actually due to ,de ,rheita1 in which the objective is double1 apparently of two plano-convex lenses1 the weaker ahead1 and used with a concave eye lens4 ,if properly proportioned such a doublet would have less than a quarter the spherical aberration of the equivalent double convex lens4 ,hevelius also mentions the earlier form of re-inverting telescope above referred to1 and speaks rather highly of its performance4 ,to judge from his numerous drawings of the moon made in #afdc and #afdd1 his telescopes were much better than those of ,scheiner and ,fontana1 but still woefully lacking in sharp definition4 ,nevertheless the copper plates of the ,selenographia1 representing every phase of the moon1 placed the lunar details with remarkable accuracy and formed for more than a century the best lunar atlas available4 ,one acquires an abiding respect for the patience and skill of these old astronomers in seeing how much they did with means utterly inadequate4 ,one may get a fair idea of the size1 appearance1 and mounting of telescopes in this early day from ,fig4 #h1 which shows a somewhat advanced construction credited by ,hevelius to a suggestion in ,descartes' ,dioptrica4 ,appearances indicate that the tube was somewhere about six feet long1 approximately two inches in aperture1 and that it had a draw tube for focussing4 ,the offset head of the mount to allow observing near the zenith is worth an extra glance4 ,incidentally ,hevelius1 with perhaps pardonable pride1 also explains the 8,polemoscope10 a little invention of his own1 made1 he tells us1 in #afcg4 ,it is nothing else than the first periscope1 constructed as shown in ,fig4 #i1 a tube c with two right angled branches1 a fairly long one e for the objective f1 a #de mirror at g1 another at a1 and finally the concave ocular at b4 ,it was of modest size1 of tubes #a inch in diameter1 the longer tube being #bb inches and the upper branch #h inches1 a size well suited for trench or parapet4 ,illustration3 ,,fig4 #h4--;,a ,seventh ,century ,astronomer and his ,telescope4 ,even in these days of his youth ,hevelius had learned much of practical optics as then known1 had devised and was using very rational methods of observing sun-spots by projection in a darkened room1 and gives perhaps the first useful hints at testing telescopes by such solar observations and on the planets4 ,he was later to do much in the development and mounting of long telescopes and in observation1 although1 while progressive in other respects1 he very curiously never seemed to grasp the importance of telescopic sights and consistently refused to use them4 ,telescope construction was now to fall into more skillful hands4 ,shortly after #afej ,christian ,huygens 7#afbi-afie71 and his accomplished brother ,constantine awakened to a keen interest in astronomy and devised new and excellent methods of forming accurate tools and of grinding and polishing lenses4 ,illustration3 ,,fig4 #i4--,the first ,periscope4 ,by #afee they had completed an instrument of #ab feet focus with which the study of ,saturn was begun1 ,titan the chief satellite discovered1 and the ring recognized4 ,pushing further1 they constructed a telescope of #bc feet focal length and #b inches aperture1 with which four years later ,christian ,huygens finally solved the mystery of ,saturn's ring4 ,evidently this glass1 which bore a power of #ajj1 was of good defining quality1 as attested by a sketch of ,mars late in #afie showing plainly ,syrtis ,major1 from observation of which ,huygens determined the rotation period to be about #bd hours4 ,the ,huygens brothers were seemingly the first fully to grasp the advantage of very long focus in cutting down the aberrations1 the aperture being kept moderate4 ,their usual proportions were about as indicated above1 the aperture being kept somewhere nearly as the square root of the focus in case of the larger glasses4 ,in the next two decades the focal length of telescopes was pushed by all hands to desperate extremes4 ,the ,huygens brothers extended themselves to glasses up to #baj feet focus and built many shorter ones1 a famous example of which1 of #f inches aperture and #abc feet focal length1 presented to the ,royal ,society1 is still in its possession4 ,auzout produced even longer telescopes1 and ,divini and ,campani1 in ,rome1 of whom the last named made ,cassini's telescopes for the ,observatory of ,paris1 were not far behind4 ,the ,english makers were similarly busy1 and ,hevelius in ,danzig was keeping up the record4 ,illustration3 ,,fig4 #aj4--;,christian ,huygens4 ,clearly these enormously long telescopes could not well be mounted in tubes and the users were driven to aerial mountings1 in which the objective was at the upper end of a spar or girder and the eye piece at the lower4 ,figure #aa shows an actual construction by ,hevelius for an objective of #aej feet focal length4 ,in this case the main support was a ,t beam of wooden planks well braced together4 ,additional stiffness was given by light wooden diaphragms at short intervals with apertures of about #h inches next to the objective1 and gradually increasing downwards4 ,the whole was lined up by equalizing tackle in the vertical plane1 and spreaders with other tackle at the joints of the #dj;foot sections of the main beam4 ,the mast which supported the whole was nearly #ij feet high4 ,so unwieldly and inconvenient were these long affairs that1 quite apart from their usual optical imperfections1 it is little wonder that they led to no results commensurate with their size4 ,in fact nearly all the productive work was done with telescopes from #bj to #ce feet long1 with apertures roughly between #b and #c inches4 ,illustration3 ,,fig4 #aa4--;,hevelius' #aej-;foot ,telescope4 ,dominique ,cassini to be sure1 scrutinizing ,saturn in #afhd with objectives by ,campani1 of #ajj and #acf feet focus picked up the satellites ,tethys and ,dione1 but he had previously found ,iapetus with a #ag-;foot glass1 and ,rhea with one of #cd feet4 ,the longer glasses above mentioned had aerial mounts but the smaller ones were in tubes supported on a sort of ladder tripod4 ,a #bj-;foot objective1 power #ij1 gave ,cassini the division in ,saturn's ring4 ,a struggle was still being kept up for the non-spherical curves urged by ,descartes4 ,it is quite evident that ,huygens had a go at them1 and ,hevelius thought at one time that he had mastered the hyperbolic figure1 but his published drawings give no indication that he had reduced spherical aberration to any perceptible degree4 ,at this time the main thing was to get good glass and give it true figure and polish1 in which ,huygens and ,campani excelled1 as the work on ,saturn witnesses4 ,these were the days of the dawn of popular astronomy and many a gentleman was aroused to at least a casual interest in observing the ,heavens4 ,notes ,pepys in his immortal ,diary3 8,i find ,reeves there1 it being a mighty fine bright night1 and so upon my leads1 though very sleepy1 till one in the morning1 looking on the moon and ,jupiter1 with this twelve foot glass1 and another of six foot1 that he hath brought with him to-night1 and the sights mighty pleasant1 and one of the glasses ,i will buy40 ,little poor ,pepys probably saw1 by reason of his severe astigmatism1 but astronomy was in the air with the impulse that comes to every science after a period of brilliant discovery4 ,another such stimulus came near the end of the eighteenth century1 with the labors of ,sir ,william ,herschel4 ,just at this juncture comes one of the interesting episodes of telescopic history1 the ineffectual and abandoned experiments on reflecting instruments4 ,illustration3 ,,fig4 #ab4--;,gregory's ,diagram of his ,telescope4 ,in #affc ,james ,gregory 7#afch-afge7 a famous ,scottish mathematician1 published his ,optica ,promota1 in which he described the rather elegant construction which bears his name1 a perforated parabolic mirror with an elliptical mirror forward of the focus returning an image to the ocular through the perforation4 ,it was convenient in that it gave an erect image1 and it was sound theoretically1 and1 as the future proved1 practically1 but the curves were quite too much for the contemporary opticians4 ,figure #ab shows the diagrammatic construction as published4 ,the next year ,gregory started ,reive1 a ,london optician1 doubtless the same mentioned by ,pepys1 on the construction of a #f foot telescope4 ,this rather ambitious effort failed of material success through the inability of ,reive to give the needed figures to the mirrors1#d and of it nothing further appears until the ingenious ,robert ,hooke 7#afce-agjc7 executed in #afgd a ,gregorian1 apparently without any notable results4 ,there is a well defined tradition that ,gregory himself was using one in #afge1 at the time of his death1 but the invention then dropped out of sight4 #d ,he attempted to polish them on cloth1 which in itself was sufficient to guarantee failure4 ,no greater influence on the art attended the next attempt at a reflector1 by ,isaac ,newton 7#afdc-agbg74 ,this was an early outcome of his notable discovery of the dispersion of light by prisms1 which led him to despair of improving refracting telescopes and turned his mind to reflectors4 ,unhappily in an experiment to determine whether refraction and dispersion were proportional he committed the singular blunder of raising the refractive index of a water-filled prism to equality with glass by dissolving sugar of lead in it4 ,without realizing the impropriety of thus varying two quite unknown quantities at once in his crucial experiment1 he promptly jumped to the conclusion that refraction and dispersion varied in exact proportion in all substances1 so that if two prisms or lenses dispersed light to the same extent they must also equally refract it4 ,it would be interesting to know just how the fact of his bungling was passed along to posterity4 ,as a nave apologist once remarked1 it was not to be found in his 8,optics40 ,but ,sir ,david ,brewster and ,sir ,john ,herschel1 both staunch admirers of the great philosopher1 state the fact very positively4 ,if one may hazard a guess it crept out at ,cambridge and was passed along1 perhaps to ,sir ,william ,herschel1 via the unpublished history of research that is rich in picturesque details of the mare's nests of science4 ,at all events a mistake with a great name behind it carries far1 and the result was to delay the production of the achromatic telescope by some three quarters of a century4 ,turning from refractors he presented to the ,royal ,society just after his election as ,fellow in #afgb1 the little six-inch model of his device which was received with acclamation and then lay on the shelf without making the slightest impression on the art1 for full half a century4 ,newton1 by dropping the notion of direct view through the tube1 hit upon by far the simplest way of getting the image outside it1 by a plane mirror a little inside focus and inclined at #de1 but injudiciously abandoned the parabolic mirror of his original paper on dispersion4 ,his invention therefore as actually made public was of the combination with a spherical concave mirror of a plane mirror of elliptical form at #de1 a construction which in later papers he defended as fully adequate4#e #e ,in ,fig #ac1 ,a is the support of the tube and focussing screw1 ,b the main mirror1 an inch in diameter1 ,,cd the oblique mirror1 ,e the principal focus1 ,f the eye lens1 and ,g the member from which the oblique mirror is carried4 ,illustration3 ,,fig4 #ac4--,newton's ,model of his ,reflector4 ,his error in judgment doubtless came from lack of practical astronomical experience1 for he assumed that the whole real trouble with existing telescopes was chromatic aberration1 which in fact worried the observer little more than the faults due to other causes1 since the very low luminosity toward the ends of the spectrum enormously lessens the indistinctness due to dispersion4 ,as a matter of fact the long focus objective of small aperture did very creditable work1 and its errors would not compare unfavorably with those of a spherical concave mirror of the wide aperture planned by ,newton4 ,had he actually made one of his telescopes of fair dimensions and power the definition would infallibly have been wrecked by the aberrations due to spherical figure4#f #f ,in fact a 8four foot telescope of ,mr4 ,newton's invention0 brought before the ,royal ,society two weeks after his original paper1 proved only fair in quality1 was returned somewhat improved at the next meeting1 and then was referred to ,mr4 ,hooke to be perfected as far as might be1 after which nothing more was heard of it4 ,illustration3 ,,fig4 #ad4--;,de ,berc's sketch of ,cassegrain's ,telescope4 ,it is quite likely that appreciation of this1 and the grave doubts of both ,newton and ,huygens as to obtaining a proper parabolic curve checked further developments4 ,about the beginning of the year #afgb ,m4 ,cassegrain communicated to ,m4 de ,berc a design for a reflecting telescope1 which eventually found its way into the ,philosophical ,transactions of ,may in that year1 after previous publication in the ,journal des ,savans4 ,figure #ad shows de ,berc's rough original sketch4 ,it differed from ,gregory's construction in that the latter's elliptical concave mirror placed outside the main focus1 was replaced by a convex mirror placed inside focus4 ,the image was therefore inverted4 ,the inventor is referred to in histories of science as 8,cassegrain1 a ,frenchman40 ,he was in fact ,sieur ,guillaume ,cassegrain1 sculptor in the service of ,louis ,quatorze1 modeller and founder of many statues4 ,in #afff he was paid #abjj livres for executing a bust of the ,king modelled by ,bertin1 and later made many replicas from the antique for the decoration of ,his ,majesty's gardens at ,versailles4 ,he disappeared from the royal records in #afhd and probably died within a year or two of that date4 ,at the period here concerned he apparently1 like de ,berc1 was of ,chartres4 ,familiar with working bronzes and with the art of the founder1 he was a very likely person to have executed specula4 ,although there is no certainty that he actually made a telescope1 a contemporary reference in the ,journal des ,savans speaks of his invention as a 8petite lunette d'approche10 and one does not usually suggest the dimensions of a thing non-existent4 ,how long he had been working upon it prior to the period about the beginning of #afgb when he disclosed the device to de ,berc is unknown4 ,probably ,newton's invention was the earlier1 but the two were independent1 and it was somewhat ungenerous of ,newton to criticise ,cassegrain1 as he did1 for using spherical mirrors1 on the strength of de ,berc's very superficial description1 when he himself considered the parabolic needless4 ,however1 nothing further was done1 and the devices of ,gregory1 ,newton and ,cassegrain went together into the discard for some fifty years4 ,these early experiments gave singularly little information about material for mirrors and methods of working it1 so little that those who followed1 even up to ,lord ,rosse1 had to work the problems out for themselves4 ,we know from his original paper that ,newton used bell-metal1 whitened by the addition of arsenic1 following the lore of the alchemists4 ,these speculative worthies used to alloy copper with arsenic1 thinking that by giving it a whitish cast they had reached a sort of half way point on the road to silver4 ,very silly at first thought1 but before the days of chemical analysis1 when the essential properties of the metals were unknown1 the way of the scientific experimenter was hard4 ,what the 8steely matter1 imployed in ,london0 of which ,newton speaks in an early paper was1 we do not know--very likely one of the hard alloys much richer in tin than is ordinary bell-metal4 ,nor do we know to what variety of speculum metal ,huygens refers in his correspondence with ,newton4 ,as to methods of working it ,newton only disclosed his scheme of pitch-polishing some thirty years after this period1 while it is a matter of previous record1 that ,huygens had been in the habit of polishing his true tools on pitch from some date unknown4 ,probably neither of them originated the practice4 ,opticians are a peculiarly secretive folk and shop methods are likely to be kept for a long time before they leak out or are rediscovered4 ,modern speculum metal is substantially a definite compound of four atoms copper and one tin 7,sn,cu#d71 practically #fh per cent copper and #cb per cent tin1 and is now1 as it was in all previous modifications1 a peculiarly mean material to cast and work4 ,thus exit the reflector4 ,the long telescope continued to grow longer with only slow improvement in quality1 but the next decade was marked by the introduction of ,huygens' eyepiece1 an immense improvement over the single lens which had gone before1 and with slight modifications in use today4 ,illustration3 ,,fig4 #ae4--;,diagram of ,huygens' ,eyepiece4 ,this is shown in section in ,fig4 #ae4 ,it consists of a field lens ,a1 plano-convex1 and an eye lens ,b of one-third the focal length1 the two being placed at the difference of their focal lengths apart with 7in later days7 a stop half way between them4 ,the eye piece is pushed inside the main focus until the rays which fall on the field lens focus through the eye lens4 ,the great gain from ,huygens' view-point was a very much enlarged clear field--about a four-fold increase--and in fact the combination is substantially achromatic1 particularly important now when high power oculars are needed4 ,still larger progress was made in giving the objective a better form with respect to spherical aberration1 the 8crossed0 lens being rather generally adopted4 ,this form is double convex1 and if of ordinary glass1 with the rear radius six times the front radius1 and gives even better results than a plano-convex in its best position-plane side to the rear4 ,objectives were rated on focal length for the green rays1 that is1 the bright central part of the spectrum1 the violet rays of course falling short and the red running beyond4 ,to give customary dimensions1 a telescope of #c inches aperture1 with magnifying power of #ajj1 would be of about #cj feet focus with the violet nearly #f inches short and the red a similar amount long4 ,it is vast credit to the early observers that with such slender means they did so much4 ,but in fact the long telescope had reached a mechanical impasse1 so that the last quarter of the seventeenth century and the first quarter of the next were marked chiefly by the development of astronomy of position with instruments of modest dimensions4 ,illustration3 ,,fig4 #af4--,the ,first ,reflector4 ,john ,hadley1 #agbb4 ,in due time the new order came and with astounding suddenness4 ,just at the end of #agbb ,james ,bradley 7#afib-agfb7 measured the diameter of ,venus with an objective of #bab ft4 #c in4 focal length2 about three months later ,john ,hadley 7#afhb-agdd7 presented to the ,royal ,society the first reflecting telescope worthy the name1 and the old order practically ended4 ,john ,hadley should in fact be regarded as the real inventor of the reflector in quite the same sense that ,mr4 ,edison has been held1 de jure and de facto1 the inventor of the incandescent electric lamp4 ,actually ,hadley's case is the stronger of the two1 for the only things which could have been cited against him were abandoned experiments fifty years old4 ,moreover he took successfully the essential step at which ,gregory and ,newton had stumbled or turned back--parabolizing his speculum4 ,the instrument he presented was of approximately #f inches aperture and #fb inches focal length1 which he had made and tested some three years previously2 on a substantial alt-azimuth mount with slow motions4 ,he used the ,newtonian oblique mirror and the instrument was provided with both convex and concave eye lenses1 with magnifications up to about #bcj4 ,the whole arrangement is shown in ,fig4 #af which is for the most part self explanatory4 ,it is worth noting that the speculum is positioned in the wooden tube by pressing it forward against three equidistant studs by three corresponding screws at the rear1 that a slider moved by a traversing screw in a wide groove carries the small mirror and the ocular1 that there is a convenient door for access to the mirror1 and also a suitable finder4 ,the motion in altitude is obtained by a key winding its cord against gravity4 ,that in azimuth is by a roller support along a horizontal runway carried by an upright1 and is obtained by the key with a cord pull off in one direction1 and in the other1 by springs within the main upright1 turning a post of which the head carries cheek pieces on which rest the trunnions of the tube4 ,a few months later this telescope was carefully tested1 by ,bradley and the ,rev4 ,j4 ,pound1 against the ,huygens objective of #abc feet focus possessed by the ,royal ,society1 and with altogether satisfactory results4 ,hadley's reflector would show everything which could be seen by the long instrument1 bearing as much power and with equal definition1 though somewhat lessened light4 ,in particular they saw all five satellites of ,saturn1 ,cassini's division1 which the inventor himself had seen the previous year even in the northern edge of the ring beyond the planet1 and the shadow of the ring upon the ball4 ,the casting of the large speculum was far from perfect1 with many spots that failed to take polish1 but the figure must have been rather good4 ,a spherical mirror of these dimensions would give an aberration blur something like twenty times the width of ,cassini's division1 and the chance of seeing all five satellites with it would be negligibly small4 ,further1 ,hadley presently disclosed to others not only the method he used in polishing and parabolizing specula1 but his method of testing for true figure by the aberrations disclosed as he worked the figure away from the sphere--a scheme frequently used even to this day4 ,the effect of ,hadley's work was profound4 ,under his guidance others began to produce well figured mirrors1 in particular ,molyneux and ,hawksbee2 reflecting telescopes became fairly common2 and in the beginning of the next decade ,james ,short1 7#agaj-agfh71 possessed of craftsmanship that approached wizardry1 not only fully mastered the art of figuring the paraboloid1 but at once took up the ,gregorian construction with its ellipsoidal small mirror1 with much success4 ,his specula were of great relative aperture1 ,f_/#d to ,f_/#f1 and from the excellent quality of his metal some of them have retained their fine polish and definition after more than a century4 ,he is said to have gone even up to #ab inches in diameter4 ,his exact methods of working died with him4 ,even his tools he ordered to be destroyed before his death4 ,the ,cassegrain reflector1 properly having a parabolic large mirror and a hyperbolic small one1 seems very rarely to have been made in the eighteenth century1 though one certainly came into the hands of ,ramsden 7#agce-ahjj74 ,few refractors for astronomical use were made after the advent of the reflector1 which was1 and is1 however1 badly suited for the purposes of a portable spy-glass1 owing to trouble from stray light4 ,the refractor therefore permanently held its own in this function1 despite its length and uncorrected aberrations4 ,relief was near at hand1 for hardly had ,short started on his notable career when ,chester ,moor ,hall1 ,esq4 7#agjd-agga7 a gentleman of ,essex1 designed and caused to be constructed the first achromatic telescope1 with an objective of crown and flint glass4 ,he is stated to have been studying the problem for several years1 led to it by the erroneous belief 7shared by ,gregory long before7 that the human eye was an example of an achromatic instrument4 ,be this as it may ,hall had his telescopes made by ,george ,bast of ,london at least as early as #agcc1 and according to the best available evidence several instruments were produced1 one of them of above #b inches aperture on a focal length of about #bj inches 7,f_/#h7 and further1 subsequently such instruments were made and sold by ,bast and other opticians4 ,these facts are clear and yet1 with knowledge of them among ,london workmen as well as among ,hall's friends1 the invention made no impression1 until it was again brought to light1 and patented1 by the celebrated ,john ,dolland 7#agjf-agfa7 in the year #ageh4 ,physical considerations give a clue to this singular neglect4 ,the only glasses differing materially in dispersion available in ,hall's day were the ordinary crown1 and such flint as was in use in the glass cutting trade1--what we would now know as a light flint1 and far from homogeneous at that4 ,illustration3 ,lodge 8,pioneers of ,science40 ,,fig4 #ag4--;,john ,dolland4 ,out of such material it was practically very hard 7as the ,dollands quickly found7 to make a double objective decently free from spherical aberration1 especially for one working1 as ,hall quite assuredly did1 by rule of thumb4 ,with the additional handicap of flint full of faults it is altogether likely that these first achromatics1 while embodying the correct principles1 were not good enough to make effective headway against the cheaper and simpler spy-glass of the time4 ,dolland1 although in #agec he strongly supported ,newton's error in a ,royal ,society paper against ,euler's belief in achromatism1 shifted his view a couple of years later and after a considerable period of skilful and well ordered experimenting published his discovery of achromatism early in #ageh1 for which a patent was granted him ,april #ai1 while in the same year the ,royal ,society honored him with the ,copley medal4 ,from that time until his death1 late in #agfa1 he and his son ,peter ,dolland 7#agcj-ahbj7 were actively producing achromatic glasses4 ,the ,dollands were admirable craftsmen and their early product was probably considerably better than were ,hall's objectives but they felt the lack of suitable flint and soon after ,john ,dolland's death1 about #agfe1 the son sought relief in the triple objective of which an early example is shown in ,fig4 #ah1 and which1 with some modifications1 was his standard form for many years4 ,illustration3 ,,fig4 #ah4--,peter ,dolland's ,triple ,objective4 ,other opticians began to make achromatics1 and1 ,peter ,dolland having threatened action for infringement1 a petition was brought by #ce opticians of ,london in #agfd for the annulment of ,john ,dolland's patent1 alleging that he was not the original inventor but had knowledge of ,chester ,moor ,hall's prior work4 ,in the list was ,george ,bast1 who in fact did make ,hall's objectives twenty five years before ,dolland1 and also one ,robert ,rew of ,coldbath ,fields1 who claimed in #agee to have informed ,dolland of the construction of ,hall's objective4 ,this was just the time when ,dolland came to the right about face on achromatism1 and it may well be that from ,rew or elsewhere he may have learned that a duplex achromatic lens had really been produced4 ,but his ,royal ,society paper shows that his result came from honest investigations1 and at worst he is in about the position of ,galileo a century and a half before4 ,the petition apparently brought no action1 perhaps because ,peter ,dolland next year sued ,champneys1 one of the signers1 and obtained judgment4 ,it was in this case that the judge 7,lord ,camden7 delivered the oft quoted dictum3 8,it was not the person who locked up his invention in his scrutoire that ought to profit by a patent for such invention1 but he who brought it forth for the benefit of the public4#g0 #g ,commonly1 but it appears erroneously1 ascribed to ,lord ,mansfield4 ,this was sound equity enough1 assuming the facts to be as stated1 but while ,hall did not publish the invention admittedly made by him1 it had certainly become known to many4 ,chester ,moor ,hall was a substantial and respected lawyer1 a bencher of the ,inner ,temple1 and one is inclined to think that his alleged concealment was purely constructive1 in his failing to contest ,dolland's claim4 ,had he appeared at the trial with his fighting blood up1 there is every reason to believe that he could have established a perfectly good case of public use quite aside from his proof of technical priority4 ,however1 having clearly lost his own claims through laches1 he not improbably was quite content to let the tradesmen fight it out among themselves4 ,hall's telescopes were in fact known to be in existence as late as #ahbg4 ,as the eighteenth century drew toward its ending the reflecting telescope1 chiefly in the ,gregorian form1 held the field in astronomical work1 the old refractor of many draw tubes was the spy-glass of popular use1 and the newly introduced achromatic was the instrument of 8the exclusive trade40 ,no glass of suitable quality for well corrected objectives had been produced1 and that available was not to be had in discs large enough for serious work4 ,a #c-;inch objective was reckoned rather large4 ,,chapter ,,ii ,,the ,,modern ,,telescope ,the chief link between the old and the new1 in instrumental as well as observational astronomy1 was ,sir ,william ,herschel 7#agch-ahbb74 ,in the first place he carried the figuring of his mirrors to a point not approached by his predecessors1 and second1 he taught by example the immense value of aperture in definition and grasp of light4 ,his life has never been adequately written1 but ,miss ,clerke's 8,the ,herschels and ,modern ,astronomy0 is extremely well worth the reading as a record of achievement that knew not the impossible4 ,illustration3 ,miss ,clerke's ,herschel ,modern ,astronomy 7,macmillan74 ,,fig4 #ai4--,sir ,william ,herschel4 ,he was the son of a capable band-master of ,hanover1 brought up as a musician1 in a family of exceptional musical abilities1 and in #ageg jumped his military responsibilities and emigrated to ,england1 to the world's great gain4 ,for nearly a decade he struggled upward in his art1 taking meanwhile every opportunity for self education1 not only in the theory of music but in mathematics and the languages1 and in #agfg we find him settled in fashionable ,bath1 oboist in a famous orchestra1 and organist of the ,octagon ,chapel4 ,his abilities brought him many pupils1 and ultimately he became director of the orchestra in which he had played1 and the musical dictator of the famous old resort4 ,in #aggb came his inspiration in the loan of a #b-;foot ,gregorian reflector1 and a little casual star-gazing with it4 ,it was the opening of the kingdom of the skies1 and he sought to purchase a telescope of his own in ,london1 only to find the price too great for his means4 7,even a #b-;foot1 of #d inches aperture1 by ,short was listed at five-and-thirty guineas47 ,then after some futile attempts at making a plain refractor he settled down to hard work at casting and polishing specula4 ,although possessed of great mechanical abilities the difficult technique of the new art long baffled him1 and he cast and worked some #bjj small discs in the production of his first successful telescopes1 to say nothing of a still greater number in larger sizes in his immediately subsequent career4 ,as time went on he scored a larger proportion of successes1 but at the start good figure seems to have been largely fortuitous4 ,inside of a couple of years1 however1 he had mastered something of the art and turned out a #e-;foot instrument which seems to have been of excellent quality1 followed later by a #g-;foot 7aperture #f inches7 even better1 and then by others still bigger4 ,the best of ,herschel's specula must have been of exquisite figure4 ,his #g-;foot was tested at ,greenwich against one of ,short's of #i inches aperture much to the latter's disadvantage4 ,his discovery with the #g-;foot1 of the 8,georgium ,sidus0 7,uranus7 in #agha won him immediate fame and recognition1 beside spurring him to greater efforts1 especially in the direction of larger apertures1 of which he had fully grasped the importance4 ,in #aghb he successfully completed a #ab-;inch speculum of #bj feet focus1 followed in #aghh by an #ah-;inch of the same length4 ,the previous year he first arranged his reflector as a 8front view0 telescope--the so-called ,herschelian4 ,up to this time he1 except for a few ,gregorians1 had used ,newton's oblique mirror4 ,the heavy loss of light 7around #dj per cent7 in the second reflection moved him to tilt the main mirror so as to throw the focal point to the edge of the aperture where one could look downward upon the image through the ocular as shown in ,fig4 #bj4 ,here ,,ss is the great speculum1 ,o the ocular and i the image formed near the rim of the tube4 ,in itself the tilting would seriously impair the definition1 but ,herschel wisely built his telescopes of moderate relative aperture 7,f_/#aj to ,f_/#bj71 so that this difficulty was considerably lessened1 while the saving of light1 amounting to nearly a stellar magnitude1 was important4 ,meanwhile he was hard at work on his greatest mirror1 of #dh inches clear aperture and #dj feet focal length1 the father of the great line of modern telescopes4 ,it was finished in the summer of #aghi4 ,the speculum was #di inches in over-all diameter1 #c inches thick and weighed as cast #baah lbs4 ,the completion of this instrument1 which would rank as large even today1 was made notable by the immediate discovery of two new satellites of ,saturn1 ,enceladus and ,mimas4 ,it also proved of very great value in sweeping for nebul1 but its usefulness seems to have been much limited by the flexure of the mirror under its great weight1 and by its rapid tarnishing4 ,it required repolishing1 which meant refiguring1 at least every two years1 a prodigious task4#h #h ,this was probably due not only to unfavorable climate1 but to the fact that ,herschel1 with all his ingenuity1 does not appear to have mastered the casting difficulty1 and was constrained to make his big speculum of ,cu #ge per cent1 ,sn #be per cent1 a composition working rather easily and taking beautiful1 but far from permanent1 polish4 ,he never seems to have used practically the ,sn,cu#d formula1 devised empirically by ,mudge 7,phil4 ,trans4 #fg1 #bih71 and in quite general use thereafter up to the present time4 ,illustration3 ,,fig4 #bj4--;,herschel's ,front ,view ,telescope4 ,it was used as a front view instrument and was arranged as shown in ,fig4 #ba4 ,obviously the front view form has against it the mechanical difficulty of supporting the observer up to quite the full focal length of the instrument in air1 a difficulty vastly increased were the mount an equatorial one1 so that for the great modern reflectors the ,cassegrain form1 looked into axially upward1 and in length only a third or a quarter of the principal focus1 is almost universal4 ,as soon as the excellent results obtained by ,herschel became generally known1 a large demand arose for his telescopes1 which he filled in so far as he could spare the time from his regular work1 and not the least of his services to science was the distribution of telescopes of high quality and consequent strong stimulus to general interest in astronomy4 ,two of his instruments1 of #d-;and #g-;feet focus respectively1 fell into the worthy hands of ,schrter at ,lilienthal and did sterling service in making his great systematic study of the lunar surface4 ,at the start even ,herschel's #g-;foot telescope brought #bjj guineas1 and the funds thus won he promptly turned to research4 ,illustration3 ,miss ,clerke's ,herschel ,modern ,astronomy 7,macmillan74 ,,fig4 #ba4--;,herschel's ,forty-foot ,telescope4 ,we sometimes think of the late eighteenth century as a time of license unbounded and the higher life contemned1 but ,herschel wakened a general interest in unapplied science that has hardly since been equalled and never surpassed4 ,try to picture social and official ,washington rushing to do honor to some astronomer who by luck had found the trans-,neptunian planet2 the diplomatic corps crowding his doors1 and his very way to the ,naval ,observatory blocked by the limousines of the curious and admiring1 and some idea may be gained of what really happened to the unassuming music master from ,bath who suddenly found himself famous4 ,great as were the advances made by ,herschel the reflector was destined to fall into disuse for many years4 ,the fact was that the specula had to be refigured1 as in the case of the great #dj-;foot telescope1 quite too often to meet the requirements of the ordinary user1 professional or amateur4 ,only those capable of doing their own figuring could keep their instruments conveniently in service4 ,sir ,w4 ,herschel always had relays of specula at hand for his smaller instruments1 and when his distinguished son1 ,sir ,john ,f4 ,w4 ,herschel1 went on his famous observing expedition to the ,cape of ,good ,hope in #ahcd-ch he took along his polishing machine and three specula for his #bj-;foot telescope4 ,and he needed them indeed1 for a surface would sometimes go bad even in a week1 and regularly became quite useless in #b or #c months4 ,makers who used the harder speculum metal1 very brittle and scarcely to be touched by a file1 fared better1 and some small mirrors1 well cared for1 have held serviceable polish for many years4 ,many of these instruments of ,herschel's time1 too1 were of very admirable performance4 ,some of ,herschel's own #g-;foot telescopes give evidence of exquisite figure and he not only commonly used magnifying powers up to some #hj per inch of aperture1 a good stiff figure for a telescope old or new1 but went above #b1jjj1 even nearly to #f1jjj on one of his #f-;inch mirrors without losing the roundness of the star image4 8,empty magnification0 of course1 gaining no detail whatever1 but evidence of good workmanship4 ,many years later the ,rev4 ,w4 ,r4 ,dawes1 the famous ,english observer1 had a #e-;inch ,gregorian1 commonly referred to as 8,the ,jewel10 on which he used #dcj diameters1 and pushed to #b1jjj on ,polaris without distortion of the disc4 ,comparing it with a #e-;foot 7approximately #d-;inch aperture7 refractor1 he reports the ,gregorian somewhat inferior in illuminating power2 8,but in sharpness of definition1 smallness of discs of stars1 and hardness of outline of planets it is superior40 ,all of which shows that while methods and material may have improved1 the elders did not in the least lack skill4 ,the next step forward1 and a momentous one1 was to be taken in the achromatic refractor4 ,its general principles were understood1 but clear and homogeneous glass1 particularly flint glass1 was not to be had in pieces of any size4 8,optical glass10 as we understand the term1 was unknown4 ,it is a curious and dramatic fact that to a single man was due not only the origin of the art but the optical glass industry of the world4 ,if the capacity for taking infinite pains be genius1 then the term rightfully belongs to ,pierre ,louis ,guinand4 ,he was a ,swiss artisan living in the ,canton of ,neuchatel near ,chaux-de-,fonds1 maker of bells for repeaters1 and becoming interested in constructing telescopes imported some flint glass from ,england and found it bad4 ,he thereupon undertook the task of making better1 and from #aghd kept steadily at his experiments1 failure only spurring him on to redoubled efforts4 ,all he could earn at his trade went into his furnaces1 until gradually he won success1 and his glass began to be heard of2 for by #agii he was producing flawless discs of flint as much as #f inches in diameter4 ,what is more1 to ,guinand is probably due the production of the denser1 more highly refractive flints1 especially valuable for achromatic telescopes4 ,the making of optical glass has always been an art rather than a science4 ,it is one thing to know the exact composition of a glass and quite another to know in what order and proportion the ingredients went into the furnace1 to what temperature they were carried1 and for how long1 and just how the fused mass must be treated to free the products from bubbles and stri4 ,even today1 though much has been learned by scientific investigation in the past few years1 it is far from easy to produce two consecutive meltings near enough in refractive power to be treated as optically identical1 or to produce large discs optically homogeneous4 ,what ,guinand won by sheer experience was invaluable4 ,he was persuaded in #ahje to move to ,munich and eventually to join forces with ,fraunhofer1 an association which made both the ,german optical glass industry and the modern refractor4 ,he returned to ,switzerland in #ahad and continued to produce perfect discs of larger and larger dimensions4 ,one set of #ab inches worked up by ,cauchoix in ,paris furnished what was for some years the world's largest refractor4 ,guinaud died in #ahbd1 but his son ,henry1 moving to ,paris1 brought his treasure of practical knowledge to the glass works there1 where it has been handed down1 in effect from father to son1 gaining steadily by accretion1 through successive firms to the present one of ,parra-,mantois4 ,bontemps1 one of the early pupils of ,henry ,guinand1 emigrated to ,england at the ,revolution of #ahdh and brought the art to the famous firm of ,chance in ,birmingham4 ,most of its early secrets have long been open1 but the minute teachings of experience are a tremendously valuable asset even now4 ,illustration3 ,,fig4 #bb4--;,dr4 ,joseph von ,fraunhofer1 the ,father of ,astrophysics4 ,to ,fraunhofer1 the greatest master of applied optics in the nineteenth century1 is due the astronomical telescope in substantially its present form4 ,not only did he become under ,guinand's instruction extraordinarily skillful in glass making but he practically devised the art of working it with mathematical precision on an automatic machine1 and the science of correctly designing achromatic objectives4 ,the form which he originated 7,fig4 #bc7 was the first in which the aberrations were treated with adequate completeness1 and1 particularly for small instruments1 is unexcelled even now4 ,the curvatures here shown are extreme1 the better to show their relations4 ,the front radius of the crown is about #b times longer than the rear radius1 the front of the flint is slightly flatter than the back of the crown1 and the rear of the flint is only slightly convex4 ,fraunhofer's workmanship was of the utmost exactness and it is not putting the case too strongly to say that a first class example of the master's craft1 in good condition1 would compare well in color-correction1 definition1 and field1 with the best modern instruments4 ,illustration3 ,,fig4 #bc4 ,the work done by the elder ,struve at ,dorpat with ,fraunhofer's first large telescope 7#i4f inches aperture and #agj inches focal length7 tells the story of its quality1 and the ,knigsberg heliometer1 the first of its class1 likewise1 while even today some of his smaller instruments are still doing good service4 ,it was he who put in practice the now general convention of a relative aperture of about ,f_/#ae1 and standardized the terrestrial eyepiece into the design quite widely used today4 ,the improvements since his time have been relatively slight1 due mainly to the recent production of varieties of optical glass unknown a century ago4 ,fraunhofer was born in ,straubing1 ,bavaria1 ,march #f1 #aghg4 ,self-educated like ,herschel1 he attained to an extraordinary combination of theoretical and practical knowledge that went far in laying the foundations of astrophysics4 ,the first mapping of the solar spectrum1 the invention of the diffraction grating and its application to determining the wave length of light1 the first exact investigation of the refraction and dispersion of glass and other substances1 the invention of the objective prism1 and its use in studying the spectra of stars and planets1 the recognition of the correspondence of the sodium lines to the ,d lines in the sun1 and the earliest suggestion of the diffraction theory of resolution later worked out by ,lord ,rayleigh and ,professor ,abb1 make a long list of notable achievements4 ,to these may be added his perfecting of the achromatic telescope1 the equatorial mounting and its clockwork drive1 the improvement of the heliometer1 the invention of the stage micrometer1 several types of ocular micrometers1 and the automatic ruling engine4 ,he died at the height of his creative powers ,june #g1 #ahbf1 and lies buried at ,munich under the sublime ascription1 by none better earned1 ,approximavit ,sidera4 ,from ,fraunhofer's time1 at the hands of ,merz his immediate successor1 ,cauchoix in ,france1 and ,tully in ,england1 the achromatic refractor steadily won its way4 ,reflecting telescopes1 despite the sensational work of ,lord ,rosse on his #f-;foot mirror of #ec feet focus 7unequalled in aperture until the #f-;foot of the ,dominion ,observatory seventy years later71 and the even more successful instrument of ,mr4 ,lassell 7#d feet aperture1 #ci feet focus71 were passing out of use1 for the reason already noted1 that repolishing meant refiguring and the user had to be at once astronomer and superlatively skilled optician4 ,these large specula1 too1 were extremely prone to serious flexure and could hardly have been used at all except for the equilibrating levers devised by ,thomas ,grubb about #ahcd1 and used effectively on the ,rosse instrument4 ,these are in effect a group of upwardly pressing counterbalanced planes distributing among them the downward component of the mirror's weight so as to keep the figure true in any position of the tube4 ,such was the situation in the #ej's of the last century1 when the reflector was quite unexpectedly pushed to the front as a practical instrument by almost simultaneous activity in ,germany and ,france4 ,the starting point in each was ,liebig's simple chemical method of silvering glass1 which quickly and easily lays on a thin reflecting film capable of a beautiful polish4 ,the honor of technical priority in its application to silvering telescope specula worked in glass belongs to ,dr4 ,karl ,august ,steinheil 7#ahja-ahgj7 who produced about the beginning of #ahef an instrument of #d-;inch aperture reported to have given with a power of #ajj a wonderfully good image4 ,the publication was merely from a news item in the 8,allgemeine ,zeitung0 of ,augsburg1 ,march #bd1 #ahef1 so it is little wonder that the invention passed for a time unnoticed4 ,early the next year1 ,feb4 #af1 #aheg1 working quite independently1 exactly the same thing was brought before the ,french ,academy of ,sciences by another distinguished physicist1 ,jean ,bernard ,lon ,foucault1 immortal for his proof of the earth's rotation by the pendulum experiment1 his measurement of the velocity of light1 and the discovery of the electrical eddy currents that bear his name4 ,illustration3 ,,fig4 #bd4--;,dr4 ,karl ,august ,steinheil4 ,,fig4 #be4--;,jean ,bernard ,lon ,foucault4 ,the ,inventors of the ,silver-on-,glass ,reflector4 ,to ,foucault1 chiefly1 the world owes the development of the modern silver-on-glass reflector1 for not being a professional optician he had no hesitation in making public his admirable methods of working and testing1 the latter now universally employed4 ,it is worth noting that his method of figuring was1 physically1 exactly what ,jesse ,ramsden 7#agce-ahjj7 had pointed out in #aggi1 7,phil4 ,tr4 #aggi1 #dbg7 geometrically4 ,one of ,foucault's very early instruments mounted equatorially by ,scrtan is shown in ,fig4 #bf4 ,illustration3 ,,fig4 #bf4--;,early ,foucault ,reflector4 ,the immediate result of the admirable work of ,steinheil and ,foucault was the extensive use of the new reflector1 and its rapid development as a convenient and practical instrument1 especially in ,england in the skillful hands of ,with1 ,browning1 and ,calver4 ,not the least of its advantages was its great superiority over the older type in light-grasp1 silver being a better reflector than speculum metal in the ratio of very nearly #g to #e4 ,from this time on both refractors and reflectors have been fully available to the user of telescopes4 ,in details of construction both have gained somewhat mechanically4 ,as we have seen1 tubes were often of wood1 and not uncommonly the mountings also4 ,at the present time metal work of every kind being more readily available1 tubes and mountings of telescopes of every size are quite universally of metal1 save for the tripod-legs of the portable instruments4 ,the tubes of the smaller refractors1 say #c to #e inches in aperture1 are generally of brass1 though in high grade instruments this is rapidly being replaced by aluminum1 which saves considerable weight4 ,tubes above #e or #f inches are commonly of steel1 painted or lacquered4 ,the beautifully polished brass of the smaller tubes1 easily damaged and objectionably shiny1 is giving way to a serviceable matt finish in hard lacquer4 ,mountings1 too1 are now more often in iron and steel or aluminum than in brass1 the first named quite universally in the working parts1 for which the aluminum is rather soft4 ,the typical modern refractor1 even of modest size1 is a good bit more of a machine than it looks at first glance4 ,in principle it is outlined in ,fig4 #e1 in practice it is much more complex in detail and requires the nicest of workmanship4 ,in fact if one were to take completely apart a well-made small refractor1 including its optical and mechanical parts one would reckon up some #cj to #dj separate pieces1 not counting screws1 all of which must be accurately fitted and assembled if the instrument is to work properly4 ,illustration3 ,,fig4 #bg4--,longitudinal ,section of ,modern ,refractor4 ,fig4 #bg shows such an instrument in section from end to end1 as one would find it could he lay it open longitudinally4 ,a is the objective cap covering the objective ,b in its adjustable cell ,c1 which is squared precisely to the axis of the main tube ,d4 ,looking along this one finds the first of the diaphragms1 ,e4 ,these are commonly #c to #f in number spaced about equally down the tube1 and are far more important than they look4 ,their function is not to narrow the beam of light that reaches the ocular1 but to trap light which might enter the tube obliquely and be reflected from its sides into the ocular1 filling it with stray glare4 ,no amount of simple blackening will answer the purpose1 for even dead black paint such as opticians use reflects at very oblique incidence quite #aj to #bj per cent of the beam4 ,the importance of both diaphragms and thorough blackening has been realized for at least a century and a half1 and one can hardly lay too much stress upon the matter4 ,the diaphragms should be so proportioned that1 when looking up the tube from the edge of an aperture of just the size and position of the biggest lens in the largest eyepiece1 no part of the edge of the objective is cut off1 and no part of the side of the tube is visible beyond the nearest diaphragm4 ,going further down the tube past a diaphragm or two one comes to the clamping screws ,f4 ,these serve to hold the instrument to its mounting4 ,they may be set in separate bases screwed in place on the inside of the tube1 or may be set in the two ends of a lengthwise strap thus secured4 ,they are placed at the balance point as nearly as may be1 generally nearer the eye end than the objective4 ,then1 after one or more diaphragms1 comes the guide ring ,g1 which steadies the main draw tube ,h1 and the rack ,i by which it is moved for the focussing in turning the milled head of the pinion ,j4 ,the end ring ,k of the main tube furnishes the other bearing of ,h1 and both ,g and ,k are commonly recessed for accurately fitted cloth lining rings ,l1 ,l1 to give the draw tube the necessary smoothness of motion4 ,for the same reason ,i and ,j have to be cut and fitted with the utmost exactness so as to work evenly and without backlash4 ,h is fitted at its outer end with a slide ring and tube ,m1 generally again cloth lined to steady the sliding eyepiece tube ,n4 ,this is terminated by the spring collar ,o1 in which fits the eyepiece ,p1 generally of the two lens form2 and finally comes the eyepiece cap ,q set at the proper distance from the eye lens and with an aperture of carefully determined size4 ,one thus gets pretty well down in the alphabet without going much into the smaller details of construction4 ,both objective mount and ocular are somewhat complex in fact1 and the former is almost always made adjustable in instruments of above #c or #d inches aperture1 as shown in ,fig4 #bh1 the form used by ,cooke1 the famous maker of ,york1 ,england4 ,unless the optical axis of the objective is true with the tube bad images result4 ,illustration3 ,,fig4 #bh4--;,adjustable ,cell for ,objective4 ,to the upper end of the tube is fitted a flanged counter-cell c1 to an outward flange f1 tapped for #c close pairs of adjusting screws as s#a1 s#aa spaced at #abj apart4 ,the objective cell itself1 b1 is recessed for the objective which is held in place by an interior or exterior ring d4 ,the two lenses of the achromatic objective are usually very slightly separated by spacers1 either tiny bits of tinfoil #abj apart1 or a very thin ring with its upper edge cut down save at #c points4 ,this precaution is to insure that the lenses are quite uniformly supported instead of touching at uncertain points1 and quite usually the pair as a whole rests below on three corresponding spacers4 ,of each pair of adjusting screws one as #a in the pair s#aa is threaded to push the counter cell out1 the adjacent one1 #b1 to pull it in1 so that when adjustment is made the objective is firmly held4 ,of the lenses that form the objective1 the concave flint is commonly at the rear and the convex crown in front4 ,at the eye end the ocular ordinarily consists of two lenses each burnished into a brass screw ring1 a tube1 flange1 cap1 and diaphragm arranged as shown in ,fig4 #bi4 ,there are many varieties of ocular as will presently be shown1 but this is a typical form4 ,figure #cj shows a complete modern refractor of four inches aperture on a portable equatorial stand with slow motion in right ascension and diagonal eye piece4 ,reflectors1 used in this country less than they deserve1 are1 when properly mounted1 likewise possessed of many parts4 ,the smaller ones1 such as are likely to come into the reader's hands1 are almost always in the ,newtonian form1 with a small oblique mirror to bring the image outside the tube4 ,illustration3 ,,fig4 #bi4--,the ,eye-,piece and its ,fittings4 ,the ,gregorian form has entirely vanished4 ,its only special merit was its erect image1 which gave it high value as a terrestrial telescope before the days of achromatics1 but from its construction it was almost impossible to keep the field from being flooded with stray light1 and the achromatic soon displaced it4 ,the ,cassegranian construction on the other hand1 shorter and with aberrations much reduced1 has proved important for obtaining long equivalent focus in a short mount1 and is almost universally applied to large reflectors1 for which a ,newtonian mirror is also generally provided4 ,figure #ca shows in section a typical reflector of the ,newtonian form4 ,here ,a is the main tube1 fitted near its outer end with a ring ,b carrying the small elliptical mirror ,c1 which is set at #de to the axis of the tube4 ,at the bottom of the tube is the parabolic main mirror ,d1 mounted in its cell ,e4 ,just opposite the #de small mirror is a hole in the tube to which is fitted the eye piece mounting ,f1 carrying the eyepiece ,g1 fitted to a spring collar ,h1 screwed into a draw tube ,i1 sliding in its mounting and brought to focus by the rack-and-pinion ,j4 ,illustration3 ,,fig4 #cj4--,portable ,equatorial ,refractor 7,brashear74 ,at ,k1 ,k1 are two rings fixed to the tube and bearing smoothly against the rings ,l ,l rigidly fixed to the bar ,m carried by the polar axis of the mount4 ,the whole tube can therefore be rotated about its axis so as to bring the eye piece into a convenient position for observation4 ,one or more handles1 ,n1 are provided for this purpose4 ,illustration3 ,,fig4 #ca4--,longitudinal ,section of ,newtonian ,reflector4 ,brackets shown in dotted lines at ,o1 ,o1 carry the usual finder1 and a hinged door ,p near the lower end of the tube enables one to remove or replace the close fitting metal cover that protects the main mirror when not in use4 ,similarly a cover is fitted to the small mirror1 easily reached from the upper end of the tube4 ,the proportions here shown are approximately those commonly found in medium sized instruments1 say #g to #aj inches aperture4 ,the focal ratio is somewhere about ,f_/#f1 the diagonal mirror is inside of focus by about the diameter of the main mirror1 and its minor axis is from to that diameter4 ,illustration3 ,,fig4 #cb4--,reflector with ,skeleton ,tube 7,brashear74 ,note that the tube is not provided with diaphragms4 ,it is merely blackened as thoroughly as possible1 although stray light is quite as serious here as in a refractor4 ,one could fit diaphragms effectively only in a tube of much larger diameter than the mirror1 which would be inconvenient in many ways4 ,a much better way of dealing with the difficulty is shown in ,fig4 #cb in which the tube is reduced to a skeleton1 a construction common in large instruments4 ,nothing is blacker than a clear opening into the darkness of night1 and in addition there can be no localized air currents1 which often injure definition in an ordinary tube4 ,illustration3 ,,fig4 #cc4 ,instruments by different makers vary somewhat in detail4 ,a good type of mirror mounting is that shown in ,fig4 #cc1 and used for many years past by ,browning1 one of the famous ,english makers4 ,here the mirror ,a1 the back of which is made accurately plane1 is seated in its counter-cell ,b1 of which a wide annulus ,f1 ,f1 is also a good plane1 and is lightly held in place by a retaining ring4 ,this counter cell rests in the outer cell ,c on three equidistant studs regulated by the concentric push-and-pull adjusting screws ,d1 ,d1 ,e1 ,e4 ,the outer cell may be solid1 or a skeleton for lightness and better equalization of temperature4 ,small specula may be well supported on any flat surface substantial enough to be thoroughly rigid1 with one or more thicknesses of soft1 thick1 smooth cloth between1 best of all ,brussels carpet4 ,such was the common method of support in instruments of moderate dimensions prior to the day of glass specula4 ,sir ,john ,herschel speaks of thus carrying specula of more than a hundred-weight1 but something akin to ,browning's plan is generally preferable4 ,there is also considerable variety in the means used for supporting the small mirror centrally in the tube4 ,in the early telescopes it was borne by a single stiff arm which was none too stiff and produced by diffraction a long diametral flaring ray in the images of bright stars4 ,a great improvement was introduced by ,browning more than a half century ago1 in the support shown in ,fig4 #cd4 ,here the ring ,a1 7,b1 ,fig4 #ca7 carries three narrow strips of thin spring steel1 ,b1 extending radially inward to a central hub which carries the mirror ,d1 on adjusting screws ,e4 ,outside the ring the tension screws ,c enable the mirror to be accurately centered and held in place4 ,rarely1 the mirror is replaced by a totally reflecting right angled prism which saves some light1 but unless for small instruments is rather heavy and hard to obtain of the requisite quality and precision of figure4 ,a typical modern reflector by ,brashear1 of #f inches aperture1 is shown in ,fig4 #ce1 complete with circles and driving clock1 the latter contained in the hollow iron pier1 an arrangement usual in ,american-made instruments4 ,illustration3 ,,fig4 #cd4--,support of ,diagonal ,mirror 7,browning47 ,recent reflectors1 particularly in this country1 have four supporting strips instead of three1 which gives a little added stiffness1 and produces in star images but four diffraction rays instead of the six produced by the three strip arrangement1 each strip giving a diametral ray4 ,in some constructions the ring ,a is arranged to carry the eyepiece fittings1 placed at the very end of the tube and arranged for rotating about the optical axis of the telescope4 ,this allows the ocular to be brought to any position without turning the whole tube4 ,in small instruments a fixed eyepiece can be used without much inconvenience if located on the north side of the tube 7in moderate north latitudes74 ,reflectors are easily given a much greater relative aperture than is practicable in a single achromatic objective4 ,in fact they are usually given apertures of ,f_/#e to ,f_/#h and now and then are pushed to or even below ,f_/#c4 ,such mirrors have been successfully used for photography2#i and less frequently for visual observation1 mounted in the ,cassegranian form1 which commonly increases the virtual focal length at least three or four times4 ,a telescope so arranged1 with an aperture of a foot or more as in some recent examples1 makes a very powerful and compact instrument4 #i ,an ,f_/#c mirror of #am aperture by ,zeiss was installed in the observatory at ,bergedorf in #aiaa1 and a similar one by ,schaer is mounted at ,carre1 near ,geneva4 ,illustration3 ,,fig4 #ce4--,small ,equatorially ,mounted ,reflector4 ,this is the form commonly adopted for the large reflectors of recent construction1 a type being the #fj-;inch telescope of the ,mount ,wilson ,observatory of which the primary focus is #be feet and the ordinary equivalent focus as a ,cassegranian #hj feet4 ,comparatively few small reflectors have been made or used in the ,united ,states1 although the climatic conditions here are more favorable than in ,england1 where the reflector originated and has been very fully developed4 ,the explanation may lie in our smaller number of non-professional active astronomers who are steadily at observational work1 and can therefore use reflectors to the best advantage4 ,the relative advantages of refractors and reflectors have long been a matter of acrimonious dispute4 ,in fact1 more of the genuine odium theologicum has gone into the consideration of this matter than usually attaches to differences in scientific opinion4 ,a good many misunderstandings have been due to the fact that until recently few observers were practically familiar with both instruments1 and the professional astronomer was a little inclined to look on the reflector as fit only for amateurs4 ,the comparison is somewhat clarified at present by the fact that the old speculum metal reflector has passed out of use1 and the case now stands as between the ordinary refracting telescope such as has just been described1 and the silver-on-glass reflector discussed immediately thereafter4 ,the facts in the case are comparatively simple4 ,of two telescopes having the same clear aperture1 one a reflector and the other a refractor1 each assumed to be thoroughly well figured1 as it can be in fact today1 the theoretical resolving power is the same1 for this is determined merely by the aperture1 so that the only possible difference between the two would be in the residual imperfection in the performance of the refractor due to its not being perfectly achromatic4 ,this difference is substantially a negligible one for many1 but not all1 purposes4 ,likewise1 the general definition of the pair1 assuming first-class workmanship1 would be equal4 ,of the two1 the single surface of the mirror is somewhat more difficult to figure with the necessary precision than is any single surface of the refractor1 but reflectors can be1 and are1 given so perfect a parabolic figure that the image is in no wise inferior to that produced by the best refractors1 and the two types of telescopes will stand under favorable circumstances the same proportional magnifying powers4 ,the mirror is much more seriously affected by changes of temperature and by flexure than is the objective1 since in the former case the successive surfaces of the two lenses in the achromatic combination to a considerable extent compensate each other's slight changes of curvature1 which act only by still slighter changes of refraction1 while the mirror surface stands alone and any change in curvature produces double the defect on the reflected ray4 ,it is therefore necessary1 as we shall see presently1 to take particular precautions in working with a reflecting telescope1 which is1 so to speak1 materially more tender as regards external conditions than the refractor4 ,as regards light-grasp1 the power of rendering faint objects visible1 there is more room for honest variety of opinion4 ,it was often assumed in earlier days that a reflector was not much brighter than a refractor of half the aperture1 i4e41 of one quarter the working area4 ,this might have been true in the case of an old speculum metal reflector in bad condition1 but is certainly a libel on the silver-on-glass instrument1 which ,foucault on the other hand claimed to be1 aperture for aperture1 brighter than the refractor4 ,such a relation might in fact temporarily exist1 but it is far from typical4 ,the real relation depends merely on the light losses demonstrably occurring in the two types of telescopes4 ,these are now quite well known4 ,the losses in a refractor are those due to absorption of light in the two lenses1 plus those due to the four free surfaces of these lenses4 ,the former item in objectives of moderate size aggregates hardly more than #b to #c per cent4 ,the latter1 assuming the polish to be quite perfect1 amount to #ah to #bj per cent of the incident light1 for the glasses commonly used4 ,the total light transmitted is therefore not over #hj per cent of the whole1 more often somewhat under this figure4 ,for example1 a test by ,steinheil of one of ,fraunhofer's refractors gave a transmission of #gh per cent1 and other tests show similar results4 ,the relation between the light transmitted by glass of various thickness is very simple4 ,if unit thickness transmits m per cent of the incident light then n units in thickness will pass mn per cent4 ,thus if one half inch passes 4#ih1 two inches will transmit 4#ihd1 or 4#ibb4 ,evidently the bigger the objective the greater the absorptive loss4 ,if the loss by reflection at a single surface leaves m per cent to be transmitted then n surfaces will transmit mn4 ,and m being usually about 4#ie1 the four surfaces of an objective let pass nearly 4#hae1 and the thicker objective as a whole transmits approximately #ge per cent4 ,as to the reflector the whole relation hinges on the coefficient of reflection from a silvered surface1 under the circumstances of the comparison4 ,in the case of a reflecting telescope as a whole1 there are commonly two reflections from silver and if the coefficient of reflection is m then the total light reflected is m4 ,now the reflectivity of a silver-on-glass film has been repeatedly measured4 7,chant ,ap4 ,j4 #ba1 #baa7 found values slightly in excess of #ie per cent1 ,rayleigh 7,sci4 ,papers #b1 #d7 got #ic4i1 ,zeiss 7,landolt u4 ,bornstein1 ,tabellen7 about #ic4j for light of average wave length4 ,taking the last named value1 a double reflection would return substantially #hf4e per cent of the incident light4 ,no allowance is here made for any effect of selective reflection1 since for the bright visual rays1 which alone we are considering1 there is very slight selective effect4 ,in the photographic case it must be taken into account1 and the absorption in glass becomes a serious factor in the comparison1 amounting for the photographic rays to as much as #cj to #dj per cent in large instruments4 ,now in comparing reflector and refractor one must subtract the light stopped by the small mirror and its supports1 commonly from #e to #g per cent4 ,one is therefore forced to the conclusion that with silver coatings fresh and very carefully polished reflector and refractor will show for equal aperture equal light grasp4 ,but as things actually go even fresh silver films are quite often below 4#ij in reflectivity and in general tarnish rather rapidly1 so that in fact the reflector falls below the refractor by just about the amount by which the silver films are out of condition4 ,for example ,chant 7loc4 cit47 found after three months his reflectivity had fallen to 4#fi4 ,a mirror very badly tarnished by fifteen weeks of exposure to dampness and dust1 uncovered1 was found by the writer down to a scant 4#dj4 ,the line of ,fig4 #cf shows the relative equivalent apertures of refractors corresponding to a #aj inch reflector at coefficients of reflection for a single silvered surface varying from 4#ie to 4#ej at which point the film would be so evidently bad as to require immediate renewal4 ,the relation is obviously linear when the transmission of the objective is1 as here1 assumed constant4 ,the estimates of skilled observers from actual comparisons fall in well with the line1 showing reflectivities generally around 4#hj to 4#he for well polished films in good condition4 ,the long and short of the situation is that a silvered reflector deteriorates and at intervals varying from a few months to a year or two depending on situation1 climate1 and usage1 requires repolishing or replacement of the film4 ,this is a fussy job1 but quickly done if everything goes well4 ,illustration3 ,,fig4 #cf4--,relative ,light-grasp of ,reflector and ,refractor4 ,as to working field the reflector as ordinarily proportioned is at a disadvantage chiefly because it works at ,f_/#e or ,f_/#f instead of at ,f_/#ae4 ,at equal focal ratios there is no substantial difference between reflector and refractor in this respect1 unless one goes into special constructions1 as in photographic telescopes4 ,in two items1 first cost and convenience in observing1 the reflector has the advantage in the moderate sizes4 ,roughly1 the reflector simply mounted costs about one half to a quarter the refractor of equal light grasp and somewhat less resolving power1 the discrepancy getting bigger in large instruments 7#b feet aperture and upwards74 ,as to case of observing1 the small refractor is a truly neck-wringing instrument for altitudes above #de or thereabouts1 just the situation in which the equivalent reflector is most convenient4 ,in considering the subject of mounts these relations will appear more clearly4 ,practically the man who is observing rather steadily and can give his telescope a fixed mount can make admirable use of a reflector and will not find the perhaps yearly or even half yearly re-silvering at all burdensome after he has acquired the knack--chiefly cleanliness and attention to detail4 ,if1 like many really enthusiastic amateurs1 he can get only an occasional evening for observing1 and from circumstances has to use a portable mount set up on his lawn1 or even roof1 when fortune favors an evening's work1 he will find a refractor always in condition1 easy to set up1 and requiring a minimum of time to get into action4 ,the reflector is much the more tender instrument1 with1 however1 the invaluable quality of precise achromatism1 to compensate for the extra care it requires for its best performance4 ,it suffers more than the refractor1 as a rule1 from scattered light1 for imperfect polish of the film gives a field generally presenting a brighter background than the field of a good objective4 ,after all the preference depends greatly on the use to which the telescope is to be put4 ,for astrophysical work in general1 ,professor ,george ,e4 ,hale1 than whom certainly no one is better qualified to judge1 emphatically endorses the reflector4 ,most large observatories are now-a-days equipped with both refractors and reflectors4 ,,chapter ,,iii ,,optical ,,glass ,,and ,,its ,,working ,glass1 one of the most remarkable and useful products of man's devising1 had an origin now quite lost in the mists of antiquity4 ,it dates back certainly near a thousand years before the ,christian era1 perhaps many centuries more4 ,respecting its origin there are only traditions of the place1 quite probably ,syria1 and of the accidental melting together of sand and soda4 ,the product1 sodium silicate1 readily becomes a liquid1 i4e41 8water-glass10 but the elder ,pliny1 who tells the story1 recounts the later production of a stable vitreous body by the addition of a mineral which was probably a magnesia limestone4 ,this combination would give a good permanent glass1 whether the story is true or not1 and very long before ,pliny's time glass was made in great variety of composition and color4 ,in fact in default of porcelain glass was used in ,roman times relatively more than now4 ,but without knowledge of optics there was no need for glass of optical quality1 it was well into the ,renaissance before its manufacture had reached a point where anything of the sort could be made available even in small pieces1 and it is barely over a century since glass-making passed beyond the crudest empiricism4 ,glass is substantially a solid solution of silica with a variety of metallic oxides1 chiefly those of sodium1 potassium1 calcium and lead1 sometimes magnesium1 boron1 zinc1 barium and others4 ,by itself silica is too refractory to work easily1 though silica glass has some very valuable properties1 and the alkaline oxides in particular serve as the fluxes in common use4 ,other oxides are added to obtain various desired properties1 and some impurities may go with them4 ,the melted mixture is thus a somewhat complex solution containing frequently half a dozen ingredients4 ,each has its own natural melting and vaporizing point1 so that while the blend remains fairly uniform it may tend to lose some constituent while molten1 or in cooling to promote the crystallization of another1 if held too near its particular freezing point4 ,some combinations are more likely to give trouble from this cause than others1 and while a very wide variety of oxides can be coerced into solution with silica1 a comparatively limited number produce a homogeneous and colorless glass useful for optical purposes4 ,many mixtures entirely suitable for common commercial purposes are out of the question for lens making1 through tendency to surface deterioration by weathering1 lack of homogeneous quality1 or objectionable coloration4 ,a very small amount of iron in the sand used at the start gives the green tinge familiar in cheap bottles1 which materially decreases the transparency4 ,the bottle maker often adds oxide of manganese to the mixture1 which naturally of itself gives the glass a pinkish tinge1 and so apparently whitens it by compensating the one absorption by another4 ,the resulting glass looks all right on a casual glance1 but really cuts off a very considerable amount of light4 ,a further difficulty is that glass differs very much in its degree of fluidity1 and its components sometimes seem to undergo mutual reactions that evolve persistent fine bubbles1 besides reacting with the fireclay of the melting pot and absorbing impurities from it4 ,the molten glass is somewhat viscous and far from homogeneous4 ,its character suggests thick syrup poured into water1 and producing streaks and eddies of varying density4 ,imagine such a mixture suddenly frozen1 and you have a good idea of a common condition in glass1 transparent1 but full of stri4 ,these are frequent enough in poor window glass1 and are almost impossible completely to get rid of1 especially in optical glass of some of the most valuable varieties4 ,the great improvement introduced by ,guinand was constant stirring of the molten mass with a cylinder of fire clay1 bringing bubbles to the surface and keeping the mass thoroughly mixed from its complete fusion until1 very slowly cooling1 it became too viscous to stir longer4 ,the fine art of the process seems to be the exact combination of temperature1 time1 and stirring1 suitable for each composition of the glass4 ,there are1 too1 losses by volatilization during melting1 and even afterwards1 that must be reckoned with in the proportions of the various materials put into the melting1 and in the temperatures reached and maintained4 ,one cannot deduce accurately the percentage mixture of the raw materials from an analysis of the glass1 and it is notorious that the product even of the best manufacturers not infrequently fails to run quite true to type4 ,therefore the optical properties of each melting have carefully to be ascertained1 and the product listed either as a very slight variant from its standard type1 or as an odd lot1 useful1 but quite special in properties4 ,some of these odd meltings in fact have optical peculiarities the regular reproduction of which would be very desirable4 ,the purity of the materials is of the utmost importance in producing high grade glass for optical or other purposes4 ,the silica is usually introduced in the form of the purest of white sand carrying only a few hundredths of one per cent of impurities in the way of iron1 alumina and alkali4 ,the ordinary alkalis go in preferably as carbonates1 which can be obtained of great purity2 although in most commercial glass the soda is used in the form of 8salt-cake10 crude sodium sulphate4 ,calcium1 magnesium1 and barium generally enter the melt as carbonates1 zinc and lead as oxides4 ,alumina1 like iron1 is generally an impurity derived from felspar in the sand1 but occasionally enters intentionally as pure natural felspar1 or as chemically prepared hydrate4 ,a few glasses contain a minute amount of arsenic1 generally used in the form of arsenious acid1 and still more rarely other elements enter1 ordinarily as oxides4 ,whatever the materials1 they are commonly rather fine ground and very thoroughly mixed1 preferably by machinery1 before going into the furnaces4 ,glass furnaces are in these days commonly gas fired1 and fall into two general classes1 those in which the charge is melted in a huge tank above which the gas flames play1 and those in which the charge is placed in crucibles or pots open or nearly closed1 directly heated by the gas4 ,in the tank furnaces the production is substantially continuous1 the active melting taking place at one end1 where the materials are introduced1 while the clear molten glass flows to the cooler end of the tank or to a cooler compartment1 whence it is withdrawn for working4 ,the ordinary method of making optical glass is by a modification of the pot process1 each pot being fired separately to permit better regulation of the temperature4 ,the pots themselves are of the purest of fire clay1 of moderate capacity1 half a ton or so1 and arched over to protect the contents from the direct play of the gases1 leaving a side opening sufficient for charging and stirring4 ,the fundamental difference between the making of optical glass and the ordinary commercial varieties lies in the individual treatment of each charge necessary to secure uniformity and regularity1 carried even to the extent of cooling each melting very slowly in its own pot1 which is finally broken up to recover the contents4 ,the tank furnaces are under heat week in and week out1 may hold several hundred tons1 and on this account cannot so readily be held to exactness of composition and quality4 ,the optical glass works1 too1 is provided with a particularly efficient set of preheating and annealing kilns1 for the heat treatment of pots and glass must be of the most careful and thorough kind4 ,the production of a melting of optical glass begins with a very gradual heating of the pot to a bright red heat in one of the kilns4 ,it is then transferred to its furnace which has been brought to a similar temperature1 sealed in by slabs of firebrick1 leaving its mouth easy of access1 and then the heat is pushed up to near the melting temperature of the mixture in production1 which varies over a rather wide range1 from a moderate white heat to the utmost that a regenerative gas furnace can conveniently produce4 ,after the heating comes the rather careful process of charging4 ,the mixture is added a portion at a time1 since the fused material tends to foam1 and the raw material as a solid is more bulky than the fluid4 ,the chemical reactions as the mass fuses are somewhat complex4 ,in their simplest form they represent the formation of silicates4 ,at high temperatures the silica acts as a fairly strong acid1 and decomposes the fused carbonates of sodium and potassium with evolution of gas4 ,this is the rationale of the fluxing action of such alkaline substances of rather low melting point4 ,other mixtures act somewhat analogously but in a fashion commonly too complex to follow4 ,the final result is a thick solution1 and the chief concern of the optical glass maker is to keep it homogeneous1 free from bubbles1 and as nearly colorless as practicable4 ,to the first two ends the temperature is pushed up to gain fluidity1 and frequently substances are added 7e4g41 arsenic7 which by volatility or chemical effect tend to form large bubbles from the entrained gases1 capable of clearing themselves from the fluid where fine bubbles would remain4 ,for the same purpose is the stirring process4 ,the stirrer is a hard baked cylinder of fire clay fastened to an iron bar4 ,first heated in the mouth of the pot1 the stirrer is plunged in the molten glass and given a steady rotating motion1 the long bar being swivelled and furnished with a wooden handle for the workman4 ,this stirring is kept up pretty steadily while the heat is very slowly reduced until the mass is too thick to manage1 the process taking1 for various mixtures and conditions1 from three or four hours to the better part of a day4 ,illustration3 ,,fig4 #cg4--,testing ,optical ,glass in the ,rough4 ,then begins the careful and tedious process of cooling4 ,fairly rapid until the mass is solid enough to prevent the formation of fresh stri1 the cooling is continued more slowly1 in the furnace or after removal to the annealing oven1 until the crucible is cool enough for handling1 the whole process generally taking a week or more4 ,then the real trouble begins4 ,the crucible is broken away and there is found a more or less cracked mass of glass1 sometimes badly broken up1 again furnishing a clear lump weighing some hundreds of pounds4 ,this glass is then carefully picked over and examined for flaws1 stri and other imperfections4 ,these can sometimes be chipped away with more or less breaking up of the mass4 ,the inspection of the glass in the raw is facilitated by the scheme shown in elevation ,fig4 #cg4 ,here ,a is a tank with parallel sides of plate glass4 ,in it is placed ,b the rough block of glass1 and the tank is then filled with a liquid which can be brought to the same refractive power as the glass1 as in ,newton's disastrous experiment4 ,when equality is reached for1 say1 yellow light1 one can see directly through the block1 the rays no longer being refracted at its surface1 and any interior stri are readily seen even in a mass a foot or more thick4 ,before adding the liquid a ray would be skewed1 as ,c1 ,d1 ,e1 ,f1 afterwards it would go straight through2 ,c1 ,d1 ,g1 ,h4 ,the fraction that passes inspection may be found to be from much less than a quarter to a half of the whole4 ,this good glass is then ready for the next operation1 forming and fine annealing4 ,the final form to be reached is a disc or block1 and the chunks of perfect glass are heated in a kiln until plastic1 and then moulded into the required shapes1 sometimes concave or convex discs suitable for small lenses4 ,then the blocks are transferred to a kiln and allowed to cool off very gradually1 for several days or weeks according to the size of the blocks and the severity of the requirements they must meet4 ,in the highest class of work the annealing oven has thermostatic control and close watch is kept by the pyrometer4 ,it is clear that the chance of getting a large and perfect chunk from the crucible is far smaller than that of getting fragments of a few pounds1 so that the production of a perfect disc for a large objective requires both skill and luck4 ,little wonder therefore that the price of discs for the manufacture of objectives increases substantially as the cube of the diameter4 ,the process of optical glass making as here described is the customary one1 used little changed since the days of ,guinand4 ,the great advances of the last quarter century have been in the production of new varieties having certain desirable qualities1 and in a better understanding of the conditions that bring a uniform product of high quality4 ,during the world war the greatly increased demand brought most extraordinary activity in the manufacture1 and especially in the scientific study of the problems involved1 both here and abroad4 ,the result has been a long step toward quantity production1 the discovery that modifications of the tank process could serve to produce certain varieties of optical glass of at least fair quality1 and great improvements in the precision and rapidity of annealing4 ,these last are due to the use of the electric furnace1 the study of the strains during annealing under polarized light1 and scientific pyrometry4 ,it is found that cooling can be much hastened over certain ranges of temperature1 and the total time required very greatly shortened4 ,it has also been discovered1 thanks to captured instruments1 that some of the glasses commonly regarded as almost impossible to free from bubbles have in fact yielded to improved methods of treatment4 ,conventionally optical glass is of two classes1 crown and flint4 ,originally the former was a simple compound of silica with soda and potash1 sometimes also lime or magnesia1 while the latter was rich in lead oxide and with less of alkali4 ,the crown had a low index of refraction and small dispersion1 the flint a high index and strong dispersion4 ,crown glass was the material of general use1 while the flint glass was the variety used in cut glass manufacture by reason of its brilliancy due to the qualities just noted4 ,illustration3 ,,fig4 #ch4--,the ,index of ,refraction4 ,the refractive index is the ratio between the sine of the angle of incidence on a lens surface and that of the angle of refraction in passing the surface4 ,fig4 #ch shows the relation of the incident and refracted rays in passing from air into the glass lens surface ,l1 and the sines of the angles which determine n1 the conventional symbol for the index of refraction4 ,here i is the angle of incidence and r the angle of refraction i4e4 n s_/s4 ,the indices of refraction are usually given for specific colors representing certain lines in the spectrum1 commonly ,a1 the potassium line in the extreme red1 ,c the red line due to hydrogen1 ,d the sodium line1 ,f the blue hydrogen line and ,g the blue-violet line hydrogen line1 and are distinguished as nc1 nd1 nf1 etc4 ,the standard dispersion 7dn7 for visual rays is given as between ,c and ,f1 while the standard refractivity is taken for ,d1 in the bright yellow part of the spectrum4 7,note4 ,for the convenience of those who are rusty on their trigonometry1 ,fig4 #ci shows the simpler trigonometric functions of an angle4 ,thus the sine of the angle ,a is1 numerically1 the length of the radius divided into the length of the line dropped from the end of the radius to the horizontal base line1 i4e4 bc_/,ob1 the tangent is da_/,ob1 and the cosine ,oc_/,ob47 ,ordinarily the index of refraction of the crown was taken as about #c_/b1 that of the flint as about #h_/e4 ,as time has gone on and especially since the new glasses from the ,jena works were introduced about #ce years ago1 one cannot define crowns and flints in any such simple fashion1 for there are crowns of high index and flints of low dispersion4 ,illustration3 ,,fig4#ci4--,the ,simple ,trigonometric ,functions of an ,angle4 ,the following table gives the optical data and chemical analyses of a few typical optical glasses4 ,the list includes common crowns and flints1 a typical baryta crown and light flint1 and a telescope crown and flint for the better achromatization of objectives1 as developed at the ,jena works4 ,the thing most conspicuous here as distinguishing crowns from flints is that the latter have greater relative dispersion in the blue1 the former in the red end of the spectrum1 as shown by the bracketed ratios4 ,this as we shall see is of serious consequence in making achromatic objectives4 ,in general1 too1 the values of for flints are much lower than for crowns1 and the indices of refraction themselves commonly higher4 ,as we have just seen1 glass comes to the optician in blocks or discs1 for miscellaneous use the former1 three or four inches square and an inch think1 more or less2 for telescope making the latter4 ,the discs are commonly some ten percent greater in diameter than the finished objective for which they are intended1 and in thickness from #a_/h to #a_/aj the diameter4 ,they are commonly well annealed and given a preliminary polish on both sides to facilitate close inspection4 ,,characteristics ,,of ,,optical ,,glasses ---------------------------------------- ----------------------- ,bracketed numbers are dn proportions of dn ,glass nd ----- ------------------------ 7,f-,c7 ,d-,a ,f-,d ,g-,f ---- ---- ---- dn dn dn ---------------------------------------- --------------------- ,boro-silicate #a4ejfi 4#jjhac #fb4c 4#jjebi 4#jjefi 4#jjdeg crown 74#fea7 74#gja7 74#efb7 ,zinco-silicate #a4eagj 4#jjhei #fj4b 4#jjeee 4#jjfje 4#jjdhe 7hard7 crown 74#fdf7 74#gjd7 74#efe7 ,dense baryta #a4ehii 4#jjigj #fj4h 4#jjfba 4#jjfhc 4#jjedf crown 74#fdj7 74#gjd7 74#efc7 ,baryta light #a4egah 4#jaacc #ej4d 4#jjgjf 4#jjhjc 4#jjffj flint 74#fbc7 74#gji7 74#ehb7 ,common light #a4egaj 4#jacbg #dc4j 4#jjhai 4#jjidc 4#jjgia flint 74#fag7 74#gaj7 74#eif7 ,common dense #a4faaf 4#jafch #cg4c 4#jjiie 4#jaagj 4#jjiia flint 74#fjg7 74#gad7 74#fjg7 ,very dense #a4fdhi 4#jaiai #cc4h 4#jaaeb 4#jacgb 4#jaahj flint 74#fjj7 74#gad7 74#fae7 ,densest flint #a4geda 4#jbgdc #bg4e 4#jafjg 4#jaigd 4#jagcj 74#ehe7 74#gbj7 74#fcj7 99,telescope #a4ebhe 4#jjhff #fa4j 4#jjeeg 4#jjfaj 4#jjdic crown 74#fdc7 74#gje7 74#egj7 99,telescope #a4ebhf 4#jajbe #ea4f 4#jjfed 4#jjgbc 4#jjeia flint 74#fch7 74#gje7 74#egf7 99 ,optical data close approximations only4 ---------------------------------------- -------------------------------- ,analysis of glasses in percentages ---------------------------------------- ------------------- ,si ,b#b ,k#b ,na#b ,,al#b;,as#b;,as#b;,fe#b,mn#b,sb#b ,o#b ,o#c,zn,o ,pb,o ,ba,o ,o ,o ,ca,o ,o#c ,o#e ,o#c ,o#c ,o#c ,o#c ,mg,o ---------------------------------------- ------------------- #gd4h #e4i -- -- -- #g4aaaa4c -- 4#ge -- 4#jf -- 4#jf #fe4d #b4eb4j -- #i4fae4j #e4j -- -- -- 4#d -- 4#a #cg4eae4j -- -- #da4j -- -- #e4j #a4e #ea4g -- #g4jaj4jbj4j #i4e #a4e -- -- 4#cj #ed4c #a4e --#cc4j -- #h4j #c4j -- -- 4#bj #ed4h -- --#cg4j -- #e4h 4#h 4#fj 4#d -- -- 4#gj -- -- 4#bj #dj4j -- --#eb4f -- #f4e 4#e -- -- 4#cj -- -- 4#ji #bi4c -- --#fg4e -- #c4j -- -- -- -- 4#bj -- 4#jd ------ #ee4b -- -- -- #bb4j #e4g #g4ee4i -- -- -- #c4g #ei4iab4g -- -- -- #e4a #c4e -- -- -- -- #b4g #af4a ---------------------------------------- -------------------- ,the first step toward the telescope is the testing of these discs of glass1 first for the presence or absence of stri and other imperfections2 second1 for the perfection of the annealing4 ,the maker has usually looked out for all the grosser imperfections before the discs left his works1 but a much closer inspection is needed in order to make the best use of the glass4 ,illustration3 ,,fig4 #dj4--,testing ,glass for ,stri4 ,bad stri are of course seen easily1 as they would be in a window pane1 but such gross imperfections are often in reality less damaging than the apparently slighter ones which must be searched for4 ,the simplest test is to focus a good telescope on an artificial star1 remove the eyepiece and bring the eye into its place4 ,when the eye is in focus the whole aperture of the objective is uniformly filled with light1 and if the disc to be tested be placed in front of it1 any inequality in refraction will announce itself by an inequality of illumination4 ,a rough judgment as to the seriousness of the defect may be formed from the area affected and the amount by which it affects the local intensity of illumination4 ,fig4 #dj shows the arrangement for the test1 ,a being the eye1 ,b the objective and ,c the disc4 ,the artificial star is conveniently made by setting a black bottle in the sun a hundred feet or so away and getting the reflection from its shoulder4 ,illustration3 ,,fig4 #da4--,the ,mirror ,test for ,stri4 ,a somewhat more delicate test1 very commonly used1 is shown in ,fig4 #da4 ,here ,a is a truly spherical mirror silvered on the front4 ,at ,b very close to its centre of curvature is placed a lamp with a screen in front of it perforated with a hole #a_/cb inch or so in diameter4 ,the rays reflected from the mirror come back quite exactly upon themselves and when the eye is placed at ,c1 their reflected focus1 the whole mirror ,a is uniformly lighted just as the lens was in ,fig4 #dj1 with the incidental advantage that it is much easier and cheaper to obtain a spherical mirror for testing a sizeable disc than an objective of similar size and quality4 ,now placing the disc ,d in front of the mirror1 the light passing twice through it shows up the slightest stria or other imperfection as a streak or spot in the field4 ,its place is obvious and can be at once marked on the glass1 but its exact position in the substance of the disc is not so obvious4 ,to determine this1 which may indicate that the fault can be ground out in shaping the lens1 a modification of the first test serves well1 as indeed it does for the general examination of large discs4 ,instead of using a distant artificial star and a telescope1 one uses the lamp and screen1 or even a candle flame ten feet or more away and a condensing lens of rather short focus1 which may or may not be achromatic1 so that the eye will get into its focus conveniently while the lens is held in the hand4 ,fig4 #db shows the arrangement4 ,here ,a is the eye1 ,b the condensing lens1 ,c the disc and ,d the source of light4 ,the condensing lens may be held on either side of the disc as convenience suggests1 and either disc or lens may be moved4 ,the operation is substantially the examination of a large disc piecemeal1 instead of all at once by the use of a big objective or mirror4 ,illustration3 ,,fig4 #db4--,locating ,stri in the ,substance of a ,disc4 ,now when a stria has been noted mark its location as to the surface1 and1 moving the eye a little1 look for parallax of the fault with respect to the surface mark4 ,if it appears to shift try a mark on the opposite surface in the same way4 ,comparison of the two inspections will show about where the fault lies with respect to the surfaces1 and therefore what is the chance of working it out4 ,sometimes a look edgewise of the disc will help in the diagnosis4 ,numerous barely detectable stri are usually worse than one or two conspicuous ones1 for the latter frequently throw the light they transmit so wide of the focus that it does not affect the image1 which could be greatly damaged by slight blurs of light that just miss focus4 ,given a disc that passes well the tests for stri and the like the next step is to examine the perfection of the annealing1 which in its larger aspect is revealed by an examination in polarized light4 ,illustration3 ,,fig4 #dc4--,testing a ,disc in ,polarized ,light4 ,for this purpose the disc is set up against a frame placed on table or floor with a good exposure to skylight behind it1 and inclined about #ce from the vertical4 ,behind it is laid a flat shiny surface to serve as polarizer4 ,black enamel cloth smoothly laid1 a glass plate backed with black paint1 or even a smooth board painted with asphalt paint will answer excellently4 ,then holding a ,nicol prism before the eye and looking perpendicular to the face of the disc1 rotate the prism on its axis4 ,fig4 #dc shows the arrangement1 ,a being the eye1 ,b the ,nicol1 ,c the disc1 and ,d the polarizer behind it4 ,if annealing has left no strain the only effect of rotating the ,nicol will be to change the field from bright to dark and back again as if the disc were not there4 ,generally a pattern in the form of a somewhat hazy ,maltese cross will appear1 with its arms crossing the disc1 growing darker and lighter alternately as the ,nicol is turned4 ,if the cross is strongly marked but symmetrical and well centered the annealing is fair--better as the cross is fainter and hazier--altogether bad if colors show plainly or if the cross is decentered or distorted4 ,the test is extremely sensitive1 so that holding a finger on the surface of the disc may produce local strain that will show as a faint cloudy spot4 ,a disc free of stri and noticeable annealing strains is usually1 but not invariably1 good1 for too frequent reheating in the moulding or annealing process occasionally leaves the glass slightly altered1 the effect extending1 at worst1 to the crystallization or devitrification to which reference has been made4 ,given a good pair of discs the first step towards fashioning them into an objective is roughing to the approximate form desired4 ,as a guide to the shaping of the necessary curves1 templets must be made from the designed curves of the objective as precisely as possible4 ,these are laid out by striking the necessary radii with beam compass or pivoted wire and scribing the curve on thin steel1 brass1 zinc or glass4 ,the two last are the easier to work since they break closely to form4 ,from these templets the roughing tools are turned up1 commonly from cast iron1 and with these1 supplied with carborundum or even sand1 and water1 the discs1 bearing against the revolving tool1 are ground to the general shape required4 ,they are then secured to a slowly revolving table1 bearing edgewise against a revolving grindstone1 and ground truly circular and of the proper final diameter4 ,at this point begins the really careful work of fine grinding1 which must bring the lens very close to its exact final shape4 ,here again tools of cast iron1 or sometimes brass1 are used1 very precisely brought to shape according to the templets4 ,they are grooved on the face to facilitate the even distribution of the abrasive1 emery or fine carborundum1 and the work is generally done on a special grinding machine1 which moves the tool over the firmly supported disc in a complicated series of strokes imitating more or less closely the strokes found to be most effective in hand polishing4 ,in general terms the operator in handwork at this task supports the disc on a firm vertical post1 by cementing it to a suitable holder1 and then moves the tool over it in a series of straight or oval strokes1 meanwhile walking around the post4 ,a skilful operator watches the progress of his work1 varies the length and position of his strokes accordingly1 and1 despite the unavoidable wear on the tool1 can both keep its figure true and impart a true figure to the glass4 ,illustration3 ,,fig4 #dd4--;,dr4 ,draper's ,polishing ,machine4 ,the polishing machine1 of which a type used by ,dr4 ,draper is shown in ,fig4 #dd1 produces a similar motion1 the disc slowly revolving and the rather small tool moving over it in oval strokes kept off the center4 ,more often the tool is of approximately the same diameter as the disc under it4 ,the general character of the motion is evident from the construction4 ,the disc a is chucked by c c on the bed1 turned by the post d and worm wheel e4 ,this is operated from the pulleys1 i1 g1 which drive through k1 the crank m1 adjustable in throw by the nuts n1 n1 and in position of tool by the clamps r1 r4 ,the motion may be considerably varied by adjustment of the machine1 always keeping the stroke from repeating on the same part of the disc1 by making the period of the revolution and of the stroke incommensurable so far as may be4 ,even in spectacle grinding machines the stroke may repeat only once in hundreds of times1 and even this frequency in a big objective would1 if followed in the polishing1 leave tool marks which could be detected in the final testing4 ,in the fine grinding1 especially near the end of the process1 the templets do not give sufficient precision in testing the curves1 and recourse is had to the spherometer1 by which measurements down to about #a_/ajjjjj inch can be consistently made4 ,the next stage of operations is polishing1 which transforms the grey translucency of the fine ground lens into the clear and brilliant surface which at last permits rigorous optical tests to be used for the final finish of the lens4 ,this polishing is done generally on the fine grinding machine but with a very different tool and with rouge of the utmost fineness4 ,the polishing tool is in any case ground true and is then faced with a somewhat yielding material to carry the charge of rouge4 ,cheap lenses are commonly worked on a cloth polisher1 a texture similar to billiard cloth being suitable1 or sometimes on paper worked dry4 ,with care either may produce a fairly good surface1 with1 however1 a tendency to polish out the minute hollows left by grinding rather than to cut a true surface clear down to their bottoms4 ,hence cloth or paper is likely to leave microscopic inequalities apparently polished1 and this may be sufficient to scatter over the field a very perceptible amount of light which should go to forming the image4 ,all first class objectives and mirrors are in fact polished on optician's pitch4 ,this is not the ordinary pitch of commerce but a substance of various composition1 sometimes an asphaltic compound1 again on a base of tar1 or of resin brought to the right consistency by turpentine4 ,whatever the exact composition1 the fundamental property is that the material1 apparently fairly hard and even brittle when cold1 is actually somewhat plastic to continued pressure4 ,sealing wax has something of this quality1 for a stick which may readily be broken will yet bend under its own weight if supported at the ends4 ,if the fine grinding process has been properly carried out the lens has received its correct form as nearly as gauges and the spherometer can determine it4 ,the next step is to polish the surface as brilliantly and evenly as possible4 ,to this end advantage is taken of the plastic quality already mentioned1 that the glass may form its own tool4 ,the base of the tool may be anything convenient1 metal1 glass or even wood4 ,its working surface is made as nearly of the right curvature as practicable and it is then coated with warm pitch to a thickness of an eighth of an inch more or less1 either continuously or in squares1 and while still slightly warm the tool is placed against the fine ground disc1 the exact shape of which it takes4 ,when cold the pitch surface can easily be cut out into squares or symmetrically pitted with a suitable tool1 at once facilitating the distribution of the rouge and water that serves for polishing1 and permitting delicate adjustment of the working curvature in a way about to be described4 ,fig4 #de shows the squared surface of the tool as it would be used for polishing a plane or very slightly convex or concave surface4 ,supplied with the thin abrasive paste1 it is allowed to settle1 cold1 into its final contact with the glass1 and then the process of polishing by hand or machine is started4 ,the action of the tool must be uniform to avoid changing the shape of the lens4 ,it can be regulated as it was in the grinding1 by varying the length and character of the stroke1 but even more delicately by varying the extent of surface covered by the pitch actually working on the glass4 ,illustration3 ,,fig4 #de4--,tool for ,flat ,surface4 ,illustration3 ,,fig4 #df4--,tool for ,concave ,surface4 ,this is done by channeling or boring away pitch near the rim or center of the tool as the case may be4 ,fig4 #df shows a tool which has been thus treated so that the squares are progressively smaller near the periphery4 ,such a spacing tends to produce a concave surface from a flat tool or to increase the concavity from a curved one4 ,trimming down the squares towards the centre produces the opposite result4 ,broadly1 the principle is that the tool cuts the more in the areas where the contact surfaces are the greater4 ,this is not wholly by reason of greater abrading surface1 but also because where the contact is greater in area the pitch settles less1 from the diminished pressure1 thus increasing the effective contact4 ,clearly the effect of trimming away is correlated with the form and length of stroke1 and the temper of the pitch1 and in fact it requires the wisdom of the serpent to combine these various factors so as to produce the perfectly uniform and regular action required in polishing4 ,now and then1 at brief intervals1 the operation is stopped to supply rouge and to avoid changing the conditions by the heat of friction4 ,especially must heating be looked out for in hand polishing of lenses which is often done with the glass uppermost for easier inspection of the work4 ,polishing1 if the fine grinding has been judiciously done is1 for moderate sized surfaces1 a matter of only a few hours4 ,it proceeds quite slowly at first while the hills are being ground down and then rather suddenly comes up brilliantly as the polisher reaches the bottoms of the valleys4 ,large lenses and mirrors may require many days4 ,now begins the final and extraordinarily delicate process of figuring4 ,the lens or mirror has its appointed form as nearly as the most precise mechanical methods can tell--say down to one or two hundred-thousandths of an inch4 ,from the optical standpoint the result may be thoroughly bad1 for an error of a few millionths of an inch may be serious in the final performance4 ,the periphery may be by such an amount longer or shorter in radius than it should be1 or there may be an intermediate zone that has gone astray4 ,in case of a mirror the original polishing is generally intended to leave a spherical surface which must be converted into a paraboloidal one by a change in curvature totalling only a few hundred-thousandths of an inch and seriously affected by much smaller variations4 ,the figuring is done in a fashion very similar to the polishing4 ,the first step is to find out by optical tests such as are described in ,chapter ,,ix the location of the errors existing after the polishing1 and once found1 they must be eliminated by patient and cautious work on the surface4 ,every optical expert has his own favorite methods of working out the figure4 ,if there is a hollow zone the whole surface must be worked down to its level by repolishing2 if1 on the other hand1 there is an annular hump1 one may repolish with stroke and tool-face adapted to cut it down1 or one may cautiously polish it out until it merges with the general level4 ,polishing is commonly done with tools of approximately the size of the work1 but in figuring there is great difference of practice1 some expert workers depending entirely on manipulation of a full sized tool1 others working locally with small polishers1 even with the ball of the thumb1 in removing slight aberrations4 ,in small work where the glass can be depended on for homogeneity and the tools are easily kept true the former method is the usual one1 but in big objectives the latter is often easier and may successfully reach faults otherwise very difficult to eliminate4 ,among well known makers of telescopes the ,clarks and their equally skilled successors the ,lundins1 father and son1 developed the art of local retouching to a point little short of wizardry2 the late ,dr4 ,brashear depended almost entirely on the adroitly used polishing machine2 ,sir ,howard ,grubb uses local correction in certain cases1 and in general the cautiously modified polisher2 while some of the ,continental experts are reported to have developed the local method very thoroughly4 ,the truth probably is that the particular error in hand should determine the method of attack and that its success depends entirely on the skill of the operator4 ,as to the perfection of the objectives figured in either way1 no systematic difference due to the method of figuring can be detected by the most delicate tests4 ,in any case the figuring operation is long and tedious1 especially in large work where problems of supporting to avoid flexure arise1 where temperature effects on tool and glass involve long delays between tests and correction1 and where in the last resort non-spherical surfaces must often be resorted to in bringing the image to its final perfection4 ,the final test of goodness is performance1 a clean round image without a trace of spherical or zonal aberration and the color correction the best the glasses will allow4 ,constant and rigorous testing must be applied all through the process of figuring1 and the result seems to depend on a combination of experience1 intuition and tactual expertness rarely united in any one person4 ,sir ,howard ,grubb1 in a paper to be commended to anyone interested in objectives1 once forcibly said3 8,i may safely say that ,i have never finished any objective over #aj inches diameter1 in the working of which ,i did not meet with some new experience1 some new set of conditions which ,i had not met before1 and which had then to be met by special and newly devised arrangements40 ,the making of reflecting telescopes is not much easier since although only one surface has to be worked1 that one has to be figured with extraordinary care1 flexure has to be guarded against at every stage of the working1 and afterwards1 temperature change is a busy foe1 while testing for correct figure1 the surface being non-spherical1 is considerably more troublesome4 ,an expert can make a good mirror with far less actual labor than an objective of similar aperture1 but when one reads ,dr4 ,henry ,draper's statement that in spite of knowing at first hand the methods and grinding machines of ,lord ,rosse and ,mr4 ,lassell1 he ground over a hundred mirrors1 and spent three years of time1 before he could get a correct figure with reasonable facility1 one certainly gains a high respect for the skill acquired4 ,this chapter is necessarily sketchy and not in the least intended to give the reader a complete account of technical glass manufacture1 far less of the intricate and almost incommunicable art of making objectives and mirrors4 ,it may however lead to a better understanding of the difference between the optical glass industry and the fabrication of commercial glass1 and lead the reader to a fuller realization of how fine a work of art is a finished objective or mirror as compared with the crude efforts of the early makers or the hasty bungling of too many of their successors4 ,for further details on making1 properties and working of optical glass see3 ,,hovestadt3 8,jenaer ,glas40 ,,rosenhain3 8,glass ,manufacture40 ,,sir ,,howard ,,grubb3 8,telescopic ,objectives and ,mirrors3 ,their ,preparation and ,testing40 ,nature #cd1 #he4 ,,dr4 ,,henry ,,draper3 8,on the ,construction of a ,silvered ,glass ,telescope40 7,smithsonian ,contributions to ,knowledge1 ,vol4 #cd47 ,g4 ,w4 ,,ritchey3 ,on the ,modern ,reflecting ,telescope and the ,making and ,testing of ,optical ,mirrors4 7,smithsonian ,contributions to ,knowledge1 ,vol4 #cd47 ,,lord ,,rayleigh3 ,polishing of ,glass ,surfaces4 7,proc4 ,opt4 ,convention1 #aije1 p4 #gc47 ,,bottone3 8,lens ,making for ,amateurs40 ,,chapter ,,iv ,,the ,,properties ,,of ,,objectives ,,and ,,mirrors ,the path of the rays through an ordinary telescope has been shown in ,fig4 #e4 ,in principle all the rays from a point in the distant object should unite precisely in a corresponding point in the image which is viewed by the eyepiece4 ,practically it takes very careful design and construction of the objective to make them meet in such orderly fashion even over an angular space of a single degree1 and the wider the view required the more difficult the construction4 ,we have spoken in the account of the early workers of their struggles to avoid chromatic and spherical aberrations1 and it is chiefly these that still1 in less measure1 worry their successors4 ,illustration3 ,,fig4 #dg4--;,chromatic ,aberration of ,convex ,lens4 ,the first named is due to the fact that a prism does not bend light of all colors equally1 but spreads them out into a spectrum2 red refracted the least1 violet the most4 ,since a lens may be regarded as an assemblage of prisms1 of small angle near the centre and greater near the edge1 it must on the whole and all over bend the blue and violet rays to meet on the axis nearer the rear surface than the corresponding red rays1 as shown in ,fig4 #dg4 ,here the incident ray a is split up by the prismatic effect of the lens1 the red coming to a focus at r1 the violet at v4 ,one can readily see this chromatic aberration by covering up most of a common reading glass with his hand and looking through the edge portion at a bright light1 which will be spread out into a colored band4 ,if the lens is concave the violet rays will still be the more bent1 but now outwards1 as shown in ,fig4 #dh4 ,the incident ray a is split up and the violet is bent toward v1 proceeding as if coming straight from a virtual focus v in front of the lens1 and nearer it than the corresponding red focus r4 ,evidently if we could combine a convex lens1 bending the violet inward too much1 with a concave one1 bending it outward too much1 the two opposite variations might compensate each other so that red and violet would come to the same focus--which is the principle of the achromatic objective4 ,illustration3 ,,fig4 #dh4--;,chromatic ,aberration of ,concave ,lens4 ,if the refractive powers of the lenses were exactly proportional to their dispersive powers1 as ,newton erroneously thought1 it is evident that the concave lens would pitch all the rays outwards to an amount which would annul both the chromatic variation and the total refraction of the convex lens1 leaving the pair without power to bring anything to a focus4 ,fortunately flint glass as compared with crown glass has nearly double the dispersion between red and violet1 and only about #bj greater refractive power for the intermediate yellow ray4 ,hence1 the prismatic dispersive effect being proportional to the total curvature of the lens1 the chromatic aberration of a crown glass lens will be cured by a concave flint lens of about half the total curvature1 and1 the refractions being about as #e to #f1 of the total power4 ,since the 8power0 of any lens is the reciprocal of its focal length1 a crown glass convex lens of focal length #c1 and a concave flint lens of focal length #e 7negative7 will form an approximately achromatic combination4 ,the power of the combination will be the algebraic sum of the powers of the components so that the focal length of the pair will be about #e_/b that of the crown lens with which we started4 ,to be more precise the condition of achromatism is n n #j where is the reciprocal of a radius and n1 or n1 is the difference in refractive index between the rays chosen to be brought to exact focus together1 as the red and the blue or violet4 ,this conventional equation simply states that the sum of the reciprocals of the radii of the crown lens multiplied by the dispersion of the crown1 must equal the corresponding quantity for the flint lens if the two total dispersions are to annul each other1 leaving the combination achromatic4 ,whatever glass is used the power of a lens made of it is ,p7 #a_/;f7 7n - #a7 so that it will be seen that1 other things being equal1 a glass of high index of refraction tends to give moderate curves in an objective4 ,also1 referring to the condition of achromatism1 the greater the difference in dispersion between the two glasses the less curvatures will be required for a given focal length1 a condition advantageous for various reasons4 ,the determination of achromatism for any pair of glasses and focal length is greatly facilitated by employing the auxiliary quantity which is tabulated in all lists of optical glass as a short cut to a somewhat less manageable algebraic expression4 ,using this we can figure achromatism for unity focal length at once1 ,p _/7-7 ,p _/7-7 7n,d-#a7_/n being the powers of the leading and following lenses respectively4 ,the combined lens will bring the rays of the two chosen colors1 as red and blue1 to focus at the same point on the axis4 ,it does not necessarily give to the red and blue images of an object the same exact size4 ,failure in this respect is known as chromatic difference of magnification1 but the fault is small and may generally be neglected in telescope objectives4 ,we have now seen how an objective may be made achromatic and of determinate focal length1 but the solution is in terms of the sums of the respective curvatures of the crown and flint lenses1 and gives no information about the radii of the individual surfaces4 ,the relation between these is all-important in the final performance4 ,illustration3 ,,fig4 #di4--,spherical ,aberration of ,convex ,lens4 ,for in a convex lens with spherical surfaces the rays striking near the edge1 of whatever color1 are pitched inwards too much compared with rays striking the more moderate curvatures near the axis1 as shown in ,fig4 #di4 ,the ray a b thus comes to a focus shorter than the ray a b4 ,this constitutes the fault of spherical aberration1 which the old astronomers1 following the suggestions of ,descartes1 tried ineffectually to cure by forming lenses with non-spherical surfaces4 ,illustration3 ,,fig4 #ej4--,spherical ,aberration of ,concave ,lens4 ,fig4 #ej suggests the remedy1 for the outer ray a is pitched out toward b as if it came from a focal point c1 while the ray nearer the center a is much less bent toward b as if it came from c4 ,the spherical aberrations of a concave lens therefore1 being opposite to those of a convex lens1 the two must1 at least to a certain extent1 compensate each other as when combined in an achromatic objective4 ,so in fact they do1 and1 if the curves that go to make up the total curvatures of the two are properly chosen1 the total spherical aberration can be made negligibly small1 at least on and near the axis4 ,taking into account this condition1 therefore1 at once gives us a clue to the distribution of the total curvatures and hence to the radii of the two lenses4 ,spherical aberration1 however1 involves not only the curvatures but the indices of refraction1 so that exact correction depends in part on the choice of glasses wherewith to obtain achromatization4 ,in amount spherical aberration varies with the square of the aperture and inversely with the cube of the focal length i4e4 with a_/f4 ,it is reckoned as when1 as in ,fig4 #di1 the rim rays come to the shorter focus1 as-1 when they come to the longer focus4 ,in any event1 since the spherical aberration of a lens may be varied in above the ratio of #d3a1 for the same total power1 merely by changing the ratio of the radii1 it is evident that the two lenses being fairly correct in total curvature might be given considerable variations in curvature and still mutually annul the axial spherical aberration4 ,such is in fact the case1 so that to get determinate forms for the lenses one must introduce some further condition or make some assumption that will pin down the separate curvatures to some definite relations4 ,the requirement may be entirely arbitrary1 but in working out the theory of objectives has usually been chosen to give the lens some real or hypothetical additional advantage4 ,the commonest arbitrary requirement is that the crown glass lens shall be equiconvex1 merely to avoid making an extra tool4 ,this fixes one pair of radii1 and the flint lens is then given the required compensating aberration choosing the easiest form to make4 ,this results in the objective of ,fig4 #ea4 ,illustration3 ,,fig4 #ea4--,objectives with ,equiconvex ,crown4 ,probably nine tenths of all objectives are of this general form1 equiconvex crown and nearly or quite plano-concave flint4 ,the inside radii may be the same1 in which case the lenses should be cemented1 or they may differ slightly in either direction as a1 ,fig4 #ea with the front of the flint less curved than the rear of the crown1 and b where the flint has the sharper curve4 ,the resulting lens if ordinary glasses are chosen gives excellent correction of the spherical aberration on the axis1 but not much away from it1 yielding a rather narrow sharp field4 ,only a few exceptional combinations of glasses relieve this situation materially4 ,the identity of the inner radii so that the surfaces can be cemented is known historically as ,clairault's condition1 and since it fixes two curvatures at identity somewhat limits the choice of glasses1 while to get proper corrections demands quite wide variations in the contact radii for comparatively small variations in the optical constants of the glass4 ,when two adjacent curves are identical they should be cemented1 otherwise rays reflected from say the third surface of ,fig4 #ea will be reflected again from the second surface1 and passing through the rear lens in almost the path of the original ray will come to nearly the same focus1 producing a troublesome 8ghost40 ,hence the curvatures of the second and third surfaces when not cemented are varied one way or the other by two or three per cent1 enough to throw the twice reflected rays far out of focus4 ,in this case1 as in most others1 the analytical expression for the fundamental curvature to be determined turns up in the form of a quadratic equation1 so that the result takes the form a b and there are two sets of radii that meet the requirements4 ,of these the one presenting the gentler curves is ordinarily chosen4 ,fig4 #eb a and c shows the two cemented forms1 thus related1 for a common pair of crown and flint glasses1 both cleanly corrected for chromatic and axial spherical aberration4 ,nearly a century ago ,sir ,john ,herschel proposed another defining condition1 that the spherical aberration should be removed both for parallel incident rays and for those proceeding from a nearer point on the axis1 say ten or more times the focal length in front of the objective4 ,this condition had little practical value in itself1 and its chief merit was that it approximated one that became of real importance if the second point were taken far enough away4 ,illustration3 ,,fig4 #eb4--;,allied ,forms of ,cemented ,objectives4 ,a little later ,gauss suggested that the spherical aberration should be annulled for two different colors1 much as the chromatic aberration is treated4 ,and1 being a mathematical wizard1 he succeeded in working out the very intricate theory1 which resulted in an objective approximately of the form shown in ,fig4 #ec4 ,it does not give a wide field but is valuable for spectroscopic work1 where keen definition in all colors is essential4 ,troublesome to compute1 and difficult to mount and center1 the type has not been much used1 though there are fine examples of about #i inches aperture at ,princeton1 ,utrecht1 and ,copenhagen1 and a few smaller ones elsewhere1 chiefly for spectroscopic use4 ,it was ,fraunhofer who found and applied the determining condition of the highest practical value for most purposes4 ,this condition was absence of coma1 the comet shaped blur generally seen in the outer portions of a wide field4 ,it is due to the fact that parallel oblique rays passing through the opposite rims of the lens and through points near its center do not commonly come to the same focus1 and it practically is akin to a spherical aberration for oblique rays which greatly reduces the extent of the sharp field4 ,it is reckoned when the blur points outwards1-when it points inwards1 and is directly proportional to the tangent of the obliquity and the square of the aperture1 and inversely to the square of the focal length i4e4 it varies with atan7u7_/f4 ,illustration3 ,,fig4 #ec4--;,gaussian ,objective4 ,just how ,fraunhofer solved the problem is quite unknown1 but solve it he did1 and very completely1 as he indicates in one of his later papers in which he speaks of his objective as reducing all the aberrations to a minimum1 and as ,seidel proved #cj years later in the analysis of one of ,fraunhofer's objectives4 ,very probably he worked by tracing axial and oblique rays through the objective form by trigonometrical computation1 thus finding his way to a standard form for the glasses he used4#aj #aj ,more recently his condition proves to be quite the exact equivalent of ,abb's sine condition which states that the sine of the angle made with the optical axis by a ray entering the objective from a given axial point shall bear a uniform ratio to the sine of the corresponding angle of emergence1 whatever the point of incidence4 ,for parallel rays along the axis this reduces to the requirement that the sines of the angles of emergence shall be proportional to the respective distances of the incident rays from the axis4 ,fraunhofer's objective1 of which ,fig4 #ed;a is an example worked by modern formul for the sine condition1 gives very exact corrections over a field of #b-c when the glasses are suitably chosen and hence is invaluable for any work requiring a wide angle of view4 ,with certain combinations of glasses the coma-free condition may be combined successfully with ,clairault's1 although ordinarily the coma-free form falls between the two forms clear of spherical aberration1 as in ,fig4 #eb1 b1 which has its oblique rays well compensated but retains serious axial faults4 ,illustration3 ,,fig4 #ed4--,the ,fraunhofer ,types4 ,fraunhofer's objective has for all advantageous combinations of glasses the front radius of the flint longer than the rear radius of the crown hence the two must be separated by spacers at the edge1 which in small lenses in simple cells is slightly inconvenient4 ,however1 the common attempt to simplify mounting by making the front flint radius the shorter almost invariably violates the sine condition and reduces the sharp field1 fortunately not a very serious matter for most astronomical work4 ,the only material objection to the ,fraunhofer type is the strong curvature of the rear radius of the crown which gives a form somewhat susceptible to flexure in large objectives4 ,this is met in the flint-ahead form1 developed essentially by ,steinheil1 and used in most of the objectives of his famous firm4 ,fig4 #ed;b shows the flint-ahead objective corresponding to ,fig4 #ed;a4 ,obviously its curves are mechanically rather resistant to flexure4#aa #aa ,it is interesting to note that in computing ,fig4 #ed;a for the sine condition1 the other root of the quadratic gave roughly the ,gaussian form of ,fig4 #ec4 ,illustration3 ,,fig4 #ee4--;,clark ,objective4 ,mechanical considerations are not unimportant in large objectives1 and ,fig4 #ee1 a highly useful form introduced by the ,clarks and used in recent years for all their big lenses1 is a case in point4 ,here there is an interval of about the proportion shown between the crown and flint components4 ,this secures effective ventilation allowing the lenses to come quickly to their steady temperature1 and enables the inner surfaces to be cleaned readily and freed of moisture4 ,optically it lessens the deviation from the sine condition otherwise practically inseparable from the equiconvex crown1 reduces the chromatic difference of spherical aberration1 and gives an easy way of controlling the color correction by slightly varying the separation of the lenses4 ,one further special case is worth noting1 that of annulling the spherical aberration for rays passing through the lens in both directions4 ,by proper choice of glass and curvatures this can be accomplished to a close approximation and the resulting form is shown in ,fig4 #ef4 ,the front of the crown is notably flat and the rear of the flint conspicuously curved1 the shape in fact being intermediate between ,figs4 #eb;b and #eb;c4 ,the type is useful in reading telescopes and the like1 and for some spectroscopic applications4 ,illustration3 ,,fig4 #ef4--;,corrected in ,both ,directions4 ,there are two well known forms of aberration not yet considered2 astigmatism and curvature of field4 ,the former is due to the fact that when the path of the rays is away from the axis1 as from an extended object1 those coming from a line radial to the axis1 and those from a line tangent to a circle about the axis1 do not come to the same focus4 ,the net result is that the axial and tangential elements are brought to focus in two coaxial surfaces touching at the axis and departing more and more widely from each other as they depart from it4 ,both surfaces have considerable curvature1 that for tangential lines being the sharper4 ,it is possible by suitable choice of glasses and their curvatures to bring both image surfaces together into an approximate plane for a moderate angular space about the axis without seriously damaging the corrections for chromatic and spherical aberration4 ,to do this generally requires at least three lenses1 and photographic objectives thus designed 7anastigmats7 may give a substantially flat field over a total angle of #ej to #fj with corrections perfect from the ordinary photographic standpoint4 ,if one demands the rigorous precision of corrections called for in astronomical work1 the possible angle is very much reduced4 ,few astrographic lenses cover more than a #aj or #ae field1 and the wider the relative aperture the harder it is to get an anastigmatically flat field free of material errors4 ,astigmatism is rarely noticeable in ordinary telescopes1 but is sometimes conspicuous in eyepieces4 ,curvature of field results from the tendency of oblique rays in objectives1 otherwise well corrected1 to come to shorter focus than axial rays1 from their more considerable refraction resulting from greatly increased angles of incidence4 ,this applies to both the astigmatic image surfaces1 which are concave toward the objective in all ordinary cases4 ,fortunately both these faults are negligible near the axis4 ,they are both proportional to tanu_/f where u is the obliquity to the axis and f the focal length2 turn up with serious effect in wide angled lenses such as are used in photography1 but may generally be forgotten in telescopes of the ordinary ,f ratios1 like ,f_/#ab to ,f_/#af4 ,so also one may commonly forget a group of residual aberrations of higher orders1 but below about ,f_/#h look out for trouble4 ,objectives of wider aperture require a very careful choice of special glasses or the sub-division of the curvatures by the use of three or more lenses instead of two4 ,fig4 #eg shows a cemented triplet of ,steinheil's design1 with a crown lens between two flints4 ,such triplets are made up to about #d inches diameter and of apertures ranging from ,f_/#d to ,f_/#e4 ,illustration3 ,,fig4 #eg4--,steinheil ,triple ,objective4 ,illustration3 ,,fig4 #eh4--,tolles ,quadruple ,objective4 ,in cases of demand for extreme relative aperture1 objectives composed of four cemented elements have now and then been produced4 ,an example is shown in ,fig4 #eh1 a four-part objective of #a inch aperture made by ,tolles years ago for a small hand telescope4 ,its performance1 although it worked at ,f_/#d1 was reported to be excellent even up to #ge diameters4 ,the main difficulty with these objectives of high aperture is the relatively great curvature of field due to short focal length which prevents full utilization of the improved corrections off the axis4 ,distortion is similarly due to the fact that magnification is not quite the same for rays passing at different distances from the axis4 ,it varies in general with the cube of the distance from the axis1 and is usually negligible save in photographic telescopes1 ordinary visual fields being too small to show it conspicuously4 ,distortion is most readily avoided by adopting the form of a symmetrical doublet of at least four lenses as in common photographic use4 ,no simple achromatic pair gives a field wholly free of distortion and also of the ordinary aberrations1 except very near the axis1 and in measuring plates taken with such simple objectives corrections for distortion are generally required4 ,at times it becomes necessary to depart somewhat from the objective form which theoretically gives the least aberrations in order to meet some specific requirement4 ,luckily one may modify the ratios of the curves very perceptibly without serious results4 ,the aberrations produced come on gradually and not by jumps4 ,illustration3 ,,fig4 #ei4--8;,bent0 ,objective4 ,a case in point is that of the so-called 8bent0 objective in which the curvatures are all changed symmetrically1 as if one had put his fingers on the periphery and his thumbs on the centre of the whole affair1 and had sprung it noticeably one way or the other4 ,the corrections in general are slightly deteriorated but the field may be in effect materially flattened and improved4 ,an extreme case is the photographic landscape lens4 ,figure #ei is an actual example from a telescope where low power and very large angular view were required4 ,the objective was first designed from carefully chosen glass to meet accurately the sine condition4 ,even so the field1 which covered an apparent angle of fully #dj1 fell off seriously at the edge4 ,bearing in mind the rest of the system1 the objective was then 8bent0 into the form given by the dotted lines1 and the telescope then showed beautiful definition clear to the periphery of the field1 without any visible loss in the centre4 ,this spurious flattening cannot be pushed far without getting into trouble for it does not cure the astigmatic difference of focus1 but it is sometimes very useful4 ,practically curvature of field is an outstanding error that cannot be remedied in objectives required to stand high magnifying powers1 except by going to the anastigmatic forms similar to those used in photography4#ab #ab ,the curvature of the image is the thing which sets a limit to shortening the relative focus1 as already noted1 for the astigmatic image surfaces as we have seen1 fall rapidly apart away from the axis1 and both curvatures are considerable4 ,the tangential is the greater1 corresponding roughly to a radius notably less than the focal length1 while the radial fits a radius of less than this length with all ordinary glasses1 given forms correcting the ordinary aberrations4 ,the curves are concave towards the objective except in 8anastigmats0 and some objectives having bad aberrations otherwise4 ,their approximate curvatures assuming a semiangular aperture for an achromatic objective not over say #e1 have been shown to be1 to focus unity r #a 7#a_/7-77_/n - _/n771 and t #c #a_/7-77_/n - _/n7 r and t being the respective reciprocals of the radii4 ,the surfaces are really somewhat egg shaped rather than spherical as one departs from the axis4 ,aside from curvature the chief residual error in objectives is imperfection of achromatism4 ,this arises from the fact that crown and flint glasses do not disperse the various colors quite in the same ratio4 ,the crown gives slightly disproportionate importance to the red end of the spectrum1 the flint to the violet end--the so-called 8irrationality of dispersion40 ,hence if a pair of lenses match up accurately for two chosen colors like those represented by the ,c and ,f lines1 they will fail of mutual compensation elsewhere4 ,figure #fj shows the situation4 ,here the spectra from crown and flint glasses are brought to exactly the same extent between the ,c and ,f lines1 which serve as landmarks4 ,clearly if two prisms or lenses are thus adjusted to the same refractions for ,c and ,f1 the light passing through the combination will still be slightly colored in virtue of the differences elsewhere in the spectrum4 ,these residual color differences produce what is known as the 8secondary spectrum40 ,what this does in the case of an achromatic lens may be clearly seen from the figure2 ,c and ,f having exactly the same refractions in the flint and crown1 come to the same focus4 ,for ,d1 the yellow line of sodium1 the flint lens refracts a shade the less1 hence is not quite powerful enough to balance the crown1 which therefore brings ,d to a focus a little shorter than ,c and ,f4 ,on the other hand for ,a and ,g1 the flint refracts a bit more than the crown1 overbalances it and brings these red and violet rays to a focus a little longer than the joint ,c and ,f focus4 ,illustration3 ,,fig4 #fj4--;,irrationality of ,dispersion4 ,the difference for ,d is quite small1 roughly about #a_/bjjj of the focal length1 while the red runs long by nearly three times that amount1 the violet by about four4 ,towards the ,h line the difference increases rapidly and in large telescopes the actual range of focus for the various colors amounts to several inches4 ,this difficulty cannot be avoided by any choice among ordinary pairs of glasses1 which are nearly alike in the matter of secondary spectrum4 ,in the latter part of the last century determined efforts were made to produce glasses that would give more nearly an equal run of dispersion1 at first by ,english experimenters1 and then with final success by ,schott and ,abb at ,jena4 ,both crown and flint had to be quite abnormal in composition1 especially the latter1 and the pair were of very nearly the same refractive index and with small difference in the quantity which we have seen determines the general amount of curvature4 ,moreover it proved to be extremely hard to get the crown quite homogeneous and it is listed by ,schott with the reservation that it is not free from bubbles and stri4 ,nevertheless the new glasses reduce the secondary spectrum greatly1 to about of its ordinary value1 in the average4 ,it is difficult to get rid of the spherical aberration1 however1 from the sharp curves required and the small difference between the glasses1 and it seems to be impracticable on this account to go to greater aperture than about ,f_/#bj4 ,figure #fa shows the deeply curved form necessary even at half the relative aperture usable with common glasses4 ,at ,f_/#bj the secondary spectrum from the latter is not conspicuous and ,roe 7,pop4 ,ast4 #ah1 #aic71 testing side by side a small ,steinheil of the new glasses1 and a ,clark of the old1 of almost identical size and focal ratio1 found no difference in their practical performance4 ,another attack on the same problem was more successfully made by ,h4 ,d4 ,taylor4 ,realizing the difficulty found with a doublet objective of even the best matched of the new glasses1 he adopted the plan of getting a flint of exactly the right dispersion by averaging the dispersions of a properly selected pair of flints formed into lenses of the appropriate relative curvatures4 ,illustration3 ,,fig4 #fa4--;,apochromatic ,doublet4 ,illustration3 ,,fig4 #fb4--;,apochromatic ,triplet4 ,the resulting form of objective is made1 especially1 by ,cooke of ,york1 and also by ,continental makers1 and carries the name of 8photo-visual0 since the exactness of corrections is carried well into the violet1 so that one can see and photograph at the same focus4 ,the residual chromatic error is very small1 not above #a_/h to #a_/aj the ordinary secondary spectrum4 ,by this construction it is practicable to increase the aperture to ,f_/#ab or ,f_/#aj while still retaining moderate curvatures and reducing the residual spherical aberration4 ,there are a round dozen triplet forms possible1 of which the best1 adopted by ,taylor1 is shown in ,fig4 #fb4 ,it has the duplex flint ahead--first a baryta light flint1 then a borosilicate flint1 and to the rear a special light crown4 ,the two latter glasses have been under some suspicion as to permanence1 but the difficulty has of late years been reported as remedied4 ,be that as it may1 neither doublets nor triplets with reduced secondary spectrum have come into any large use for astronomical purposes4 ,their increased cost is considerable1#ac their aperture even in the triplet1 rather small for astrophotography1 and their achromatism is still lacking the perfection reached by a mirror4 #ac ,the doublet costs about one and a half times1 and the triplet more than twice the price of an ordinary achromatic of the same aperture4 ,the matter of achromatism is further complicated by the fact that objectives are usually over-achromatized to compensate for the chromatic errors in the eyepiece1 and especially in the eye4 ,as a general rule an outstanding error in any part of an optical system can be more or less perfectly balanced by an opposite error anywhere else in the system--the particular point chosen being a matter of convenience with respect to other corrections4 ,the eye being quite uncorrected for color the image produced even by a reflector is likely to show a colored fringe if at all bright1 the more conspicuous as the relative aperture of the pupil increases4 ,for low power eyepieces the emerging ray may quite fill a wide pupil and then the chromatic error is troublesome4 ,hence it has been the custom of skilled opticians1 from the time of ,fraunhofer1 who probably started the practice1 to overdo the correction of the objective just a little to balance the fault of the eye4 ,what actually happens is shown in ,fig4 #fc1 which gives the results of achromatization as practiced by some of the world's adepts4 ,the shortest focus is in the yellow green1 not far from the line ,d4 ,the longest is in the violet1 and ,f1 instead of coinciding in focus with ,c as it is conventionally supposed to do1 actually coincides with the deep and faint red near the line marked ,b4 ,hence the visible effect is to lengthen the focus for blue enough to make up for the tendency of the eye in the other direction4 ,the resulting image then should show no conspicuous rim of red or blue4 ,the actual adjustment of the color correction is almost wholly a matter of skilled judgment but ,fig4 #fc shows that of the great makers to be quite uniform4 ,the smallest overcorrection is found in the ,grubb objective1 the largest in the ,fraunhofer4 ,the differences seem to be due mainly to individual variations of opinion as to what diameter of pupil should be taken as typical for the eye4 ,the common practice is to get the best possible adjustment for a fairly high power1 corresponding to a beam hardly #a_/fd inch in diameter entering the pupil4 ,in any case the bigger the pencil of rays utilized by the eye1 i4e41 the lower the power1 the more overcorrection must be provided1 so that telescopes intended1 like comet seekers1 for regular use with low powers must be designed accordingly1 either as respects objective or ocular4 ,illustration3 ,,fig4 #fc4--;,achromatization ,curves by ,various ,makers4 #a4 ,fraunhofer #b4 ,clark #c4 ,steinheil #d4 ,hastings-,brashear #e4 ,grubb ,the differences concerned in this chromatic correction for power are by no means negligible in observing1 and an objective actually conforming to the ,c to ,f correction assumed in tables of optical glass would produce a decidedly unpleasant impression when used with various powers on bright objects4 ,and the values for implied in the actual color correction are not immaterial in computing the best form for a proposed objective4 #a is from ,franunhofer's own hands1 the instrument of #i4f inches aperture and #agj inches focus in the ,berlin ,observatory4 #b ,the ,clark refractor of the ,lowell ,observatory1 #bd inches aperture and #chf inches focal length4 ,this is of the usual ,clark form1 crown ahead1 with lenses separated by about of their diameter4 #c is a ,steinheil refractor at ,potsdam of #e4c inches aperture1 and #he inches focus4 #d is from the fine equatorial at ,johns ,hopkins ,university1 designed by ,professor ,hastings and executed by ,brashear4 ,the objective was designed with special reference to minimizing the spherical aberration not only for one chosen wave length but for all others1 has the flint lens ahead1 aperture #i4d inches1 focal length #adb inches1 and the lenses separated by inch in the final adjustment of the corrections4 #e is from the ,potsdam equatorial by ,grubb1 #h4e inches aperture #abd inches focus4 ,the great similarity of the color curves is evident at a glance1 the differences due to variations in the glass being on the whole much less significant than those resulting from the adjustment for power4 ,really very little can be done to the color correction without going to the new special glasses1 the use of which involves other difficulties1 and leaves the matter of adjustment for power quite in the air1 to be brought down by special eye pieces4 ,now and then a melting of glass has a run of dispersion somewhat more favorable than usual1 but there is small chance of getting large discs of special characteristics1 and the maker has to take his chance1 minute differences in chromatic quality being far less important than uniformity and good annealing4 ,regarding the aberrations of mirrors something has been said in ,chap4 ,i1 but it may be well here to show the practical side of the matter by a few simple illustrations4 ,figure #fd shows the simplest form of concave mirror--a spherical surface1 in this instance of #ij aperture1 the better to show its properties4 ,if light proceeded radially outward from ,c1 the center of curvature of the surface1 evidently any ray would strike the surface perpendicularly as at a and would be turned squarely back upon itself1 passing again through the center of curvature as indicated in the figure4 ,a ray1 however1 proceeding parallel to the axis and striking the surface as at bb will be deflected by twice the angle of incidence as is the case with all reflected rays4 ,but this angle is measured by the radius ,cb from the center of curvature and the reflected ray makes an angle ,cb,f with the radius1 equal to ,f,cb4 ,for points very near the axis b,f1 therefore1 equals ,,fc1 and substantially also equals c,f4 ,thus rays near the axis and parallel to it meet at ,f the focus half1 way from c to ,c4 ,the equivalent focal length of a spherical concave mirror of small aperture is therefore half its radius of curvature4 ,illustration3 ,,fig4 #fd4--,reflection from ,concave ,spherical ,mirror4 ,but obviously for large angles of incidence these convenient equalities do not hold4 ,as the upper half of the figure shows1 the ray parallel to the axis and incident on the mirror #de away at e is turned straight down1 for it falls upon a surface inclined to it by #de and is therefore deflected by #ij1 cutting the axis far inside the nominal focus1 at d4 ,following up other rays nearer the axis it appears that there is no longer a focal point but a cusp-like focal surface1 known to geometrical optics as a caustic and permitting no well defined image4 ,a paraboloidal reflecting surface as in ,fig4 #fe has the property of bringing to a single point focus all rays parallel to its axis while quite failing of uniting rays proceeding from any point on its axis1 since its curvature is changing all the way out from vertex to periphery4 ,here the parallel rays a1 a1 a1 a meeting the surface are reflected to the focus ,f1 while in a perfectly symmetrical way the prolongation of these rays a1 a1 a1 a if incident on the convex surface of the paraboloid would be reflected in ,r1 ,r1 ,r ,r just as if they proceeded from the same focus ,f4 ,the difference between the spherical and parabolic curves is well shown in ,fig4 #ff4 ,here are sections of the former1 and in dotted lines of the latter4 ,the difference points the moral4 ,the parabola falls away toward the periphery and hence pushes outward the marginal rays4 ,but it is of relatively sharper curvature near the center and pulls in the central to meet the marginal portion4 ,in the actual construction of parabolic mirrors one always starts with a sphere which is easy to test for precision of figure at its center of curvature4 ,then the surface may be modified into a paraboloid lessening the curvature towards the periphery1 or by increasing the curvature toward the center starting in this case with a sphere of a bit longer radius as in ,fig4 #ff;a4 ,illustration3 ,,fig4 #fe4--,reflection from ,paraboloid4 ,illustration3 ,,fig4 #ff;a4 ,,fig4 #ff;b4 ,variation of ,paraboloid from ,sphere4 ,practice differs in this respect1 either process leading to the same result4 ,in any case the departure from the spherical curve is very slight--a few hundred thousandths or at most ten thousandths of an inch depending on the size and relative focus of the mirror4 ,yet this small variation makes all the difference between admirable and hopelessly bad definition4 ,however the work is done it is guided by frequent testing1 until the performance shows that a truly parabolic figure has been reached4 ,its attainment is a matter of skilled judgment and experience4 ,the weak point of the parabolic mirror is in dealing with rays coming in parallel but oblique to the axis4 ,figure #fg shows the situation plainly enough4 ,the reflected rays a1 a no longer meet in a point at the focus ,f but inside the focus for parallel rays1 at f forming a surface of aberration4 ,the practical effect is that the image rapidly deteriorates as the star passes away from the axis1 taking on an oval character that suggests a bad case of astigmatism with serious complications from coma1 which in fact is substantially the case4 ,illustration3 ,,fig4 #fg4--;,aberration of ,parabolic ,mirror4 ,even when the angular aperture is very small the focal surface is nevertheless a sphere of radius equal to one half the focal length1 and the aberrations off the axis increase approximately as the square of the relative aperture1 and directly as the angular distance from the axis4 ,the even tolerably sharp field of the mirror is therefore generally small1 rarely over #cj of arc as mirrors are customarily proportioned4 ,at the relative aperture usual with refractors1 say ,f_/#ae1 the sharp fields of the two are quite comparable in extent4 ,the most effective help for the usual aberrations#ad of the mirror is the adoption of the ,cassegrain form1 by all odds the most convenient for large instruments1 with a hyperboloid secondary mirror4 #ad ,a very useful treatment of the aberrations of parabolic mirrors by ,poor is in ,ap4 ,j4 #g1 #aad4 ,in this is given a table of the maximum dimension of a star disc off the axis in reflectors of various apertures4 ,this table condenses to the closely approximate formula a lld_/f where a is the aberrational diameter of the star disc1 in seconds of arc1 d the distance from the axis in minutes of arc1 f the denominator of the ,f ratio 7,f_/#h c47 and #aa1 a constant4 ,obviously the separating power of a telescope 7see ,chap4 ,x7 being substantially #d4ef_/;,d where ,d is the diameter of objective or mirror in inches1 the separating power will be impaired when a #d4ef_/;,d4 ,in the photographic case the critical quantity is not #d4ef_/;,d1 but the maximum image diameter tolerable for the purpose in hand4 mirror is the adoption of the ,cassegrain form1 by all odds the most convenient for large instruments1 with a hyperboloidal secondary mirror4 ,the hyperboloid is a curve of very interesting optical properties4 ,just as a spherical mirror returns again rays proceeding from its center of curvature without aberration1 and the paraboloid sends from its focus a parallel axial beam free of aberration1 or returns such a beam to an exact focus again1 so a hyperboloid1 ,fig4 #fh1 sends out a divergent beam free from aberration or brings it1 returning1 to an exact focus4 ,such a beam a1 a1 a1 in fact behaves as if it came from and returned to a virtual conjugate focus ,f on the other side of the hyperbolic surface4 ,and if the convex side be reflecting1 converging rays ,r1 ,r1 ,r1 falling upon it at ,p1 ,p1 ,p1 as if headed for the virtual focus ,f1 will actually be reflected to ,f1 now a real focus4 ,this surface being convex its aberrations off the axis are of opposite sign to those due to a concave surface1 and can in part at least1 be made to compensate the aberrations of a parabolic main mirror4 ,the rationale of the operation appears from comparison of ,figs4 #fg and #fh4 ,illustration3 ,,fig4 #fh4--,reflection from ,hyperboloid4 ,in the former the oblique rays a1 a are pitched too sharply down4 ,when reflected from the convex surface of ,fig4 #fh as a converging beam along ,r1 ,r1 ,r1 they can nevertheless1 if the hyperbola be properly proportioned1 be brought down to focus at ,f conjugate to ,f1 their approximate mutual point of convergence4 ,evidently1 however1 this compensation cannot be complete over a wide angle1 when ,f spreads into a surface1 and the net result is that while the total aberrations are materially reduced there is some residual coma together with some increase of curvature of field1 and distortion4 ,here just as in the parabolizing of the large speculum the construction is substantially empirical1 guided in the case of a skilled operator by a sort of insight derived from experience4 ,starting from a substantially spherical convexity of very nearly the required curvature the figure is gradually modified as in the earlier example until test with the truly parabolic mirror shows a flawless image for the combination4 ,the truth is that no conic surface of revolution save the sphere can be ground to true figure by any rigorous geometrical method4 ,the result must depend on the skill with which one by machine or hand can gauge minute departures from the sphere4 ,attempts have been made by the late ,professor ,schwarzchild and others to improve the corrections of reflectors so as to increase the field but they demand either very difficult curvatures imposed on both mirrors1 or the interposition of lenses1 and have thus far reached no practical result4 ,,references ,,schwarzchild3 ,untersuchungen #b1 ,geom41 ,opt4 ,,ii4 ,,sampson ,observatory #cf1 #bdh4 ,,coddington3 8,reflexion and ,refraction of ,light40 ,,herschel3 8,light40 ,,taylor3 8,applied ,optics40 ,,southall3 8,geometrical ,optics40 ,,martin3 ,ann4 ,sci4 de l',ecole ,normale1 #ahgg1 ,supplement4 ,,moser3 ,zeit4 f4 ,instrumentenkunde1 #ahhg4 ,,harting3 ,zeit4 f4 ,inst41 #ahii4 ,,harting3 ,zeit4 f4 ,inst41 #ahih4 ,,von ,,hoegh3 ,zeit4 f4 ,inst41 #ahii4 ,,steinheil ,,voit3 8,applied ,optics40 ,,collected ,,researches1 ,national ,physical ,laboratory1 ,vol4 #ad4 ,,gleichen3 8,lehrbuch d4 ,geometrische ,optik40 ,,note4--,in dealing with optical formul look out for the algebraic signs4 ,writers vary in their conventions regarding them and it sometimes is as difficult to learn how to apply a formula as to derive it from the start4 ,also1 especially in optical patents1 look out for camouflage1 as omitting to specify an optical constant1 giving examples involving glasses not produced by any manufacturer1 and even specifying curves leading to absurd properties4 ,it is a good idea to check up the achromatization and focal length before getting too trustful of a numerical design4 ,,chapter ,v ,,mountings ,a steady and convenient mounting is just as necessary to the successful use of the telescope as is a good objective4 ,no satisfactory observations for any purpose can be made with a telescope unsteadily mounted and not provided with adjustments enabling it to be moved smoothly and easily in following a celestial object4 ,broadly1 telescope mounts may be divided into two general classes1 alt-azimuth and equatorial4 ,the former class is1 as its name suggests1 arranged to be turned in azimuth about a vertical axis1 and in altitude about a horizontal axis4 ,such a mounting may be made of extreme simplicity1 but obviously it requires two motions in order to follow up any object in the field1 for the apparent motion of the heavenly bodies is in circles about the celestial pole as an axis1 and consequently inclined from the vertical by the latitude of the place of observation4 ,pointing a telescope with motions about a vertical and horizontal axis only1 therefore means that1 as a star moves in its apparent path1 it will drift away from the telescope both in azimuth and in altitude1 and require to be followed by a double motion4 ,alt-azimuth mounts may be divided into three general groups according to their construction4 ,the first and simplest of them is the pillar-and-claw stand shown in ,figure #fi4 ,this consists of a vertical pillar supported on a strong tripod1 usually of brass or iron1 and provided at its top with a long conical bearing carrying at its upper extremity a hinged joint1 bearing a bar to which the telescope is screwed as shown in the illustration4 ,if properly made the upper joint comprises a circular plate carrying the bar and held between two cheek pieces with means for taking up wear1 and providing just enough friction to permit of easy adjustment of the telescope1 which can be swung in altitude from near the zenith to the horizon or below1 and turned around its vertical axis in any direction4 ,when well made a stand of this kind is steady and smooth working1 readily capable of carrying a telescope up to about #c inches aperture4 ,it needs for its proper use a firm sub-support for the three strong hinged legs of the pillar4 ,this is conveniently made as a very solid stool with spreading legs1 or a plank of sufficient size may be firmly bolted to a well set post4 ,illustration3 ,,fig4 #fi4--,table ,mount with ,slow ,motion4 ,thus arranged the mount is a very serviceable one for small instruments4 ,its stability1 however1 depends on the base upon which it is set4 ,the writer once unwisely attempted to gain convenience by removing the legs of the stand and screwing its body firmly upon a very substantial tripod4 ,the result was a complete failure in steadiness1 owing to the rather long lever arm furnished by the height of the pillar2 and the instrument1 which had been admirably steady originally1 vibrated abominably when touched for focussing4 ,the particular stand here shown is furnished with a rack motion in altitude which is a considerable convenience in following4 ,more rarely adjustable steadying rods attached to the objective end of the instrument are brought down to its base1 but for a telescope large enough to require this a better mount is generally desirable4 ,now and then an alt-azimuth head of just the sort used in the pillar-and-claw stand is actually fitted on a tall tripod1 but such an arrangement is usually found only in cheap instruments and for such tripod mountings other fittings are desirable4 ,illustration3 ,,fig4 #gj4--;,alt-azimuth ,mount1 ,clark ,type ,t4 ,the second form of alt-azimuth mount1 is altogether of more substantial construction4 ,the vertical axis1 usually tapered and carefully ground in its bearings1 carries an oblique fork in which the telescope tube is carried on trunnions for its vertical motion4 ,the inclination of the forked head enables the telescope to be pointed directly toward the zenith and the whole mount forms the head of a well made tripod4 ,figure #gj shows an excellent type of this form of mount as used for the ,clark ,type ,t telescope1 designed for both terrestrial and astronomical observation4 ,in this particular arrangement the telescope lies in an aluminum cradle carried on the trunnions1 from which it can be readily removed by loosening the thumb screws and opening the cradle4 ,illustration3 ,,fig4 #ga4--;,alt-azimuth with ,full ,slow ,motions4 ,it can also be set longitudinally for balance in the cradle if any attachments are to be placed upon either end4 ,here the adjustment for the height of the instrument is provided both in the spread of the tripod and in the adjustable legs4 ,so mounted a telescope of #c or #d inches aperture is easily handled and capable of rendering very good service either for terrestrial or celestial work4 ,indeed the ,clarks have made instruments up to #f inches aperture1 mounted for special service in this simple manner4 ,for celestial use where fairly high powers may be required this or any similar mount can be readily furnished with slow motions either in azimuth or altitude or both4 ,figure #ga shows a #d inch telescope and mount by ,zeiss thus equipped4 ,some alt-azimuth mounts are also provided with a vertical rack motion to bring the telescope to a convenient height without disturbing the tripod4 ,a good alt-azimuth mount such as is shown in ,figs4 #gj and #ga is by no means to be despised for use with telescopes of #c or #d inch aperture4 ,the sole inconvenience to be considered is that of the two motions required in following4 ,with well fitted slow motions this is not really serious for ordinary observing with moderate powers1 for one can work very comfortably up to powers of #aej or #bjj diameters keeping the object easily in view2 but with the higher powers in which the field is very small1 only a few minutes of arc1 the double motion becomes rather a nuisance and it is extremely inconvenient even with low powers in sweeping for an object the place of which is not exactly known4 ,there are in fact two distinct kinds of following necessary in astronomical observations4 ,first1 the mere keeping of the object somewhere in the field1 and second1 holding it somewhat rigorously in position1 as in making close observations of detail or micrometrical measurements4 ,when this finer following is necessary the sooner one gets away from alt-azimuth mounts the better4 ,still another form of alt-azimuth mount is shown in ,fig4 #gb applied for a ,newtonian reflector of #f or #h inches aperture4 ,here the overhung fork carrying the tube on trunnions is supported on a stout fixed tripod1 to which it is pivoted at the front1 and it is provided at the rear with a firm bearing on a sector borne by the tripod4 ,at the front a rod with sliding coarse1 and screw fine1 adjustment provides the necessary motion in altitude4 ,the whole fork is swung about its pivot over the sector bearing by a cross screw turned by a rod with a universal joint4 ,this mount strongly suggests the original one of ,hadley1 ,fig4 #af1 and is most firm and serviceable4 ,a reflector thus mounted is remarkably convenient in that the eyepiece is always in a most accessible position1 the view always horizontal1 and the adjustments always within easy reach of the observer4 ,illustration3 ,,fig4 #gb4--;,alt-azimuth ,newtonian ,reflector4 ,whenever it is necessary to follow an object closely1 as in using a micrometer and some other auxiliaries1 the alt-azimuth mount is troublesome and some modification adjustable by a single motion1 preferably made automatic by clockwork1 becomes necessary4 ,the first step in this direction is a very simple one indeed4 ,suppose one were to tilt the azimuth axis so that it pointed to the celestial pole1 about which all the stars appear to revolve4 ,then evidently the telescope being once pointed1 a star could be followed merely by turning the tube about this tilted axis4 ,of course one could not easily reach some objects near the pole without1 perhaps1 fouling the mount1 but in general the sky is within reach and a single motion follows the star1 very easily if the original mount had a slow motion in azimuth4 ,this is in fact the simplest form of equatorial mount1 sometimes called parallactic4 ,figure #gc shows the principle applied to a small reflector4 ,an oblique block with its angle adjusted to the co-latitude of the place drops the vertical axis into line with the pole1 and the major part of the celestial vault is then within easy reach4 ,it may be regarded as the transition step from the alt-azimuth to the true equatorial4 ,it is rarely used for refractors1 and the first attempt at a real equatorial mount was in fact made by ,james ,short ,f4 ,r4 ,s4 in mounting some of his small ,gregorians4#ae ,as a matter of record this is shown1 from ,short's own paper before the ,royal ,society in #agdi1 in ,fig4 #gd4 #ae ,instruments with a polar axis were used by ,scheiner as early as #afbg2 by ,roemer about three quarters of a century later1 and previously had been employed1 using sights rather than telescopes1 by the ,chinese2 but these were far from being equatorials in the modern sense4 ,illustration3 ,,fig4 #gc4--,parallactic ,mount for ,reflector4 ,a glance shows a stand apparently most complicated1 but closer examination discloses that it is merely an equatorial on a table stand with a sweep in declination over a very wide arc1 and quite complete arrangements for setting to the exact latitude and azimuth4 ,the particular instrument shown was of #d inches aperture and about #ah inches long and was one of several produced by ,short at about this epoch4 ,illustration3 ,,fig4 #gd4--,short's ,equatorial ,mount4 ,in the instrument as shown there is first an azimuth circle ,a ,a supported on a base ,b ,b ,b ,b having levelling screws in the feet4 ,immediately under the azimuth circle is mounted a compass needle for approximate orientation1 and the circle is adjustable by a tangent screw ,c4 ,carried by the azimuth circle on a bearing supported by four pillars is a latitude circle ,d ,d for the adjustment of the polar axis1 with a slow motion screw ,e4 ,the latitude circle carries a right ascension circle ,f ,f1 with a slow motion ,g1 and this in turn carries on four pillars the declination circle ,h ,h1 and its axis adjustable by the slow motion ,k4 ,to this declination circle is secured the ,gregorian reflector ,l ,l which serves as the observing telescope4 ,all the circles are provided with verniers as well as slow motions4 ,and the instrument is1 so to speak1 a universal one for all the purposes of an equatorial1 and when the polar axis is set vertical equally adapted for use as a transit instrument1 theodolite1 azimuth instrument1 or level1 since the circles are provided with suitable levels4 ,this mount was really a very neat and complete piece of work for the purpose intended1 although scarcely suitable for mounting any but a small instrument4 ,a very similar construction was used later by ,ramsden for a small refractor4 ,it is obvious that the reach of the telescope when used as an equatorial is somewhat limited in the mount just described4 ,in modern constructions the telescope is so mounted that it may be turned readily to any part of the sky1 although often the polar axis must be swung through #ahj in order to pass freely from the extreme southern to the extreme northern heavens4 ,the two motions necessary are those in right ascension to follow the heavenly bodies in their apparent course1 and in declination to reach an object at any particular angular distance from the pole4 ,there are always provided adjustments in azimuth and for latitude over at least a small arc1 but these adjustments are altogether rudimentary as compared with the wide sweep given by ,short4 ,the fundamental construction of the equatorial involves two axes working at right angles positioned like a capital ,t4 ,the upright of the ,t is the polar axis1 fitted to a sleeve and bearing the cross of the ,t1 which is hollow and provides the bearing for the declination axis1 which again carries at right angles to itself the tube of the telescope4 ,when the sleeve which carries the upright of the ,t points to the pole the telescope tube can evidently be swung to cover an object at any altitude1 and can then be turned on its polar axis so as to follow that object in its apparent diurnal motion4 ,the front fork of a bicycle set at the proper angle with a cross axis replacing the handle bars has more than once done good service ,illustration3 ,,fig4 #ge4--,section of ,modern ,equatorial4 in an emergency4 ,figure #ge shows in section a modern equatorial mount for a medium sized telescope4 ,the mounting shown in ,fig4 #ge1 by ,zeiss1 is thoroughly typical of recent practice in instruments of moderate size4 ,the general form of this equatorial comes straight down to us from ,fraunhofer's mounting of the ,dorpat instrument4 ,it consists essentially of two axes crossed exactly at right angles4 ,p1 the polar axis1 is aligned exactly with the pole1 and is supported on a hollow iron pier provided at its top with the latitude block ,l to which the bearings of ,p are bolted4 ,d the declination axis supports the telescope tube ,t4 ,the tube is counterpoised as regards the polar axis by the weight a1 and as regards the declination axis by the weights b b4 ,at ,a1 the upper section of the pier can be set in exact azimuth by adjusting screws1 and at the base of the lower section the screws at ,b4 ,b4 allow some adjustment in latitude4 ,to such mere rudiments are the azimuth and altitude circles of ,short's mount reduced4 ,at the upper end of the polar axis is fitted the gear wheel g1 driven by a worm from the clockwork at ,c to follow the stars in their course4 ,at the lower end of the same axis is the hour circle h1 graduated for right ascension1 and a hand wheel for quick adjustment in ,r4 ,a4 ,at d is the declination circle1 which is read1 and set1 by the telescope t with a right angled prism at its upper end1 which saves the observer from leaving the eye piece for small changes4 ,f is the usual finder1 which should be applied to every telescope of #c inches aperture and above4 ,it should be of low power1 with the largest practicable field1 and has commonly an aperture or that of the main objective1 big enough to pick up readily objects to be examined and by its coarse cross wires to bring them neatly into the field4 ,at m and n are the clamping screws for the right ascension and declination axes respectively1 while o and p control the respective tangent screws for fine adjustment in ,r4 ,a4 and ,dec4 after the axes are clamped4 ,this mount has really all the mechanical refinements needed in much larger instruments and represents the class of permanently mounted telescopes used in a fixed observatory4 ,the ordinary small telescope is provided with a mount of the same general type but much simpler and1 since it is not in a fixed observatory1 has more liberal adjustments in azimuth and altitude to provide for changes of location4 ,figure #gf shows in some detail the admirable portable equatorial mounting used by the ,clarks for instruments up to about #e or #f inches aperture4 ,five inches is practically the dividing line between portable and fixed telescopes4 ,in fact a #e inch telescope of standard construction with equatorial mounting is actually too heavy for practical portability on a tripod stand4 ,the ,clarks have turned out really portable instruments of this aperture1 of relatively short focus and with aluminum tube fitted to the mounting standard for a #d inch telescope1 but the ordinary #e inch equipment of the usual focal length deserves a permanent placement4 ,in this mount the short tapered polar axis ,p is socketed between the cheeks ,a1 and tightened in any required position by the hand screws ,b4 ,the stout declination axis ,d bears the telescope and the counterweight ,c4 ,setting circles in ,r4 ,a4 and ,dec41 p and d respectively1 are carried on the two axes1 and each axis has a worm wheel and tangent screw operated by a universal joint to give the necessary slow motion4 ,illustration3 ,,fig4 #gf4--;,clark ,adjustable ,equatorial ,mount4 ,the worm wheels carry their respective axes through friction bearings and the counter poising is so exact that the instrument can be quickly swung to any part of the sky and the slow motion picked up on the instant4 ,the wide sweep of the polar axis allows immediate conversion into an alt-azimuth for terrestrial use1 or adjustment for any latitude4 ,a graduated latitude arc is customarily engraved on one of the check pieces to facilitate this adjustment4 ,ordinarily portable equatorials on tripod mounts are not provided with circles1 and have only a single slow motion1 that in ,r4 ,a4 ,a declination circle1 however1 facilitates setting up the instrument accurately and is convenient for locating an object to be swept for in ,r4 ,a4 which must often be done if one has not sidereal time at hand4 ,in ,fig4 #gf a thumb screw underneath the tripod head unclamps the mount so that it may be at once adjusted in azimuth without shifting the tripod4 ,as a rule ,american stands for fixed equatorials have the clock drive enclosed in the hollow pillar which carries the equatorial head as shown in the reflector of ,fig4 #ce1 and in the ,clark mount for refractors of medium size shown in ,fig4 #gg4 ,here a neat quadrangular pillar carries an equatorial mounting in principle very much like ,fig4 #gf1 but big enough to carry telescopes of #h to #aj inches aperture4 ,it has universal adjustment in latitude1 so that it can be used in either hemisphere1 the clock and its driving weight are enclosed in the pillar and slow motions are provided for finding in ,r4 ,a4 and ,dec4 ,the adjustment in azimuth is made by moving the pillar on its base-plate1 which is bolted to the pier4 ,the convenient connections for accurate following and the powerful clock make the mount especially good for photographic telescopes of moderate size and the whole equipment is most convenient and workmanlike4 ,it is worth noting that the circles are provided with graduations that are plain rather than minute1 in accordance with modern practice4 ,in these days of celestial photography equatorials are seldom used for determining positions except with the micrometer1 and graduated circles therefore1 primarily used merely for finding1 should be1 above all things1 easy to read4 ,all portable mounts are merely simplifications of the observatory type of ,fig4 #ge1 which1 with the addition of various labor saving devices is applied to nearly all large refractors and to many reflectors as well4 ,there is a modified equatorial mount sometimes known as the 8,english0 equatorial in which the polar axis is long and supported on two piers differing enough in height to give the proper latitude angle1 the declination axis being about midway of the polar axis4 ,a bit of the sky is cut off by the taller pier1 and the type is not especially advantageous unless in supporting a very heavy instrument1 too heavy to be readily overhung in the usual way4 ,illustration3 ,,fig4 #gg4--,universal ,observatory ,mount 7,clark #i-;inch74 ,in such case some form of the 8,english0 mounting is very important to securing freedom from flexure and thereby the perfection of driving in ,r4 ,a4 so important to photographic work4 ,the #gb inch ,dominion ,observatory reflector and the #ajj inch ,hooker telescope at ,mt4 ,wilson are thus mounted1 the former on a counterpoised declination axis crosswise the polar axis1 the original 8,english0 type2 the latter on trunnions within a long closed fork which carries the polar bearings at its ends4 ,illustration3 ,,fig4 #gh4--;,english ,equatorial ,mount 7,hooker #ajj-;inch ,telescope74 ,figure #gh shows the latter instrument1 of #ajj inches clear aperture and of #db feet principal focal length1 increased to #ace feet when used as a ,cassegrainian4 ,it is the immense stability of this mount that has enabled it to carry the long cross girder bearing the interferometer recently used in measuring the diameters of the stars4 ,note the mercury-flotation drum at each end of the polar axis4 ,the mirrors were figured by the skillful hands of ,mr4 ,ritchey4 ,illustration3 ,,fig4 #gi4--;,english ,equatorial ,mount 7#gb-;inch ,dominion ,observatory ,telescope74 ,figure #gi gives in outline the proportions and mounting of the beautiful instrument in service at the ,dominion ,observatory1 near ,victoria1 ,b4 ,c4 ,the mirror and its auxiliaries were figured by ,brashear and the very elegant mounting was by ,warner and ,swasey4 ,the main mirror is of #cj feet principal focus4 ,the #bj inch hyperboloidal mirror extends the focus as a ,cassagrainian to #ajh feet4 ,the mechanical stability of these ,english mounts for very large instruments has been amply demonstrated by this1 as by the ,hooker #ajj inch reflector4 ,they suffer less from flexure than the ,fraunhofer mount where great weights are to be carried1 although the latter is more convenient and generally useful for instruments of moderate size4 ,it is hard to say too much of the mechanical skill that has made these two colossal telescopes so completely successful as instruments of research4 ,illustration3 ,,fig4 #hj4--;,astrographic ,mount with ,bent ,pier4 ,the inconvenience of having to swing the telescope tube to clear the pier at certain points in the ,r4 ,a4 following is often a serious nuisance in photographic work requiring long exposures1 and may waste valuable time in visual work4 ,several recent forms of equatorial mount have therefore been devised to allow the telescope complete freedom of revolution in ,r4 ,a41 swinging clear of everything4 ,one such form is shown in ,fig4 #hj which is a standard astrographic mount for a ,brashear doublet and guiding telescope4 ,the pier is strongly overhung in the direction of the polar axis far enough to allow the instrument to follow through for any required period1 even to resuming operations on another night without a shift of working position4 ,illustration3 ,,fig4 #ha4--,open ,fork ,mounting4 ,another form1 even simpler and found to be extremely satisfactory even for rather large instruments1 is the open polar fork mount4 ,here the polar axis of an ordinary form is continued by a wide and stiff casting in the form of a fork within which the tube is carried on substantial trunnions1 giving it complete freedom of motion4 ,the open fork mount in its simplest form1 carrying a heliostat mirror1 is shown in ,fig4 #ha4 ,here ,a is the fork1 ,b the polar axis1 carried on an adjustable sector for variation in latitude1 ,c the declination axis carrying the mirror ,d in its cell1 ,e the slow motion in declination1 and ,f that in ,r4 ,a4 ,both axes can be unclamped for quick motion and the ,r4 ,a4 axis can readily be driven by clock or electric motor4 ,the resemblance to the fully developed ,english equatorial mount of ,fig4 #gh is obvious1 but the present arrangement gives entirely free swing to a short instrument1 is conveniently adjustable1 and altogether workmanlike4 ,it can easily carry a short focus celestial camera up to #f or #h inches aperture or a reflector of #d or #e feet focal length4 ,in ,fig4 #agc1 ,chap4 ,x a pair of these same mounts are shown at ,harvard ,observatory4 ,the nearer one1 carrying a celestial camera1 is exposed to view4 ,it is provided with a slow motion and clamp in declination1 and with an electric drive in ,r4 ,a41 quickly unclamped for swinging the camera4 ,it works very smoothly1 its weight is taken by a very simple self adjusting thrust bearing at the lower end of the polar axis1 and altogether it is about the simplest and cheapest equatorial mount of first class quality that can be devised for carrying instruments of moderate length4 ,several others are in use at the ,harvard ,observatory and very similar ones of a larger growth carry the #bd inch ,newtonian reflector there used for stellar photography and the #af inch ,metcalf photographic doublet4 ,illustration3 ,,fig4 #hb4--,mounting of ,mt4 ,wilson #fj-;inch ,reflector4 ,illustration3 ,,fig4 #hc4--,the #fj-;inch as ,cassegrainian1 ,f #ajj4 ,in fact the open fork mount1 which was developed by the late ,dr4 ,common1 is very well suited to the mounting of big reflectors4 ,it was first adapted by him to his #c ft4 reflector and later used for his two #e ft4 mirrors1 and more recently for the #e ft4 instrument at ,mt4 ,wilson1 and a good many others of recent make4 ,dr4 ,common in order to secure the easiest possible motion in ,r4 ,a4 devised the plan of floating most of the weight assumed by the polar axis in mercury4 ,figure #hb is1 diagrammatically1 this fork mount as worked out by ,ritchey for the #e ,mt4 ,wilson reflector4 ,here ,a is the lattice tube1 ,b the polar axis1 ,c the fork and ,d the hollow steel drum which floats the axis in the mercury trough ,e4 ,the great mirror is here shown worked as a simple ,newtonian of #be ft4 focal length4 ,as a matter of fact it is used much of the time as a ,cassegranian4 ,to this end the upper section of tube carrying the oblique mirror is removed and a shorter tube carrying any one of three hyperboloidal mirrors is put in its place4 ,fig4 #hc is the normal arrangement for visual or photographic work on the long focus1 #ajj ft4 ,the dotted lines show the path of the rays and it will be noticed that the great mirror is not perforated as in the usual ,cassegrainian construction1 but that the rays are brought out by a diagonal flat4 ,figure #hd is a similar arrangement used for stellar spectroscopy with a small flat and an equivalent focus of #hj ft4 ,in ,fig4 #he a radically different scheme is carried out4 ,the hyperboloidal mirror now used gives an equivalent focus of #aej ft41 and the auxiliary flat is arranged to turn on an axis parallel to the declination axis so as to send the reflected beam down the hollow polar axis into a spectrograph vault below the southern end of the axis4 ,obviously one cannot work near the pole with this arrangement but only through some #ge as indicated by the dotted lines4 ,the fork mount is not at all universal for reflectors1 as has already been seen1 and ,cassegrainian of moderate size are very commonly mounted exactly like refractors4 ,illustration3 ,,fig4 #hd4--,the #fj-;inch as ,cassegrainian1 ,f #hj4 ,illustration3 ,,fig4 #he4--,the #fj-;inch as ,polar ,cassegrainian1 ,f #aej4 ,we now come to a group of mounts which have in common the fundamental idea of a fixed eyepiece1 and incidentally better protection of the observer against the rigors of long winter nights when the seeing may be at its best but the efficiency of the observer is greatly diminished by discomfort4 ,some of the arrangements are also of value in facilitating the use of long focus objectives and mirrors and escaping the cost of the large domes which otherwise would be required4 ,perhaps the earliest example of the class is found in ,caroline ,herschel's comet seeker1 shown in ,fig4 #hf4 ,this was a ,newtonian reflector of about #f inches aperture mounted in a fashion that is almost self explanatory4 ,it was1 like all ,herschel's telescopes1 an alt-azimuth but instead of being pivoted in altitude about the mirror or the center of gravity of the whole tube1 it was pivoted on the eyepiece location and the tube was counterbalanced as shown so that it could be very easily adjusted in altitude while the whole frame turned in azimuth about a vertical post4 ,thus the observer could stand or sit at ease sweeping in a vertical circle1 and merely had to move around the post as the azimuth was changed4 ,the arrangement is not without advantages1 and was many years later adopted with modifications of detail by ,dr4 ,j4 ,w4 ,draper for the famous instrument with which he advanced so notably the art of celestial photography4 ,the same fundamental idea of freeing the observer from continual climbing about to reach the eyepiece has been carried out in various equatorially mounted comet seekers4 ,a very good example of the type is a big comet seeker by ,zeiss1 shown in ,fig4 #hg4 ,the fundamental principle is that the ocular is at the intersection of the polar and declination axis1 the telescope tube being overhung well beyond the north end of the former and counterbalanced on the latter4 ,the observer can therefore sit in his swivel chair and without stirring from it sweep rapidly over a very wide expanse of sky4 ,this particular instrument is probably the largest of regular comet seekers1 #h inches in clear aperture and #eb inches focal length with a triple objective to ensure the necessary corrections in using so great a relative aperture4 ,in this figure #a is the base with corrections in altitude and azimuth1 #b the counterpoise of the whole telescope on its base1 #c the polar axis and ,r4 ,a4 circle1 #d the overhung declination axis and its circle1 #e the counterpoise in declination1 #f the polar counterpoise1 and #g the main telescope tube4 ,the handwheel shown merely operates the gear for revolving the dome without leaving the observing chair4 ,the next step beyond the eyepiece fixed in general position is so to locate it that the observer can be thoroughly protected without including the optical parts of the telescope in such wise as to injure their performance4 ,one cannot successfully observe through an open window on account of the air currents due to temperature differences1 and in an observatory dome1 unheated as it is1 must wait after the shutter is opened until the temperature is fairly steadied4 ,except for these comet seekers practically all of the class make use of one or two auxiliary reflections to bring the image into the required direction1 and in general the field of possible view is somewhat curtailed by the mounting4 ,this is less of a disadvantage than it would appear at first thought1 for1 to begin with1 observations within #bj of the horizon or thereabouts are generally unsatisfactory1 and the advantages of a stable and convenient long focus instrument are so notable as for many purposes quite to outweigh some loss of sky-space4 ,illustration3 ,,fig4 #hf4--;,caroline ,herschel's ,comet ,seeker4 ,the simplest of the fixed eyepiece group is the polar telescope of which the rudiments are well shown in ,fig4 #hh1 a mount described by ,sir ,howard ,grubb in #ahhj1 and an example of which was installed a little later in the ,crawford ,observatory in ,cork4 ,here the polar axis ,a is the main tube of the telescope1 and in front of the objective ,b1 is held in a fork the declination cradle and mirror ,c1 by which any object within a wide sweep of declination can be brought into the field and held there by hand or clockwork through rotating the polar tube4 ,illustration3 ,,fig4 #hg4--,mounting of ,large ,comet ,seeker4 ,looked at from another slant it is a polar heliostat1 of which the telescope forms the driving axis in ,r4 ,a4 ,the whole mount was a substantial casting on wheels which ran on a pair of rails4 ,for use the instrument was rolled to a specially arranged window and through it until over its regular bearings on a pier just outside4 ,a few turns of the wheel ,d lowered it upon these1 and the back of the frame then closed the opening in the wall leaving the instrument in the open1 and the eye end inside the room4 ,the example first built was of only #d inches aperture but proved its case admirably as a most useful and convenient instrument4 ,this mount with various others of the fixed eyepiece class may be regarded as derived from the horizontal photoheliographs used at the #ahgd transit of ,venus and subsequently at many total solar eclipses4 ,given an equatorially mounted heliostat like ,fig4 #ha and it is evident that the beam from it may be turned into a horizontal telescope placed in the meridian1 7or for that matter in any convenient direction7 and held there by rotation of the mirror in ,r4 ,a41 but also in declination1 save in the case where the beam travels along the extension of the polar axis4 ,illustration3 ,,fig4 #hh4--;,grubb's ,original ,polar ,telescope4 ,for the brief exposure periods originally needed and the slow variation of the sun in declination this heliostatic telescope was easily kept in adjustment4 ,the original instruments were of #e inches aperture and #dj ft4 focal length1 and the #g inch heliostat mirror was provided with ordinary equatorial clockwork4 ,set up with the telescope pointing along the polar axis no continuous variation in declination is needed and the clock drive holds the field steadily1 as in any other equatorial4 ,figure #hi shows diagrammatically the #ab inch polar telescope used for more than twenty years past at the ,harvard ,observatory4 ,the mount was designed by ,mr4 ,w4 ,p4 ,gerrish of the ,harvard staff and contains many ingenious features4 ,unlike ,fig4 #hh this is a fixed mount1 with the eye-end comfortably housed in a room on the second floor of the main observatory building1 and the lower bearing on a substantial pier to the southward4 ,illustration3 ,,fig4 #hi4--;,diagram of ,gerrish ,polar ,telescope4 ,in the figure1 ,a is the eye end1 ,b the main tube with the objective at its lower end and prolonged by a fork supported by the bearing ,c and ,d is the declination mirror sending the beam upward4 ,the whole is rotated in ,r4 ,a4 by an electric clock drive1 and all the necessary adjustments are made from the eye end4 ,a view of the exterior is shown in ,fig4 #ij1 with the mirror and objective uncovered4 ,the rocking arm at the objective end1 operated by a small winch beside the ocular1 swings clear both mirror and objective caps in a few seconds1 and the telescope is then ready for use4 ,its focal length is #af ft4 #aj inches and it gives a sweep in declination of approximately #hj4 ,it gives excellent definition and has proved a most useful instrument4 ,a second polar telescope was set up at the ,harvard ,observatory station in ,mandeville1 ,jamaica1 in the autumn of #aijj4 ,this was intended primarily for lunar photography and was provided with a #ab inch objective of #ace ft4 #d inches focal length and an #ah inch heliostat with electric clock drive4 ,illustration3 ,,fig4 #ij4--;,gerrish ,polar ,telescope1 ,harvard ,observatory4 ,inasmuch as all instruments of this class necessarily rotate the image as the mirror turns1 the tail-piece of this telescope is also mounted for rotation by a similar drive so that the image is stationary on the plate both in position and orientation4 ,as ,mandeville is in ,n4 lat4 #ah #ja the telescope is conveniently near the horizontal4 ,the observatory of ,yale ,university has a large instrument of this class1 of #ej feet focal length1 with a #ae-;inch photographic objective and a #aj-;inch visual guiding objective working together from the same heliostat4 ,despite its simplicity and convenience the polar telescope has an obvious defect in its very modest sweep in declination1 only to be increased by the use of an exceptionally large mirror4 ,it is not therefore remarkable that the first serious attempt at a fixed eyepiece instrument for general use turned to a different construction even at the cost of an additional reflection4 ,this was the equatorial coud devised by ,m4 ,loewy of the ,paris ,observatory in #ahhb4 7,fig4 #ia47 ,in the diagram ,a is the main tube which forms the polar axis1 and ,b the eye end under shelter1 with all accessories at the observer's hand4 ,but the tube is broken by the box casing ,c containing a mirror rigidly supported at #de to the axis of the main tube and of the side tube ,d1 which is counterbalanced and is in effect a hollow declination axis carrying the objective ,e at its outer end4 ,illustration3 ,,fig4 #ia4--;,diagram of ,equatorial ,coud4 ,in lieu of the telescope tube usually carried on this declination axis we have the #de mirror1 ,f1 turning in a sleeve concentric with the objective1 which1 having a lateral aperture1 virtually gives the objectives a full sweep in declination1 save as the upper pier cuts it off4 ,the whole instrument is clock driven in ,r4 ,a41 and has the usual circles and slow motions all handily manipulated from the eye end4 ,the equatorial coud is undeniably complicated and costly1 but as constructed by ,henry ,frres it actually performs admirably even under severe tests1 and has been several times duplicated in ,french observatories4 ,the first coud erected was of #aj inches aperture and was soon followed by one of #bc4f inches aperture and #ei ft4 focus1 which is the largest yet built4 ,still another mounting suggestive of both the polar telescope and the coud is due to ,sir ,howard ,grubb1 ,fig4 #ib4 ,here as in the coud the upper part of the polar axis1 ,a1 is the telescope tube which leads into a solid casing ,b1 about which a substantial fork1 ,c1 is pivoted4 ,this fork is the extension of the side tube ,d1 which carries the objective1 and thus has free swing in declination through an angle limited by the roof of the observing room above1 and the proximity of the horizon below4 ,its useful swing1 as in the polar telescope1 is limited by the dimensions of the mirror ,e1 which receives the cone of rays from the objective and turns it up the polar tube to the eyepiece4 ,this mirror is geared to turn at half the rate of the tube ,d so that the angle ,d ,e ,a is continually bisected4 ,illustration3 ,,fig4 #ib4--;,grubb ,modified ,coud4 ,in point of fact the sole gain in this construction is the reduction in the size of mirror required1 by reason of the diminished size of the cone of rays when it reaches the mirror4 ,the plan has been very successfully worked out in the fine astrographic telescope of the ,cambridge ,observatory of #ab inches aperture and #ai4c ft4 focal length4 ,as in the other instruments of this general class the adjustments are all conveniently made from the eye end4 ,the ,cambridge instrument has a triple photo-visual objective of the form designed by ,mr4 ,h4 ,d4 ,taylor and the side tube1 when not in use1 is turned down to the horizontal and covered in by a low wheeled housing carried on a track4 ,the sky space covered is from #ae above the pole to near the horizontal4 ,it is obvious that various polar and coud forms of reflector are quite practicable and indeed one such arrangement is shown in connection with the #fj inch ,mt4 ,wilson reflector1 but we are here concerned only with the chief types of mounting which have actually proved their usefulness4 ,none of the arrangements which require the use of additional large reflecting surfaces are exempt from danger of impaired definition4 ,only superlatively fine workmanship and skill in mounting can save them from distortion and astigmatism due to flexure and warping of the mirrors1 and such troubles have not infrequently been encountered4 ,to a somewhat variant type belong several valuable constructions which utilize in the auxiliary reflecting system the clostat rather than the polar heliostat or its equivalent4 ,the clostat is simply a plane mirror mounted with its plane fixed in that of a polar axis which rotates once in #dh hours1 i4e41 at half the apparent rate of the stars4 ,illustration3 ,,fig4 #ic4--;,diagram of ,snow ,horizontal ,telescope4 ,a telescope pointed at such a mirror will hold the stars motionless in its field as if the firmament were halted la ,joshua4 ,but if a change of view is wanted the telescope must be shifted in altitude or azimuth or both4 ,this is altogether inconvenient1 so that as a matter of practice a second plane mirror is used to turn the steady beam from the clostat into any desired direction4 ,by thus shifting the mirror instead of the telescope1 the latter can be permanently fixed in the most convenient location1 at the cost of some added expense and loss of light4 ,further1 the image does not rotate as in case of the polar heliostat1 which is often an advantage4 ,an admirable type of the fixed telescope thus constituted is the ,snow telescope at ,mt4 ,wilson 7,cont4 from the ,solar ,obs4 #b1 ,hale74 ,fig4 #ic from this paper shows the equipment in plan and elevation4 ,the topography of the mountain top made it desirable to lay out the axis of the building #ae ,e4 of ,n4 and sloping downward #e toward the ,n4 ,at the right hand end of the figure is shown the clostat pier1 #bi ft4 high at its ,s end4 ,this pier carries the clostat mirror proper1 #cj inches in diameter1 on rails a a accurately ,e4 and ,w4 to allow for sliding the instrument so that its field may clear the secondary mirror of #bd inches diameter which is on an alt-azimuth fork mounting and also slides on rails b b4 ,the telescope here is a pair of parabolic mirrors each of #bd inches aperture and of #fj ft4 and #ade ft4 focus respectively4 ,the beam from the secondary clostat mirror passes first through the spectrographic laboratory shown to the left of the main pier1 and in through a long and narrow shelter house to one of these mirrors2 the one of longest focus on longitudinal focussing rails e e1 the other on similar rails c c1 with provision for sliding sidewise at d to clear the way for the longer beam4 ,the ocular end of this remarkable telescope is the spectrographic laboratory where the beam can be turned into the permanently mounted instruments1 for the details of which the original paper should be consulted4 ,the purpose of this brief description is merely to show the beautiful facility with which a clostatic telescope may be adapted to astrophysical work4 ,obviously an objective could be put in the clostat beam for any purpose for which it might be desirable4 ,such in fact is the arrangement of the tower telescopes at the ,mt4 ,wilson ,observatory4 ,in these instruments we have the ordinary clostat arrangement turned on end for the sake of getting the chief optical parts well above the ground where1 removed from the heated surface1 the definition is generally improved4 ,to be sure the focus is at or near the ground level1 but the upward air currents cause much less disturbance than the crosswise ones in the ,snow telescope4 ,the head of the first tower telescope is shown in ,fig4 #id4af ,a is the clostat mirror proper #ag inches in diameter and #ab inches thick1 ,b the secondary mirror #ab inches in the shorter axis of the ellipse1 #bb inches in the longer1 and also #ab inches thick4 ,c is the #ab inch objective of #fj ft4 focus1 and ,d the focussing gear worked by a steel ribbon from below4 #af ,contributions from the ,solar ,obs4 #bc1 ,hale1 which should be seen for details4 ,illustration3 ,,fig4 #id4--;,head of #fj-;inch ,tower ,telescope4 ,this instrument being for solar research the mirrors are arranged for convenient working with the sun fairly low on either horizon where the definition is at its best1 and can be shifted accordingly1 to the same end as in the ,snow telescope4 ,there is also provision for shifting the objective laterally at a uniform rate from below1 to provide for the use of the apparatus as spectro-heliograph4 ,the tower is of the windmill type and proved to be fairly steady in spite of its height1 high winds being rare on ,mt4 ,wilson4 ,the great thickness of the mirrors in the effort to escape distortion deserves notice4 ,they actually proved to be too thick to give thermal conductivity sufficient to prevent distortion4 ,illustration3 ,,fig4 #ie4--,porter's ,polar ,reflector4 ,in the later #aej tower telescope the mirrors are relatively less thick1 and a very interesting modification has been introduced in the tower1 in that it consists of a lattice member for member within another exterior lattice1 so that the open structure is retained1 while each member that supports the optical parts is shielded from the wind and sudden temperature change by its corresponding outer sheath4 ,still another form of mounting to give the observer access to a fixed eyepiece under shelter is found in the ingenious polar reflector by ,mr4 ,russell ,w4 ,porter of which an example with main mirror of #af inches diameter and #ae ft4 #f inches focal length was erected by him a few years ago4 ,fig4 #ie is entirely descriptive of the arrangement which from ,mr4 ,porter's account seems to have worked extremely well4 ,the chief difficulty encountered was condensation of moisture on the mirrors1 which in some climates is very difficult to prevent4 ,illustration3 ,,fig4 #if4--;,diagram of ,hartness ,turret ,telescope4 ,it is interesting to note that ,mr4 ,porter's first plan was to use the instrument as a ,herschelian with its focus thrown below the siderostat at ,f1 but the tilting of the mirror1 which was worked at ,f_/#aa4f1 produced excessive astigmatism of the images1 and the plan was abandoned in favor of the ,newtonian form shown in the figure4 ,at ,f_/#be or thereabouts the earlier scheme would probably have succeeded well4 ,still another fixed eyepiece telescope of daring and successful design is the turret telescope of the ,hon4 ,j4 ,e4 ,hartness of which the inventor erected a fine example of #aj inch aperture at ,springfield1 ,vermont4 ,the telescope is in this case a refractor1 and the feature of the mount is that the polar axis is expanded into a turret within which the observer sits comfortably1 looking into the ocular which lies in the divided declination axis and is supplied from a reflecting prism in the main beam from the objective ,figure #if shows a diagram of the mount and observatory4 ,here a is the polar turret1 bb the bearings of the declination axis1 c the main tube1 d its support1 and e the ocular end4 ,optically the telescope is merely an ordinary refractor used with a right angled prism a little larger and further up the tube than usual4 ,the turret is entered in this instance from below1 through a tunnel from the inventor's residence4 ,the telescope as shown in ,fig4 #if has a #aj inch ,brashear objective of fine optical quality1 and the light is turned into the ocular tube by a right angled prism only #b inches in the face4 ,this is an entirely practicable size for a reflecting prism and the light lost is not materially in excess of that lost in the ordinary 8star diagonal0 so necessary for the observation of stars near the zenith in an ordinary equatorial4 ,the only obvious difficulty of the construction is the support of the very large polar axis4 ,being an accomplished mechanical engineer1 ,mr4 ,hartness worked out the details of this design very successfully although the moving parts weighed some #b tons4 ,the ocular is not absolutely fixed with reference to the observer but is always conveniently placed1 and the performance of the instrument is reported as excellent in every respect1 while the sheltering of the observer from the rigors of a ,vermont winter is altogether admirable4 ,figure #ig shows the complete observatory as it stands4 ,obviously the higher the latitude the easier is this particular construction1 which lends itself readily to large instruments and has the additional advantage of freeing the observer from the insect pests which are extremely troublesome in warm weather over a large part of the world4 ,this running account of mountings makes no claim at completeness4 ,it merely shows the devices in common use and some which point the way to further progress4 ,the main requirements in a mount are steadiness1 and smoothness of motion4 ,even an alt-azimuth mount with its need of two motions1 if smooth working and steady1 is preferable to a shaky and jerky equatorial4 ,remember that the ,herschels did immortal work without equatorial mountings1 and used high powers at that4 ,a clock driven equatorial is a great convenience and practically indispensable for the photographic work that makes so large a part of modern astronomy1 but for eye observations one gets on very fairly without the clock4 ,illustration3 ,,fig4 #ig4--;,hartness ,turret ,observatory from the ,n4 ,e4 ,circles arc a necessity in all but the small telescopes used on portable tripods1 otherwise much time will be wasted in finding4 ,in any event do not skimp on the finder1 which should be of ample aperture and wide field1 say the aperture of the main objective1 and #c to #e in field4 ,superior definition is needless1 light1 and sky room enough to locate objects quickly being the fundamental requisites4 ,as a final word see that all the adjustments are within easy reach from the eyepiece1 since an object once lost from a high power ocular often proves troublesome to locate again4 ,,references ,,chambers' ,astronomy1 ,vol4 ,,ii4 ,f4 ,l4 ,o4 ,,wadsworth3 ,ap4 ,j41 #e1 #acb4 ,ranyard's mounts for reflectors4 ,g4 ,w4 ,,ritchey3 ,ap4 ,j41 #e1 #adc4 ,supporting large specula4 ,g4 ,e4 ,,hale3 ,cont4 ,solar ,obs4 #b4 ,the 8,snow0 horizontal telescope4 ,g4 ,e4 ,,hale3 ,cont4 ,solar ,obs4 #bc4 ,the #fj ft4 tower telescope4 ,j4 ,w4 ,,draper3 ,smithsonian ,contrib4 #cd4 ,mounting of his large reflector4 ,g4 ,w4 ,,ritchey3 ,smithsonian ,contrib4 #ce4 ,mounting of the ,mt4 ,wilson #fj inch reflector4 ,,sir ,h4 ,,grubb3 ,tr4 ,roy4 ,dublin ,soc4 ,ser4 #b4 #c4 ,polar ,telescopes4 ,,sir ,r4 ,s4 ,,ball3 ,m4 ,n4 #ei1 #aeb4 ,photographic polar telescope4 ,a4 ,a4 ,,common3 ,mem4 ,r4 ,a4 ,s41 #df1 #agc4 ,mounting of his #c ft4 reflector4 ,r4 ,w4 ,,porter3 ,pop4 ,ast41 #bd1 #cjh4 ,polar reflecting telescope4 ,,james ,,hartness3 ,trans4 ,a4 ,s4 ,m4 ,e41 #aiaa1 ,turret ,telescope4 ,,sir ,,david ,,gill3 ,enc4 ,brit41 #aath ,ed4 ,telescope4 ,admirable summary of mounts4 ,,chapter ,,vi ,,eye ,,pieces ,the eyepiece of a telescope is merely an instrument for magnifying the image produced by the objective or mirror4 ,if one looks through a telescope without its eyepiece1 drawing the eye back from the focus to its ordinary distance of distinct vision1 the image is clearly seen as if suspended in air1 or it can be received on a bit of ground glass4 ,it appears larger or smaller than the object seen by the naked eye1 in proportion as the focal length of the objective is larger or smaller than the distance to which the eye has to drop back to see the image clearly4 ,this real image1 the quality of which depends on the exactness of correction of the objective or mirror1 is then to be magnified so much as may be desirable1 by the eyepiece of the instrument4 ,in broad terms1 then1 the eyepiece is a simple microscope applied to the image of an object instead of the object itself4 ,and looking at the matter in the simplest way the magnifying power of any simple lens depends on the focal length of that lens compared with the ordinary seeing distance of the eye4 ,if this be taken at #aj inches as it often conventionally is1 then a lens of #a inch focus brings clear vision down to an inch from the object1 increases the apparent angle covered by the object #aj times and hence gives a magnifying power of #aj4 ,but if the objective has a focal length of #ajj inches the image1 as we have just seen1 is already magnified #aj times as the naked eye sees it1 hence with an objective of #ajj inches focus and a #a inch eyepiece the total magnification is #ajj diameters4 ,and this expresses the general law1 for if we took the normal seeing distance of the naked eye at some other value than #aj inches1 say #ab inches then we should have to reckon the image as magnified by #h times so far as the objective inches is concerned1 but #ab times due to the #a inch eyepiece1 and so forth4 ,thus the magnifying power of any eyepiece is ,f_/f where ,f is the focal length of the objective or mirror and f that of the eyepiece4 ,the focal distance of the eye quite drops out of the reckoning4 ,all these facts appear very quickly if one explores the image from an objective with a slip of ground glass and a pocket lens4 ,an ordinary camera tells the same story4 ,a distant object which covers #a will cover on the ground glass #a reckoned on a radius equal to the focal length of the lens4 ,if this is equal to the ordinary distance of clear vision1 an eye at the same distance will see the image 7or the distant object7 covering the same #a4 ,the geometry of the situation is as follows3 ,let o ,fig4 #e1 ,chap4 #a1 be the objective4 ,this lens1 as in an ordinary camera1 forms an inverted image of an object ,a ,b at its focus1 as at a b1 and for any point1 as a1 of the image there is a corresponding point of the object lying on the straight line from ,a to that point through the center1 c1 of the objective4 ,a pair of rays #a1 #b1 diverging from the object point ,a pass through rim and center of o respectively and meet in ,a4 ,after crossing at this point they fall on the eye lens e1 and if a is nearly in the principal focus of e1 the rays #a and #b will emerge substantially parallel so that the eye will unite them to form a clear image4 ,now if ,f is the focal length of o1 and f that of a1 the object forming the image subtends at the center of the objective1 o1 an angle ,a c ,b1 and for a distant object this will be sensibly the angle under which the eye sees the same object4 ,if ,l is the half linear dimension of the image1 the eye sees half the object covering the angle whose tangent is ,l_/,f4 ,similarly half the image ab is seen through the eye lens e as covering a half angle whose tangent is ,l_/f4 ,since the magnifying power of the combination1 m1 is directly as the ratio of increase in this tangent of the visual angle1 which measures the image dimension m ,f_/f1 as before ,further1 as all the light which comes in parallel through the whole opening of the objective forms a single conical beam concentrating into a focus and then diverging to enter the eye lens1 the diameter of the cone coming through the eye lens must bear the same relation to the diameter of o1 that f does to ,f4 ,any less diameter of e will cut off part of the emerging light2 any more will show an emergent beam smaller than the eye lens1 which is generally the case4 ,hence if we call p the diameter of the bright pencil of light which we see coming through the eye lens then for that particular eye lens1 m o_/p ,that is1 f p,f_/o which is quite the easiest way of measuring the focal length of an eyepiece4 ,point the telescope toward the clear sky1 focusing for a distant object so that the emergent pencil is sharply defined at the ocular1 and then measure its diameter by the help of a fine scale and a pocket lens1 taking care that scale and emergent pencil are simultaneously in sharp focus and show no parallax as the eye is shifted a bit4 ,this bright circle of the emerging beam is actually the projection by the eye lens of the focal image of the objective aperture4 ,this method of measuring power is easy and rather accurate4 ,but it leads to trouble if the measured diameter of the objective is in fact contracted by a stop anywhere along the path of the beam1 as occasionally happens4 ,examine the telescope carefully with reference to this point before thus testing the power4#ag #ag ,a more precise method1 depending on an actual measurement of the angle subtended by the diameter of the eyepiece diaphragm as seen through the eye end of the ocular and its comparison with the same angular diameter reckoned from the objective1 is given by ,schaeberle4 ,m4 ,n4 #dc1 #big4 ,the eye lens of ,fig4 #e is a simple double convex one1 such as was used by ,christopher ,scheiner and his contemporaries4 ,with a first class objective or mirror the simple eye lens such as is shown in ,fig4 #ih;a is by no means to be despised even now4 ,sir ,william ,herschel always preferred it for high powers1 and speaks with evident contempt of observers who sacrificed its advantages to gain a bigger field of view4 ,let us try to fathom the reason for his vigorously expressed opinion1 strongly backed up by experienced observers like the late ,t4 ,w4 ,webb and ,mr4 ,w4 ,f4 ,denning4 ,first of all a single lens saves about #aj of the light4 ,each surface of glass through which light passes transmits #ie to #if of that light1 so that a single lens transmits approximately #ij1 two lenses #ha and so on4 ,this loss may be enough to determine the visibility of an object4 ,sir ,wm4 ,herschel found that faint objects invisible with the ordinary two lens eyepiece came to view with the single lens4 ,probably the actual loss is less serious than its effect on seeing conditions4 ,the loss is due substantially to reflection at the surfaces1 and the light thus reflected is scattered close to1 or into1 the eye and produces stray light in the field which injures the contrast by which faint objects become visible4 ,in some eyepieces the form of the surfaces is such that reflected light is strongly concentrated where the eye sees it1 forming a 8ghost0 quite bright enough greatly to interfere with the vision of delicate contrasts4 ,the single lens has a very small sharp field1 hardly #aj in angular extent1 the image falling off rapidly in quality as it departs from the axis4 ,if plano-convex1 as is the eye lens of common two-lens oculars1 it works best with the curved side to the eye1 i4e41 reversed from its usual position1 the spherical aberration being much less in this position4 ,illustration3 ,,fig4 #ih4--,simple ,oculars4 ,herschel's report of better definition with a single lens than with an ordinary two lens ocular speaks ill for the quality of the latter then available4 ,of course the single lens gives some chromatic aberration1 generally of small account with the narrow pencils of light used in high powers4 ,a somewhat better form of eye lens occasionally used is the so-called ,coddington lens1 really devised by ,sir ,david ,brewster4 ,this1 ,fig4 #ih;b1 is derived from a glass sphere with a thick equatorial belt removed and a groove cut down centrally leaving a diameter of less than half the radius of the sphere4 ,the focus is1 for ordinary crown glass1 #c_/b the radius of the sphere1 and the field is a little improved over the simple lens1 but it falls off rather rapidly1 with considerable color toward the edge4 ,the obvious step toward fuller correction of the aberrations while retaining the advantages of the simple lens is to make the ocular achromatic1 like a minute objective1 thus correcting at once the chromatic and spherical aberrations over a reasonably large field4 ,as the components are cemented the loss of light at their common surface is negligible4 ,figure #ih;c shows such a lens4 ,if correctly designed it gives an admirably sharp field of #ae to #bj1 colorless and with very little distortion1 and is well adapted for high powers4 ,illustration3 a b ,,fig4 #ii4--,triple ,cemented ,oculars4 ,still better results in field and orthoscopy can be attained by going to a triple cemented lens1 similar to the objective of ,fig4 #eg4 ,triplets thus constituted are made abroad by ,zeiss1 ,steinheil and others1 while in this country an admirable triplet designed by ,professor ,hastings is made by ,bausch ,lomb4 ,illustration3 ,,fig4 #ajj4--,path of ,rays ,through ,huygenian ,ocular4 ,such lenses give a beautifully flat and sharp field over an angle of #bj to #cj1 quite colorless and orthoscopic4 ,fig4 #ii;a1 a form used by ,steinheil1 is an excellent example of the construction and a most useful ocular4 ,the late ,r4 ,b4 ,tolles made such triplets1 even down to inch focus1 which gave admirable results4 ,a highly specialized form of triplet is the so-called monocentric of ,steinheil ,fig4 #ii;b4 ,its peculiarity is less in the fact that all the curves are struck from the same center than in the great thickness of the front flint and the crown1 which1 as in some photographic lenses1 give added facilities for flattening the field and eliminating distortion4 ,the monocentric eyepiece has a high reputation for keen definition and is admirably achromatic and orthoscopic4 ,the sharp field is about #cb1 rather the largest given by any of the cemented combinations4 ,all these optically single lenses are quite free of ghosts1 reduce scattered light to a minimum1 and leave little to be desired in precise definition4 ,the weak point of the whole tribe is the small field1 which1 despite ,herschel's opinion1 is a real disadvantage for certain kinds of work and wastes the observer's time unless his facilities for close setting are more than usually good4 ,hence the general use of oculars of the two lens types1 all of them giving relatively wide fields1 some of them faultless also in definition and orthoscopy4 ,the earliest form1 ,fig4 #ajj1 is the very useful and common one used by ,huygens and bearing his name1 though perhaps independently devised by ,campani of ,rome4 ,probably four out of five astronomical eyepieces belong to this class4 ,the ,huygenian ocular accomplishes two useful results--first1 it gives a wider sharp field than any single lens1 and second it compensates the chromatic aberration1 which otherwise must be removed by a composite lens4 ,it usually consists of a plano-convex lens1 convex side toward the objective1 which is brought inside the objective focus and forms an image in the plane of a rear diaphragm1 and a similar eye lens of shorter focus by which this image is examined4 ,fig4 #ajj shows the course of the rays--,a being the field lens1 ,b the diaphragm and ,c the eye lens4 ,let #a1 #b1 be rays which are incident near the margin of ,a4 ,each1 in passing through the lens1 is dispersed1 the blue being more refracted than the red4 ,both rays come to a general focus at ,b1 and1 crossing1 diverge slightly towards ,c4 ,but1 on reaching ,c1 ray #a1 that was nearer the margin and the more refracted because in a zone of greater pitch1 now falls on ,c the nearer its center1 and is less refracted than ray #b which strikes ,c nearer the rim4 ,if the curvatures of ,a and ,c are properly related #a and #b emerge from ,c parallel to each other and thus unite in forming a distinct image4 ,now follow through the two branches of l marked lr1 and lv1 the red and violet components4 ,ray lv1 the more refrangible1 strikes ,c nearer the center1 and is the less refracted1 emerging from ,c substantially parallel with its mate lr1 hence blending the red and violet images1 if1 being of the same glass1 ,a and ,c have suitably related focal lengths and separation4 ,as a matter of fact the condition for this chromatic compensation is d 7f f7_/#b where d is the distance between the lenses and f1 f1 their respective focal lengths4 ,if this condition of achromatism be combined with that of equal refraction at ,a and ,c1 favorable to minimizing the spherical aberration1 we find f #c;f and d #b;f4 ,this is the conventional ,huygenian ocular with an eye lens the focus of the field lens1 spaced at double the focus of the eye lens1 with the diaphragm midway4 ,in practice the ratio of foci varies from #a3c to #a3b or even #a3a4e1 the exact figure varying with the amount of overcorrection in the objective and under-correction in the eye that has to be dealt with1 while the value of d should be adjusted by actual trial on the telescope to obtain the best color correction practicable4 ,one cannot use any chance ocular and expect the finest results4 ,illustration3 ,,fig4 #aja;a4--,airy and ,mittenzuey ,oculars4 ,the ,huygenian eyepieces are often referred to as 8negative0 inasmuch as they cannot be used directly as magnifiers1 although dealing effectively with an image rather than an object4 ,the statement is also often made that they cannot be used with cross wires4 ,this is incorrect1 for while there is noticeable distortion toward the edge of the wide field1 to say nothing of astigmatism1 in and near the center of the field the situation is a good deal better4 ,central cross wires in the plane of the diaphragm are entirely suitable for alignment of the instrument1 and over a moderate extent of field the distortion is so small that a micrometer scale in the plane of the diaphragm gives very good approximate measurements1 and indeed is widely used in microscopy4 ,it should be noted that the achromatism of this type of eyepiece is compensatory rather than real4 ,one cannot at the same time bring the images of various colors to the same size1 and also to the same plane4 ,as failure in the latter respect is comparatively unimportant1 the ,huygenian eyepiece is adjusted so far to compensate the paths of the various rays as to bring the colored images to the same size1 and in point of fact the result is very good4 ,the field of the conventional form of ,huygenian ocular is fully #dj1 and the definition1 particularly centrally1 is very excellent4 ,there are no perceptible ghosts produced1 and while some #aj of light is lost by reflection in the extra lens it is diffused in the general field and is damaging only as it injures the contrast of faint objects4 ,the theory of the ,huygenian eyepiece was elaborately given by ,littrow1 7,memoirs ,r4 ,a4 ,s4 ,vol4 #d1 p4 #eii71 wherein the somewhat intricate geometry of the situation is fully discussed4 ,various modifications of the ,huygenian type have been devised and used4 ,figure #aja;a is the ,airy form devised as a result of a somewhat full mathematical investigation by ,sir ,george ,airy1 later ,astronomer ,royal4 ,its peculiarity lies in the form of the lenses which preserve the usual #c3a ratio of focal lengths4 ,the field lens is a positive meniscus with a noticeable amount of concavity in the rear face while the eye lens is a 8crossed0 lens1 the outer curvature being about of the inner curvature4 ,the marginal field in this ocular is a little better than in the conventional ,huygenian4 ,illustration3 ,,fig4 #aja;b4--,airy and ,mittenzwey ,oculars4 ,a commoner modification now-a-days is the ,mittenzwey form1 ,fig4 #aja;b4 ,this is usually made with #b3a ratio of focal lengths1 and the field lens still a meniscus1 but less conspicuously concave than in the ,airy form4 ,the eye lens is the usual plano-convex4 ,it is widely used1 especially abroad1 and gives perhaps as large available field as any ocular yet devised1 approximately #ej1 with pretty good definition out to the margin4 ,finally1 we come to the solid eyepiece ,fig4 #ajb;a1 devised by the late ,r4 ,b4 ,tolies nearly three quarters of a century ago1 and and often made by him both for telescopes and microscopes4 ,it is practically a ,huygenian eyepiece made out of a single cylinder of glass with a curvature ratio of #a3a between the eye and the field lens4 ,a groove is cut around the long lens at about its length from the vertex of the field end4 ,this serves as a stop1 reducing the diameter of the lens to about one-half its focal length4 ,it is in fact a ,huygenian eyepiece free from the loss of light in the usual construction4 ,it gives a wide field1 more extensive than in the ordinary form1 with exquisite definition4 ,it is really a most admirable form of eyepiece which should be used far more than is now the case4 ,the late ,dr4 ,brashear is on record as believing that all negative eyepieces less than inch focus should be made in this form4 ,illustration3 a b ,,fig4 #ajb4--,tolles' ,solid and ,compensated ,oculars4 ,so far as the writer can ascertain the only reason that it is not more used is that it is somewhat more difficult to construct than the two lens form1 for its curvatures and length must be very accurately adjusted4 ,it is consequently unpopular with the constructing optician in spite of its conspicuous merits4 ,it gives no ghosts1 and the faint reflection at the eye end is widely spread so that if the exterior of the cylinder is well blackened1 as it should be1 it gives exceptional freedom from stray light4 ,still another variety of the ,huygenian ocular sometimes useful is analogous to the compensating eyepiece used in microscopy4 ,if1 as commonly is the case1 a telescope objective is over-corrected for color to correct for the chromatism of the eye in low powers1 the high powers show strong over correction1 the blue focus being longer than the red1 and the blue image therefore the larger4 ,if now the field lens of the ocular be made of heavy flint glass and the separation of the lenses suitably adjusted1 the stronger refraction of the field lens for the blue pulls up the blue focus and brings its image to substantially the dimensions of the red1 so that the eye lens performs as if there were no overcorrection of the objective4 ,the writer has experimented with an ocular of this sort as shown in ,fig4 #ajb;b and finds that the color correction is1 as might be expected1 greatly improved over a ,mittenzwey ocular of the same focus 7 inch74 ,there would be material advantage in thus varying the ocular color correction to suit the power4 ,in the ,huyghenian eyepiece the equivalent focal length ,f is given by1 ,f #b;ff_/7f f7 where f and f are the focal lengths of the field and eye lenses respectively4 ,this assumes the normal spacing1 d1 of half the sum of the focal lengths1 not always adhered to by constructors4 ,the perfectly general case1 as for any two combined lenses is1 ,f ff#a_/7;f f#a-;d7 ,illustration3 ,,fig4 #ajc4--,path of ,rays ,through ,ramsden ,ocular4 ,to obtain a flatter field1 and particularly one free from distortion the construction devised by ,ramsden is commonly used4 ,this consists1 ,fig4 #ajc1 of two plano convex lenses of equal focal length1 placed with their plane faces outward1 at a distance equal to1 or somewhat less than1 their common focal length4 ,the former spacing is the one which gives the best achromatic compensation since as before the condition for achromatism is d 7f f7 ,when thus spaced the plane surface of the field lens is exactly in the focus of the eye lens1 the combined focus ,f is the same as that of either lens1 since as just shown in any additive combination of two lenses ,f ff_/7f f-d7 and while the field is flat and colorless1 every speck of dust on the field lens is offensively in view4 ,it is therefore usual to make this ocular in the form suggested by ,airy1 in which something of the achromatic correction is sacrificed to obviate this difficulty1 and to obtain a better balance of the residual aberrations4 ,the path of the rays is shown in ,fig4 #ajc4 ,the lenses ,a and ,b are of the same focal length but are now spaced at of this length apart4 ,the two neighboring rays #a1 #b1 coming through the objective from the distant object meet at the objective focus in a point1 a1 of the image plane a b4 ,thence1 diverging1 they are so refracted by ,a and ,b as to leave the latter substantially parallel so that both appear to proceed from the point c1 of the image plane c1 d1 in the principal focus of ,b4 ,from the ordinary equation for the combination1 ,f f4 ,the combination focusses f back of the principal focus of the objective1 and the position of the eye is ,f back of the eye lens1 which is another reason for shortening the lens spacing4 ,at longer spacing the eye distance is inconveniently reduced4 ,thus constituted1 the ,ramsden ocular1 known as 8positive0 from its capability for use as a magnifier of actual objects1 gives a good flat field free from distortion over a field of nearly #ce and at some loss of definition a little more4 ,it is the form most commonly used for micrometer work4 ,in all optical instruments the aberrations increase as one departs from the axis1 so that angular field is rather a loose term depending on the maximum aberrations that can be tolerated4#ah #ah ,the angular field a is defined by tan a _/,f where is1 numerically1 the radius of the field sharp enough for the purpose in hand1 and ,f the effective focal length of the ocular4 ,of the ,ramsden ocular there are many modifications4 ,sometimes f and f are made unequal or there is departure from the simple plano-convex form4 ,more often the lenses are made achromatic1 thus getting rid of the very perceptible color in the simpler form and materially helping the definition4 ,figure #ajd;a shows such an achromatic ocular as made by ,steinheil4 ,the general arrangement is as in the ordinary ,ramsden1 but the sharp field is slightly enlarged1 a good #cf1 and the definition is improved quite noticeably4 ,a somewhat analogous form1 but considerably modified in detail1 is the ,kellner ocular1 ,fig4 #ajd;b4 ,it was devised by an optician of that name1 of ,wetzlar1 who exploited it some three quarters of a century since in a little brochure entitled 8,das orthoskopische ,okular10 as notable a blast of 8hot air0 as ever came from a modern publicity agent4 ,as made today the ,kellner ocular consists of a field lens which is commonly plano-convex1 plano side out1 but sometimes crossed or even equiconvex1 combined with a considerably smaller eye lens which is an over-corrected achromatic4 ,the focal length of the field lens is approximately #g_/d ,f1 that of the eye lens #d_/c ,f1 separated by about ,f4 ,this ocular has its front focal plane very near the field lens1 sometimes even within its substance1 and a rather short eye distance1 but it gives admirable definition and a usable field of very great extent1 colorless and orthoscopic to the edge4 ,the writer has one of #b focus1 with an achromatic triplet as eye lens1 which gives an admirable field of quite #ej4 ,illustration3 ,,fig4 #ajd4--;,achromatic and ,kellner ,oculars4 ,the ,kellner is decidedly valuable as a wide field positive ocular1 but it has in common with the two just previously described a sometimes unpleasant ghost of bright objects4 ,this arises from light reflected from the inner surface of the field lens1 and back again by the front surface to a focus4 ,this focus commonly lies not far back of the field lens and quite too near to the focus of the eye lens for comfort4 ,it should be watched for in going after faint objects with oculars of the types noted4 ,a decidedly better form of positive ocular is the modern orthoscopic as made by ,steinheil and ,zeiss1 ,fig4 #aje;a4 ,it consists of a triple achromatic field lens1 a dense flint between two crowns1 with a plano-convex eye lens of much shorter focus 7 to 7 almost in contact on its convex side4 ,the field triplet is heavily over-corrected for color1 the front focal plane is nearly ,f ahead of the front vertex of the field lens1 and the eye distance is notably greater than in the ,kellner4 ,the field is above #dj1 beautifully flat1 sharp1 and orthoscopic1 free of troublesome ghosts4 ,on the whole the writer is inclined to rate it as the best of two-lens oculars4 ,there should also here be mentioned a very useful long relief ocular1 often used for artillery sights1 and shown in ,fig4 #aje;b4 ,it consists like ,fig4 #ajd;a1 of a pair of achromatic lenses1 but they are placed with the crowns almost in contact and are frequently used with a simple plano convex field lens of much longer focus1 to render the combination more fully orthoscopic4 ,the field1 especially with the field lens1 is wide1 quite #dj as apparent angle for the whole instrument1 and the eye distance is roughly equal to the focal length4 ,it is a form of ocular that might be very advantageously used in finders1 where one often has to assume uncomfortable angles of view1 and long relief is valuable4 ,illustration3 a b ,,fig4 #aje4--,orthoscopic and ,long ,relief ,oculars4 ,whatever the apparent angular field of an ocular may be1 the real angular field of view is obtained by dividing the apparent field by the magnifying power4 ,thus the author's big ,kellner1 just mentioned1 gives a power of #bj with the objective for which it was designed1 hence a real field of #b1 while a second1 power #fe1 gives a real field of hardly #jdj1 the apparent field in this case being a trifle over #dj4 ,there is no escaping this relation1 so that high power always implies small field4 ,the limit of apparent field is due to increasing errors away from the axis1 strong curvature of the field1 and particularly astigmatism in the outer zones4 ,the eye itself can take in only about #dj so that more than this1 while attainable1 can only be utilized by peering around the marginal field4 ,for low powers the usable field is helped out by the accommodation of the eye1 but in oculars of short focus the curvature of field is the limiting factor4 ,the radius of curvature of the image is1 in a single lens approximately #c_/b ,f1 and in the common two lens forms about ,f4 ,in considering this matter ,conrady has shown 7,m4 ,n4 #gh #dde7 that for a total field of #dj the sharpness of field fails at a focal length of about #a inch for normal power of accommodation4 ,the best achromatic combinations reduce this limit to about inch4 ,at focal lengths below this the sharpest field is obtainable only with reduced aperture4 ,there is an interesting possibility of building an anastigmatic ocular on the lines of the modern photographic lens1 which ,conrady suggests1 but the need of wide field in high powers is hardly pressing enough to stimulate research4 ,illustration3 ,,fig4 #ajf4--,ordinary ,terrestrial ,ocular4 ,finally we may pass to the very simple adjunct of most small telescopes1 the terrestrial ocular which inverts the image and shows the landscape right side up4 ,whatever its exact form it consists of an inverting system which erects the inverted image produced by the objective alone1 and an eyepiece for viewing this erected image4 ,in its common form it is composed of four plano-convex lenses arranged as in ,fig4 #ajf4 ,here ,a and ,b for the inverting pair and ,c and ,d a modified ,huygenian ocular4 ,the image from the objective is formed in the front focus of ,,ab which is practically an inverted ocular1 and the erected image is formed in the usual way between ,c and ,d4 ,the apparent field is fairly good1 about #ce1 and while slightly better corrections can be gained by using lenses of specially adjusted curvatures1 as ,airy has shown1 these are seldom applied4 ,the chief objection to this erecting system is its length1 some ten times its equivalent focus4 ,now and then to save light and gain field1 the erector is a single cemented combination and the ocular like ,fig4 #ii;a or ,fig4 #ajb;a4 ,fig4 #ajg shows a terrestrial eyepiece so arranged1 from an example by the late ,r4 ,b4 ,tolles4 ,when carefully designed an apparent field of #dj or more can be secured1 with great brilliancy1 and the length of the erecting system is moderate4 ,very much akin in principle is the eyepiece microscope1 such as is made by ,zeiss to give variable power and a convenient position of the eye in connection with filar micrometers1 ,fig4 #ajh4 ,it is provided with a focussing collar and its draw tube allows varying power just as in case of an ordinary microscope4 ,in fact eyepiece microscopes have long been now and then used to advantage for high powers4 ,they are easier on the eye1 and give greater eye distance than the exceedingly small eye lenses of short focus oculars1 and using a solid eyepiece and single lens objective lose no more light than an ordinary ,huygenian ocular4 ,the erect resultant image is occasionally a convenience in astronomical use4 ,illustration3 ,,fig4 #ajg4--,tolles ,triplet ,inverting ,system4 ,illustration3 ,,fig4 #ajh4--,microscope as ,ocular4 ,illustration3 ,,fig4 #aji4--8;,davon0 ,instrument4 ,quite analogous to the eyepiece microscope is the so-called 8,davon0 micro-telescope4 ,originally developed as an attachment for the substage of a microscope to give large images of objects at a little distance it has grown also into a separate hand telescope1 monocular or binocular1 for general purposes4 ,the attachment thus developed is shown complete in ,fig4 #aji4 ,d is merely a well corrected objective set in a mount provided with ample stops4 ,the image is viewed by an ordinary microscope or special eyepiece microscope ,a1 as the case may be1 furnished with rack focussing at ,a and assembled with the objective by means of the carefully centered coupling ,c4 ,it furnishes a compact and powerful instrument1 very suitable for terrestrial or minor astronomical uses1 like the ,tolles' short-focus hand telescopes already mentioned4 ,when properly designed telescopes of this sort give nearly the field of prism glasses1 weigh much less and lose far less light for the same effective power and aperture4 ,they also have under fairly high powers rather the advantage in the matter of definition1 other things being equal4 ,,chapter ,,vii ,,hand ,,telescopes ,,and ,,binoculars ,the hand telescope finds comparatively little use in observing celestial bodies4 ,it is usually quite too small for any except very limited applications1 and cannot be given sufficient power without being difficult to keep steady except by the aid of a fixed mounting4 ,still1 for certain work1 especially the observation of variable stars1 it finds useful purpose if sufficiently compact and of good light-gathering power4 ,there is most decidedly a limit to the magnifying power which can be given to an instrument held in the hand without making the outfit too unsteady to be serviceable4 ,anything beyond #h to #aj diameters is highly troublesome1 and requires a rudimentary mount or at least steadying the hand against something in order to observe with comfort4 ,the longer the instrument the more difficult it is to manage1 and the best results with hand telescopes are to be obtained with short instruments of relatively large diameter and low power4 ,the ordinary field glass of ,galilean type comes immediately to mind and in fact the field glass is and has been much used4 ,as ordinarily constructed it is optically rather crude for astronomical purposes4 ,the objectives are rarely well figured or accurately centered and a bright star usually appears as a wobbly flare rather than a point4 ,furthermore the field is generally small1 and of quite uneven illumination from centre to periphery1 so that great caution has to be exercised in judging the brightness of a star1 according to its position in the field4 ,the lens diameter possible with a field glass of ordinary construction is limited by the limited distance between the eyes1 which must be well centered on the eyepieces to obtain clear vision4 ,the inter-pupillary distance is generally a scant #b inches so that the clear aperture of one of the objectives of a field glass is rarely carried up to #b inches4 ,the best field glasses have each objective a triple cemented lens1 and the concave lenses also triplets1 the arrangement of parts being that shown in ,fig4 #aaj4 ,glasses of this sort rarely have a magnifying power above #e4 ,in selecting a field glass with the idea of using it on the sky try it on a bright star1 real or artificial1 and if the image with careful focussing does not pull down to a pretty small and uniform point take no further interest in the instrument4 ,illustration3 ,,fig4 #aaj4--,optical ,parts of ,field ,glass4 ,the advantage of a binocular instrument is popularly much exaggerated4 ,it gives a somewhat delusive appearance of brilliancy and clearness which is psychological rather than physical4 ,during the late war a very careful research was made at the instance of the ,united ,states ,government to determine the actual value of a binocular field glass against a monocular one of exactly the same type1 the latter being cheaper1 lighter1 and in many respects much handier4 ,the difference found in point of actual seeing all sorts of objects under varying conditions of illumination was so small as to be practically negligible4 ,an increase of less than #e per cent in magnifying power enabled one to see with the monocular instrument everything that could be seen with the binocular1 equally well1 and it is altogether probable that in the matter of seeing fine detail the difference would be even less than in general use1 since it is not altogether easy to get the two sides of a binocular working together efficiently or to keep them so afterwards4 ,there has been1 therefore1 a definite field for monocular hand telescopes of good quality and moderate power and such are manufactured by some of the best ,continental makers4 ,such instruments have sometimes been shortened by building them on the exact principle of the telephoto lens1 which gives a relatively large image with a short camera extension4 ,illustration3 ,,fig4 #aaa4--,steinheil ,shortened ,telescope4 ,a much shortened telescope1 as made by ,steinheil for solar photographic purposes1 is shown in ,fig4 #aaa4 ,this instrument with a total length of about #b feet and a clear aperture of #b inches gives a solar image of inch diameter1 corresponding to an ordinary glass of more than double that total length4 ,quite the same principle has been applied to terrestrial telescopes by the same maker1 giving again an equivalent focus of about double the length of the whole instrument4 ,this identical principle has often been used in the so-called ,barlow lens1 a negative lens placed between objective and eyepiece and giving increased magnification with small increase of length2 also photographic enlargers of substantially similar function have found considerable use4 ,a highly efficient hand telescope for astronomical purposes might be constructed along this line1 the great shortening of the instrument making it possible to use somewhat higher powers than the ordinary without too much loss of steadiness4 ,there is also constructed a binocular for strictly astronomical use consisting of a pair of small hand comet-seekers4 ,one of these little instruments is shown in ,fig4 #aab4 ,it has a clear diameter of objectives of #a inch1 magnification of #e1 and a brilliant and even field of #g aperture4 ,the objectives are triplets like ,fig4 #eg1 already referred to1 the oculars achromatic doublets of the type of ,fig4 #ajd;a4 ,with the exception of these specialized astronomical field glasses the most useful and generally available hand instrument is the prism glass now in very general use4 ,it is based on reversal of the image by internal total reflection in two prisms having their reflecting surfaces perpendicular each to the other4 ,the rudiments of the process lie in the simple reversion prism shown in diagram in ,fig4 #aac4 ,illustration3 ,,fig4 #aab4--;,astronomical ,binocular4 ,this is nothing more nor less than a right angled glass prism set with its hypothenuse face parallel and with its sides at #de to the optical axis of the instrument4 ,rays falling upon one of its refracting faces at an angle of #de are refracted upon the hypothenuse face1 are there totally reflected and emerge from the second face of the prism parallel to their original course4 ,inspection of ,fig4 #aac shows that an element like ,a ,b perpendicular to the plane of the hypothenuse face is inverted by the total reflection so that it takes the position ,a ,b4 ,it is equally clear that an element exactly perpendicular to ,a ,b will be reflected from the hypothenuse face flatwise as it were1 and will emerge without its ends being reversed so that the net effect of this single reflection is to invert the image without reversing it laterally at the same time4 ,on the other hand if a second prism be placed behind the first1 flat upon its side1 with its hypothenuse face occupying a plane exactly perpendicular to that of the first prism1 the line ,a,b will be refracted1 totally reflected and refracted again out of the prism without a second inversion1 while a line perpendicular to ,a,b will be refracted endwise on the hypothenuse face of the second prism and will be inverted as was the line ,a ,b at the start4 ,illustration3 ,,fig4 #aac4--,reversion ,prism4 ,consequently two prisms thus placed will completely invert the image1 producing exactly the same effect as the ordinary inverting system ,fig4 #ajf4 ,the simple reversion prism is useful as furnishing a means1 when placed over an eye lens1 and rotated1 of revolving the image on itself1 a procedure occasionally convenient1 especially in stellar photometry4 ,the two prisms together constitute a true inverting system and have been utilized in that function1 but they give a rather small angular field and have never come into a material amount of use4 ,the exact effect of this combination1 known historically as ,dove's prisms1 is shown plainly in ,fig4 #aad4 ,the first actual prismatic inverting system was due to ,m4 ,porro1 who invented it about the middle of the last century1 and later brought it out commercially under the name of 8,lunette ,napoleon ,troisime10 as a glass for military purposes4 ,illustration3 ,,fig4 #aad4--;,dove's ,prisms4 ,illustration3 ,,fig4 #aae4--,porro's ,prism ,system4 ,the prism system of this striking form of instrument is shown in ,fig4 #aae4 ,it was composed of three right angle prisms ,a1 ,b1 and ,c4 ,a presented a cathetus face to the objective and ,b a cathetus face to the ocular4 ,obviously a vertical element brought in along a from the objective would be reflected at the hypothenuse face b1 to a position at right angles to the original one1 would enter the hypothenuse face of ,c and thence after two reflections at c and d flatwise and without change of direction would emerge1 enter the lower cathetus face of ,b and by reflection at the hypothenuse face e of ,b would be turned another #ij making a complete reversion as regards up and down at the eye placed at f4 ,an element initially at right angles to the one just considered would enter ,a1 be reflected flatwise1 in the faces of ,c be twice reflected endwise1 thereby completely inverting it1 and would again be reflected flatwise from the hypothenuse face of ,c1 thereby effecting1 as the path of the rays indicated plainly shows1 a complete inversion of the image4 ,focussing was very simply attained by a screw motion affecting the prism ,c and the whole affair was in a small flat case1 the external appearance and size of which is indicated in ,fig4 #aaf4 ,illustration3 ,,fig4 #aaf4--,lunette ,napoleon ,troisime4 ,illustration3 ,,fig4 #aag4--,porro's ,first ,form of ,prisms4 ,from ocular to objective the length was about an inch and a half4 ,it was of #aj power and took in a field of #de yards at a distance of #ajjj yards4 ,here for the first time we find a prismatic inverting system of strictly modern type4 ,and it is interesting to note that if one had wished to make a binocular 8,lunette ,napoleon ,troisime0 he would inevitably have produced an instrument with enhanced stereoscopic effect like the modern prism field glass by the mere effort to dodge the observer's nose4 ,somewhat earlier ,m4 ,porro had arranged his prisms in the present conventional form of ,fig4 #aag1 where two right angle prisms have their faces positioned in parallel planes1 but turned around by #ij as in ,fig4 #aad4 ,the ray traced through this conventional system shows that exactly the same inversion occurs here as in the original ,porro construction1 and this form is the one which has been most commonly used for prismatic inversion and is conveniently known as ,porro's first form1 it actually having been antecedent in principle and practice to the 8,lunette ,napoleon ,troisime40 ,the original published description of ,porro's work1 translated from 8,cosmos0 ,vol4 #b1 p4 #bbb 7#aheb7 et seq4 is here annexed as it sets forth the origin of the modern prism glass in unmistakable terms4 ,cosmos1 ,vol4 #b1 p4 #bbb4--8,we have wished for some time to make known to our readers the precious advantages of the 8longue-vue cornet0 or tlmetre of ,m4 ,porro4 ,ordinary spyglasses or terrestrial telescopes of small dimensions are at least #cj or #dj cm4 long when extended to give distinct vision of distant objects4 ,the length is considerably reduced by substituting for a fixed tube multiple tubes sliding into each other4 ,but the drawing out which this substitution necessitates is a somewhat grave inconvenience2 one cannot point the telescope without arranging it and losing time4 ,for a long time we have wished it were possible to have the power of viewing distant objects1 with telescopes very short and without draw4 ,m4 ,porro's 8longue-vue cornet0 seems to us to solve completely this difficult and important problem4 ,its construction rests upon an exceedingly ingenious artifice which literally folds triply the axis of the telescope and the luminous ray so that by this fact alone the length of the instrument is reduced by two-thirds4 ,let us try to give an idea of this construction3 ,behind the telescope objective ,m4 ,porro places a rectangular isosceles prism of which the hypothenuse is perpendicular to the optic axis4 ,the luminous rays from the object fall upon the rectangular faces of this prism1 are twice totally reflected1 and return upon themselves parallel to their original direction3 half way to the point where they would form the image of the object1 they are arrested by a second prism entirely similar to the first1 which returns them to their original direction and sends them to the eyepiece through which we observe the real image4 ,if the rectangular faces of the second prism were parallel to the faces of the first1 this real image would be inverted--the telescope would be an astronomical and not a terrestrial telescope4 ,but ,m4 ,porro being an optician eminently dextrous1 well divined that to effect the reinversion it sufficed to place the rectangular faces of the second prism perpendicular to the corresponding faces of the first by turning them a quarter revolution upon themselves4 ,in effect1 a quarter revolution of a reflecting surface is a half revolution for the image1 and a half revolution of the image evidently carries the bottom to the top and the right to the left1 effecting a complete inversion4 ,as the image is thus redressed independently of the eyepiece one can evidently view it with a simple two-lens ocular which decreases still further the length of the telescope so that it is finally reduced to about a quarter of that of a telescope of equal magnifying power1 field and clearness4 ,the new telescope is then a true pocket telescope even with a magnifying power of #aj or #ae4 ,its dimensions in length and bulk are those of a field glass usually magnifying only #d to #f times4 ,the more draws1 the more bother1--it here suffices to turn a little thumbscrew to find in an instant the point of sharpest vision4 ,in brilliancy necessarily cut down a little1 not by the double total reflection1 which as is well known does not lose light1 but by the quadruple passage across the substance of the two prisms1 the cornet in sharpness and amplification of the images can compare with the best hunting telescopes of the celebrated optician ,ploessl of ,vienna4 ,m4 ,porro has constructed upon the same principles a marine telescope only #ae c4m4 long with an objective of #dj m4m4 aperture which replaces an ordinary marine glass #gj c4m4 long4 ,he has done still better1--a telescope only #cj c4m4 long carries a #fj m4m4 objective and can be made by turns a day and a night glass1 by substituting by a simple movement of the hand and without dismounting anything1 one ocular for the other4 ,its brilliancy and magnification of a dozen times with the night ocular1 of twenty-five times with the day ocular1 permits observing without difficulty the eclipses of the satellites of ,jupiter4 ,this is evidently immense progress4 ,one of the most illustrious of ,german physicists1 ,m4 ,dove of ,berlin1 gave in #ahea the name of reversion prism to the combination of two prisms placed normally one behind the other so that their corresponding faces were perpendicular4 ,he presented this disposition as an important new discovery made by himself4 ,he doubtless did not know that ,m4 ,porro1 who deserves all the honor of this charming application1 had realized it long before him40 ,a little later ,m4 ,porro produced what is commonly referred to as ,porro's second form1 which is derived directly from annexing ,a ,fig4 #aae to the corresponding half of ,c as a single prism1 the other half of ,b being similarly annexed to the prism ,c1 thus forming two sphenoid prisms1 such as are shown in ,fig4 #aah which may be mounted separately or may have their faces cemented together to save loss of light by reflections4 ,the sphenoid prisms have had the reputation of being much more difficult to construct than the plain right angled prisms of the other forms shown4 ,in point of fact they are not particularly difficult to make and the best inverting eye pieces for telescopes are now constructed with sphenoid prisms like those just described4 ,illustration3 ,,fig4 #aah4--,porro's ,second ,form4 ,illustration3 ,,fig4 #aai4--;,clark ,prismatic ,eyepiece4 ,this particular arrangement lends itself very readily to a fairly compact and symmetrical mounting1 as is well shown in ,fig4 #aai which is the terrestrial prismatic eyepiece as constructed by the ,alvan ,clark corporation for application to various astronomical telescopes of their manufacture4 ,a glance at the cut shows the compactness of the arrangement1 which actually shortens the linear distance between objective and ocular by the amount of the path of the ray through the prisms instead of lengthening the distance as in the common terrestrial eyepiece4 ,the field moreover is much larger than that attainable by a construction like ,fig4 #aaj1 extending to something over #dj1 and there is no strong tendency for the illumination or definition to fall off near the edge of the field4 ,in the practical construction of prism field glasses the two right angled prisms are usually separated by a moderate space as in ,porro's original instruments so as to shorten the actual length of the prism telescope by folding the ray upon itself as in ,fig4 #abj1 which is a typical modern binocular of this class4 ,illustration3 ,,fig4 #abj4--,section of ,prism ,binocular4 ,the path of the rays is plainly shown and the manner in which the prisms fold up the total focal length of the objective is quite obvious4 ,the added stereoscopic effect obtained by the arrangement of the two sides of the instrument is practically a very material gain4 ,it gives admirable modelling of the visible field1 a perception of distance which is at least very noticeable and a certain power of penetration1 as through a mass of underbrush1 which results from the objectives to a certain extent seeing around small objects so that one or the other of them gives an image of something beyond4 ,for near objects there is some exaggeration of stereoscopic effect but on the whole for terrestrial use the net gain is decidedly in evidence4 ,a well made prism binocular is an extremely useful instrument for observation of the heavens1 provided the objectives are of fair size1 and the prisms big enough to receive the whole beam from the objective1 and well executed enough to give a thoroughly good image with a flat field4 ,the weak points of the prism glass are great loss of light through reflection at the usual #aj air-glass surfaces and the general presence of annoying ghosts of bright objects in the field4 ,most such binoculars have ,kellner eyepieces which are peculiarly bad1 as we have seen1 with respect to reflected images1 and present the plane surface of the last prism to the plane front of the field lens4 ,recently some constructors have utilized the orthoscopic eyepiece1 ,figure #aje;a1 as a substitute with great advantage in the matter of reflections4 ,the loss of light in the prism glass is really a serious matter1 between reflection at the surfaces and absorption in the thick masses of glass necessary in the prisms4 ,if of any size the transmitted light is not much over one-half of that received1 very seldom above #fj4 ,if the instrument is properly designed the apparent field is in the neighborhood of #de1 substantially flat and fairly evenly illuminated4 ,warning should here be given however that many binoculars are on the market in which the field is far from flat and equally far from being uniform4 ,in many instances the prisms are too small to take the whole bundle of rays from the objective back to the image plane without cutting down the marginal light considerably4 ,even when the field is apparently quite flat this fault of uneven illumination may exist1 and in a glass for astronomical uses it is highly objectionable4 ,before picking out a binocular for a study of the sky make very careful trial of the field with respect to flatness and clean definition of objects up to the very edge4 ,then judge as accurately as you may of the uniformity of illumination1 if possible by observation on two stars about the radius of the field apart4 ,it should be possible to observe them in any part of the field without detectable change in their apparent brilliancy4 ,if the objectives are easily removable unscrew one of them to obtain a clear idea as to the actual size of the prisms4#ai ,look out1 too1 for ghosts of bright stars4 #ai ,there are binoculars on the market which are to outward appearance prism glasses1 but which are really ordinary opera glasses mounted with intent to deceive1 sometimes bearing a slight variation on the name of some well known maker4 ,the objectives of prism glasses usually run from inch to #a inch in diameter1 and the powers from #f to #ab4 ,the bigger the objectives the better1 provided the prisms are of ample size1 while higher power than #f or #h is generally unnecessary and disadvantageous4 ,occasional glasses of magnifying power #ab to #bj or more are to be found but such powers are inconveniently great for an instrument used without support4 ,do not forget that a first class monocular prism glass is extremely convenient and satisfactory in use1 to say nothing of being considerably less in price than the instrument for two eyes4 ,a monocular prism glass1 by the way1 makes an admirable finder when fitted with coarse cross lines in the eyepiece4 ,it is particularly well suited to small telescopes without circles4 ,illustration3 ,,fig4 #aba4--;,binocular with ,extreme ,stereoscopic ,effect4 ,numerous modifications of ,porro's inverting prisms have been made adapting them to different specific purposes4 ,of these a single familiar example will suffice as showing the way in which the ,porro prism system can be treated by mere rearrangement of the prismatic elements4 ,in ,fig4 #aba is shown a special ,zeiss binocular capable of extreme stereoscopic effect4 ,it is formed of two ,porro prism telescopes with the rays brought into the objectives at right angles to the axis of the instrument by a right angled prism external to the objective4 ,the apertures of these prisms appear pointing forward in the cut4 ,as shown they are in a position of maximum stereoscopic effect4 ,being hinged the tubes can be swung up from the horizontal position1 in which latter the objectives are separated by something like eight times the interocular distance4 ,the stereoscopic effect with the tubes horizontal is of course greatly exaggerated so that it enables one to form a fair judgment as to the relative position of somewhat distant objects1 a feature useful in locating shell bursts4 ,the optical structure of one of the pair of telescopes is shown in ,fig4 #abb in which the course of the entering ray can be traced through the exterior prism of the objective and the remainder of the reversing train and thence through the eyepiece4 ,this prism erecting system is obviously derived from the 8,lunette ,napoleon ,troisime0 by bringing down the prism ,b upon the corresponding half ,a and cementing it thereto1 meanwhile placing the objective immediately under ,a4 ,one occasionally meets prismatic inverting systems differing considerably from the ,porro forms4 ,perhaps the best known of these is the so called roof prism due to ,prof4 ,abb1 ,fig4 #abc1 and occasionally useful in that the entering and emerging rays lie in the same straight line1 thus forming a direct vision system4 ,looking at it as we did at the ,porro system a vertical element in front of the prism is reversed in reflection from the two surfaces a and b1 while a corresponding horizontal element is reflected flatwise so far as these are concerned1 but is turned end for end by reflection at the roof surfaces c and d1 thus giving complete inversion4 ,in practice the prism is made as shown1 in three parts1 two of them right angled prisms1 the third containing the roof surfaces4 ,the extreme precision required in figuring the roof forms a considerable obstacle to the production of such prisms in quantity and while they have found convenient use in certain special instruments like gunsights1 where direct vision is useful1 they are not extensively employed for general purposes1 although both monocular and binocular instruments have been constructed by their aid4 ,illustration3 ,,fig4 #abb4--,path of ,ray in ,fig4 #aba4 ,illustration3 ,,fig4 #abc4--;,abb ,roof ,prism4 ,one other variety of prism involving the roof principle has found some application in field glasses manufactured by the firm of ,hensoldt4 ,the prism form used is shown in ,fig4 #abd4 ,this like other forms of roof prism is less easy to make than the conventional ,porro type4 ,numerous inverting and laterally reflecting prisms are in use for specific purposes4 ,some of them are highly ingenious and remarkably well adapted for their use1 but hardly can be said to form a material portion of telescope practice4 ,they belong rather to the technique of special instruments like gunsights and periscopes1 while some of them have been devised chiefly as ingenious substitutes for the simpler ,porro forms4 ,most prism telescopes both monocular and binocular are generally made on one or the other of the ,porro forms4 ,this is particularly true of the large binoculars which are occasionally constructed4 ,porro's second form with the sphenoid prisms seems to be best adapted to cases where shortening of the instrument is not a paramount consideration4 ,for example1 some ,zeiss short focus telescopes are regularly made in binocular form1 and supplied with inverting systems composed of two sphenoid prisms1 and with oculars constructed on the exact principle of the triple nose-piece of a microscope1 so that three powers are immediately available to the observer4 ,illustration3 ,,fig4 #abd4--;,hensoldt ,prism4 ,still less commonly binocular telescopes of considerable aperture are constructed1 primarily for astronomical use1 being provided with prismatic inversion for terrestrial employment1 but more particularly in order to gain by the lateral displacement of a ,porro system the space necessary for two objectives of considerable size4 ,as we have already seen1 the practical diameter of objectives in a binocular is limited to a trifle over #b inches unless space is so gained4 ,the largest prismatic binocular as yet constructed is one made years ago by the ,clarks1 of #f inches objective aperture and #ib inches focal length4 ,so big and powerful an instrument obviously would give admirable binocular views of the heavens and so accurately was it constructed that the reports of its performance were exceedingly good4 ,the same firm has made a good many similar binoculars of #c inch and above1 of which a typical example of #d inch aperture and #fj inch focal length is shown in ,fig4 #abe4 ,in this case the erecting systems were of ,porro's first form1 and were provided with ,kellner oculars of very wide field4 ,these binoculars constructions in instruments of such size1 however well made and agreeable for terrestrial observation1 hardly justify the expense for purely astronomical use4 ,illustration3 ,,fig4 #abe4--;,clark #d ,binocular ,telescope4 ,,chapter ,,viii ,,accessories ,aside from the ordinary equipment of oculars various accessories form an important part of the observer's equipment1 their number and character depending on the instrument in use and the purposes to which it is devoted4 ,illustration3 ,,fig4 #abf4--,star ,diagonal4 ,first in general usefulness are several special forms of eyepiece equipment supplementary to the usual oculars4 ,at the head of the list is the ordinary star diagonal for the easier viewing of objects near the zenith here shown in ,fig4 #abf4 ,it is merely a tube1 ,a1 fitting the draw tube of the telescope1 with a slotted side tube ,b1 at a right angle1 into which the ordinary ocular fits1 and a right angled prism ,c with its two faces perpendicular respectively to the axes of the main and side tubes1 and the hypothenuse face at #de to each4 ,the beam coming down the tube is totally reflected at this face and brought to focus at the ocular4 ,the lower end of the tube is closed by a cap to exclude dust4 ,one looks1 by help of this1 horizontally at zenith stars1 or1 if observing objects at rather high altitude1 views them at a comfortable angle downward4 ,the prism must be very accurately made to avoid injury to the definition1 but loses only about #aj of the light1 and adds greatly to the comfort of observing4 ,of almost equal importance is the solar diagonal devised by ,sir ,john ,herschel1 ,fig4 #abg4 ,here the tube structure ,a1 ,b1 is quite the same as in ,fig4 #abf but the right angled prism is replaced by a simple elliptical prism ,c of small angle1 #aj or less1 with its upper face accurately plane and at #de to the axes of the tubes1 resting on a lining tube ,d cut off as shown4 ,in viewing the sun only about #e of the light 7and heat7 is reflected at this upper surface to form the image at the eye piece4 ,illustration3 ,,fig4 #abg4--,solar ,diagonal4 ,any reflection from the lower polished surface is turned aside out of the field1 while the remainder of the radiation passes through the prism ,c and is concentrated below it4 ,to prevent scorching the observer the lower end of the tube is capped at ,e1 but the cap has side perforations to provide circulation for the heated air4 ,using such a prism1 the remnant of light reflected can be readily toned down by a neutral tinted glass over the ocular4 ,in the telescopes of #c inches and less aperture1 and ordinary focal ratio1 a plane parallel disc of very dark glass over the ocular gives sufficient protection to the eye4 ,this glass is preferably of neutral tint1 and commonly is a scant #a_/af inch thick4 ,some observers prefer other tints than neutral4 ,a green and a red glass superimposed give good results and so does a disc of the deepest shade of the so-called ,noviweld glass1 which is similar in effect4 ,with an aperture as large as #c inches a pair of superimposed dark glasses is worth while1 for the two will not break simultaneously from the heat and there will be time to get the eye away in safety4 ,a broken sunshade is likely to cost the observer a permanent scotoma1 blindness in a small area of the retina which will neither get better nor worse as time goes on4 ,above #c inches aperture the solar prism should be used or1 if one cares to go to fully double the cost1 there is nothing more comfortable to employ in solar observation than the polarizing eye piece1 ,fig4 #abh4 ,this shows schematically the arrangement of the device4 ,it depends on the fact that a ray of light falling on a surface of common glass at an angle of incidence of approximately #eg is polarized by the reflection so that while it is freely reflected if it falls again on a surface parallel to the first1 it is absorbed if it falls at the same incidence on a surface at right angles to the first4 ,illustration3 ,,fig4 #abh4--;,diagram of ,polarizing ,eyepiece4 ,thus in ,fig4 #abh the incident beam from the telescope falls on the black glass surface a at #eg incidence1 is again reflected from the parallel mirror b1 and then passed on1 parallel to its original path1 to the lower pair of mirrors c1 d4 ,the purpose of the second reflection is to polarize the residual light which through the convergence of the rays was incompletely polarized at the first4 ,the lower pair of mirrors c1 d1 again twice reflect the light at the polarizing angle1 and1 in the position shown1 pass it on to the ocular diminished only by the four reflections4 ,but if the second pair of mirrors be rotated together about a line parallel to b c as an axis the transmitted light begins to fade out1 and when they have been turned #ij1 so that their planes are inclined #ij to a and b 7 #cc to the plane of the paper71 the light is substantially extinguished4 ,thus by merely turning the second pair of mirrors the solar image can be reduced in brilliancy to any extent whatever1 without modifying its color in any way4 ,the typical form given to the polarizing eyepiece is similar to ,fig4 #abi4 ,here t#b is the box containing the polarizing mirrors1 a b1 fitted to the draw tube1 but for obvious reasons eccentric with it1 t#a is the rotating box containing the 8analysing0 mirrors c1 d1 and a is the ocular turning with it4 ,sometimes the polarizing mirrors are actually a pair of ,herschel prisms as in ,fig4 #abf1 facing each other1 thus getting rid of much of the heat4 ,otherwise the whole set of mirrors is of black glass to avoid back reflections4 ,in simpler constructions single mirrors are used as polarizer and analyser1 and in fact there are many variations on the polarizing solar eyepiece involving about the same principles4 ,illustration3 ,,fig4 #abi4--,polarizing ,solar ,eyepiece4 ,in any solar eyepiece a set of small diaphragms with holes from perhaps #a_/fd inch up are useful in cutting down the general glare from the surface outside of that under scrutiny4 ,these may be dropped upon the regular diaphragm of the ocular or conveniently arranged in a revolving diaphragm like that used with the older photographic lenses4 ,the measurement of celestial objects has developed a large group of important auxiliaries in the micrometers of very varied forms4 ,the simplest needs little description1 since it consists merely of a plane parallel disc of glass fitting in the focus of a positive ocular1 and etched with a network of uniform squares1 forming a reticulated micrometer by which the distance of one object from another can be estimated4 ,it can be readily calibrated by measuring a known distance or noting the time required for an equatorial star to drift across the squares parallel to one set of lines4 ,it gives merely a useful approximation1 and accurate measures must be turned over to more precise instruments4 ,illustration3 ,,fig4 #acj4--;,diagram of ,ring ,micrometer4 ,the ring micrometer due1 like so much other valuable apparatus1 to ,fraunhofer1 is convenient and widely used for determining positions4 ,it consists1 as shown in ,fig4 #acj1 of an accurately turned opaque ring1 generally of thin steel1 cemented to a plane parallel glass or otherwise suspended in the center of the eyepiece field4 ,the whole ring is generally half to two thirds the width of the field and has a moderate radial width so that both the ingress and the egress of a star can be conveniently timed4 ,it depends wholly on the measurement of time as the stars to be compared drift across the ring while the telescope is fixed1 and while a clock or chronometer operating a sounder is a desirable adjunct one can do pretty well with a couple of stop watches since only differential times are required4 ,for full directions as to its use consult ,loomis' ,practical ,astronomy1 a book which should be in the library of every one who has the least interest in celestial observations4 ,suffice it to say here that the ring micrometer is very simple in use1 and the computation of the results is quite easy4 ,in ,fig4 #acj ,f is the edge of the field1 ,r the ring1 and a b1 ab1 the paths of the stars s and s1 the former well into the field1 the latter just within the ring4 ,the necessary data comprise the time taken by each star to transverse the ring1 and the radius of the ring in angular measure1 whence the difference in ,r4 ,a4 or ,dec1 can be obtained4#bj #bj r the radius of the ring1 is given by1 r 7#ae_/b77t-t7 cos ,dec41 t-t being the seconds taken for transit4 ,difference of ,r4 ,a4 7t-t7 7,t-,t7 where 7,t-,t7 is the time taken for transit of second star4 ,to obtain differences of declination one declination should be known at least approximately1 and the second estimated from its relative position in the ring or otherwise4 ,then with these tentative values proceed as follows4 ,put x angle aob and x angle aob ,also let d approximate declination of s and d approximate declination of s ,then sin x 7#ae_/br7 cos d 7,t-,t7 sin x 7#ae_/br7 cos d 7t-t7 and finally ,difference of ,dec4 r 7cos x-cos x71 when both arcs are on the same side of center of ring4 ,if on opposite sides1 ,diff4 r 7cos x cos x74 ,illustration3 ,chamber's 8,astronomy0 7,clarendon ,press74 ,,fig4 #aca4--;,double ,image ,micrometer4 7,courtesy of ,the ,clarendon ,press47 ,there is also now and then used a square bar micrometer1 consisting of an opaque square set with a diagonal in the line of diurnal motion4 ,it is used in much the same way as the ring1 and the reductions are substantially the same4 ,it has some points of convenience but is little used1 probably on account of the great difficulty of accurate construction and the requirement1 for advantageous use1 that the telescope should be on a well adjusted equatorial stand4#ba ,the ring micrometer works reasonably well on any kind of steady mount1 requires no illumination of the field and is in permanent working adjustment4 #ba 7,for full discussion of this instrument see ,chandler1 ,mem4 ,amer4 ,acad4 ,arts ,sci4 #ahhe1 p4 #aeh74 ,still another type of micrometer capable of use without a clock-drive is the double image instrument4 ,in its usual form it is based on the principle that if a lens is cut in two along a diameter and the halves are slightly displaced along the cut all objects will be seen double1 each half of the lens forming its own set of images4 ,conversely1 if one choses two objects in the united field these can be brought together by sliding the halves of the lens as before1 and the extent of the movement needed measures the distance between them4 ,any lens in the optical system can be thus used1 from the objective to the eyepiece4 ,fig4 #aca shows a very simple double image micrometer devised by ,browning many years ago4 ,here the lens divided is a so-called ,barlow lens1 a weak achromatic negative lens sometimes used like a telephoto lens to lengthen the focus and hence vary the power of a telescope4 ,this lens is shown at ,a with the halves widely separated by the double threaded micrometer screw ,b1 which carries them apart symmetrically4 ,the ocular proper is shown at ,c4 ,double image micrometers are now mainly of historical interest1 and the principle survives chiefly in the heliometer1 a telescope with the objective divided1 and provided with sliding mechanism of the highest refinement4 ,the special function of the heliometer is the direct micrometric measurement of stellar distances too great to be within the practicable range of a filar micrometer--distances for example up to #a or even more4 ,the observations with the heliometer are somewhat laborious and demand rather intricate corrections1 but are capable of great precision4 7,see ,sir ,david ,gill's article 8,heliometer0 in the ,enc4 ,brit4 #aath ,ed474 ,at the present day celestial photography1 with micrometric measurement of the resulting plates1 has gone far in rendering needless visual measurements of distances above a very few minutes of arc1 so that it is somewhat doubtful whether a large heliometer would again be constructed4 ,illustration3 ,,fig4 #acb4--;,filar ,micrometer4 7,courtesy of ,j4 ,b4 ,lippincott ,co47 ,the astronomer's real arm of precision is the filar micrometer4 ,this is shown in outline in ,fig4 #acb1 the ocular and the plate that carries it being removed so as to display the working parts4 ,it consists of a main frame aa1 carrying a slide bb1 which is moved by the screws and milled head ,b4 ,the slide bb carries the vertical spider line mm1 and usually one or more horizontal spider lines1 line mm is the so-called fixed thread of the micrometer1 movable only as a convenience to avoid shifting the telescope4 ,on bb moves the micrometer slide cc1 carrying the movable spider line nn and the comb which records1 with mm as reference line1 the whole revolutions of the micrometer screw ,c4 ,the ocular sometimes has a sliding motion of its own on cc1 to get it positioned to the best advantage4 ,in use one star is set upon mm by the screw ,b and then ,c is turned until nn bisects the other star4 ,then the exact turns and fraction of a turn can be read off on the comb and divided head of ,c1 and reduced to angular measure by the known constant of the micrometer1 usually determined by the time of passage of a nearly equatorial star along the horizontal thread when mm1 nn1 are at a definite setting apart4 7,then r 7#ae7t-t7 cos d7_/,n where r is the value of a revolution in seconds of arc1 ,n the revolutions apart of mm1 nn1 and t and d as heretofore47 ,very generally the whole system of slides is fitted to a graduated circle1 to which the fixed horizontal thread is diametral4 ,then by turning the micrometer until the horizontal threads cut the two objects under comparison1 their position angle with reference to a graduated circle can be read off4 ,this angle is conventionally counted from #j to #cfj from north around through east4 ,illustration3 ,,fig4 #acc4--;,filar ,position ,micrometer4 ,figure #acc shows the micrometer constructed by the ,clarks for their #bd inch equatorial of the ,lowell ,observatory4 ,here ,a is the head of the main micrometer screw of which the whole turns are reckoned on the counter ,h in lieu of the comb of ,fig4 #acb4 ,b is the traversing screw for the fixed wire system1 ,c the clamping screw of the position circle1 ,d its setting pinion1 ,e the rack motion for shifting the ocular1 ,f the reading glass for the position circle1 and ,g the little electric lamp for bright wire illumination4 ,the parts correspond quite exactly with the diagram of ,fig4 #acb but the instrument is far more elegant in design than the earlier forms of micrometer and fortunately rid of the oil lamps that were once in general use4 ,a small electric lamp with reflector throws a little light on the spider lines--just enough to show them distinctly4 ,or sometimes a faint light is thus diffused in the field against which the spider lines show dark4 ,commonly either type of illumination can be used and modified as occasion requires4 ,the filar micrometer is seldom used on small telescopes1 since to work easily with it the instrument should be permanently mounted and clock-driven4 ,good work was done by some of the early observers without these aids1 but at the cost of infinite pains and much loss of time4 ,the clock drive is in fact a most important adjunct of the telescope when used for other purposes than ordinary visual observations1 though for simple seeing a smooth working slow motion in ,r4 ,a4 answers well4 ,the driving clock from the horological view-point is rudimentary4 ,it consists essentially of a weight-driven1 or sometimes spring-driven1 drum1 turning by a simple gear connection a worm which engages a carefully cut gear wheel on the polar axis1 while prevented from running away by gearing up to a fast running fly-ball governor1 which applies friction to hold the clockwork down to its rate if the speed rises by a minute amount4 ,there is no pendulum in the ordinary sense1 the regularity depending on the uniformity of the total friction--that due to the drive plus that applied by the governor4 ,figure #acd shows a simple and entirely typical driving clock by ,warner ,swasey4 ,here ,a is the main drum with its winding gear at ,b1 ,c is the bevel gear1 which is driven from another carried by ,a1 and serves to turn the worm shaft ,d2 ,e marks the fly balls driven by the multiplying gearing plainly visible4 ,the governor acts at a predetermined rotation speed to lift the spinning friction disc ,f against its fixed mate1 which can be adjusted by the screw ,g4 ,the fly-balls can be slightly shifted in effective position to complete the regulation4 ,these simple clocks1 of which there are many species differing mainly in the details of the friction device1 are capable of excellent precision if the work of driving the telescope is kept light4 ,for large and heavy instruments1 particularly if used for photographic work where great precision is required1 it is difficult to keep the variations of the driving friction within the range of compensation furnished by the governor friction alone1 and in such case recourse is often taken to constructions in which the fly balls act as relay to an electrically controlled brake1 or in which the driving power is supplied by an electric motor suitably governed either continuously or periodically4 ,for such work independent hand guiding mechanism is provided to supplement the clockwork4 ,for equatorials of the smallest sizes1 say #c to #d inches aperture1 spring operated driving clocks are occasionally used4 ,the general plan of operation is quite similar to the common weight driven forms1 and where the weights to be carried are not excessive such clocks do good work and serve a very useful purpose4 ,illustration3 ,,fig4 #acd4--,typical ,driving ,clock4 7,courtesy of ,the ,clarendon ,press47 ,an excellent type of the simple spring driving clock is shown in ,fig4 #acf as constructed by ,zeiss4 ,here #a is the winding gear1 #b the friction governor1 and #c the regulating gear4 ,it will be seen that the friction studs are carried by the fly balls themselves1 somewhat as in ,fraunhofers' construction a century since1 and the regulation is very easily and quickly made by adjusting the height of the conical friction surface above the balls4 ,for heavier work the same makers generally use a powerful weight driven train with four fly-balls and electric seconds control1 sometimes with the addition of electric motor slow motions to adjust for ,r4 ,a4 in both directions4 ,illustration3 ,,fig4 #ace4--;,clark ,driving ,clock4 ,figure #ace is a rather powerful clock of analogous form by the ,clarks4 ,it differs a little in its mechanism and especially in the friction gear in which the bearing disc is picked up by a delicately set latch and carried just long enough to effect the regulation4 ,it is really remarkable that clockworks of so simple character as these should perform as well as experience shows that they do4 ,in a few instances clocks have depended on air-fans for their regulating force1 something after the manner of the driving gear of a phonograph1 but though rather successful for light work they have found little favor in the task of driving equatorials4 ,an excellent type of a second genus is the pendulum controlled driving clock due to ,sir ,david ,gill4 ,this has a powerful weight-driven train with the usual fly-ball governor4 ,but the friction gear is controlled by a contact-making seconds pendulum in the manner shown diagrammatically in ,fig4 #acg4 ,two light leather tipped rods each controlled by an electro magnet act upon an auxiliary brake disc carried by the governor spindle which is set for normal speed with one brake rod bearing lightly on it4 ,exciting the corresponding magnet relieves the pressure and accelerates the clock1 while exciting the other adds braking effect and slows it4 ,illustration3 ,,fig4 #acf4--,spring ,operated ,driving ,clock4 ,in ,fig4 #acg is shown from the original paper1 7,m4 ,n4 ,nov41 #ahgc71 the very ingenious selective control mechanism4 ,at ,p is suspended the contact-making seconds-pendulum making momentary contact by the pin ,q with a mercury globule at ,r4 ,upon a spindle of the clock which turns once a second is fixed a vulcanite disc 1 1 1 4 ,this has a rim of silver broken at the points 1 1 1 1 by ivory spacers covering #c of circumference4 ,on each side of this disc is another1 smaller1 and with a complete silver rim4 ,one1 1 is shown1 connected with the contact spring ,v2 its mate 1 on the other side contacts with ,u1 while a third contact ,k bears on the larger disc4 ,the pair of segments 1 1 and 1 1 are connected to 1 the other pair of segments to 4 ,now suppose the discs turning with the arrows3 ,if ,k rests on one of the insulated points when the pendulum throws the battery ,c ,z into circuit nothing happens4 ,if the disc is gaining on the pendulum1 ,k1 instead of resting on as shown will contact with segment 1 1 and actuate a relay via ,v1 exciting the appropriate brake magnet4 ,illustration3 ,,fig4 #acg4--,sir ,david ,gill's ,electric ,control4 ,if the disc is losing1 ,k contacts with segment 1 1 and current will pass via and ,u to a relay that operates the other brake magnet and lets the clock accelerate4 ,a fourth disc 7not shown7 on the same spindle is entirely insulated on its edge except at points corresponding to and 1 and with a contact spring like ,k4 ,if the disc is neither gaining nor losing when the pendulum makes contact1 current flows via this fourth disc and sets the relay on the mid-point ready to act when needed4 ,this clock is the prototype of divers electrically-braked driving clocks with pendulum control1 and proved beautifully precise in action1 like various kindred devices constructed since1 though the whole genus is somewhat expensive and intricate4 ,the modern tendency in driving apparatus for telescopes1 particularly large instruments1 is to utilize an electric motor for the source of power1 using a clock mechanism merely for the purpose of accurately regulating the rate of the motor4 ,we thus have the driving clock in its simplest form as a purely mechanical device worked by a sensitive fly-ball governor4 ,the next important type is that in which the clock drive is precisely regulated by a pendulum clock1 the necessary governing power being applied electrically as in ,fig4 #acg or sometimes mechanically4 ,finally we come to the type now under consideration where the instrument itself is motor driven and the function of the clock is that of regulating the motor4 ,a very good example of such a drive is the ,gerrish apparatus used for practically all the instruments at the various ,harvard observatory stations1 and which has proved extremely successful even for the most trying work of celestial photography4 ,the schematic arrangement of the apparatus is shown in ,fig4 #ach4 ,here an electric motor shown in diagram in #a1 ,fig4 #ach1 is geared down to approximately the proper speed for turning the right ascension axis of the telescope4 ,it is supplied with current either from a battery or in practice from the electric supply which may be at hand4 ,this motor is operated on a #aaj volt circuit which supplies current through the switch #b which is controlled by the low voltage clock circuit running through the magnet #c4 ,the clock circuit can be closed and opened at two points1 one controlled by the seconds pendulum #e1 the other at #g by the stud on the timing wheel geared to the motor for one revolution per second4 ,there is also a shunt around the pendulum break1 closed by the magnet switch at #f4 ,this switch is mechanically connected to the switch #b by the rod #d1 so that the pair open and close together4 ,the control operates as follows3 ,starting with the motor at rest1 the clock circuit is switched on1 switches #b1 #f being open and #g closed4 ,at the first beat of the pendulum #b1 #f closes and the current1 shunted across the loop containing #e1 holds #b closed until the motor has started and broken the clock circuit at the timer4 ,the fly-wheel carries on until the pendulum again closes the power circuit via #b1 #f1 and current stays on the motor until the timer has completed its revolution4 ,this goes on as the motor speeds up1 the periodic power supply being shortened as the timer breaks it earlier owing to the acceleration1 until the motor comes to its steady speed at which the power is applied just long enough to maintain uniformity4 ,if the motor for any cause tends to overspeed the cut-off is earlier1 while slowing down produces a longer power-period bringing the speed back to normal4 ,the power period is generally to second4 ,the power supplied to the motor is very small even in the example here shown1 only #a ampere at #aaj volts4 ,illustration3 ,,fig4 #ach4--;,diagram of ,gerrish ,electric ,control4 ,the actual proportion of a revolution during which current is supplied the motor is therefore rigorously determined by the clock pendulum1 and the motor is selected so that its revolutions are exactly timed to this clock pendulum which has no work to do other than the circuit closing1 and can hence be regulated to keep accurate time4 ,the small fly-wheel 7#i71 the weight of which is carefully adjusted with respect to the general amount of work to be done1 attached to the motor shaft1 effectively steadies its action during the process of government4 ,this ,gerrish type has been variously modified in detail to suit the instruments to which it has been applied1 always following however the same fundamental principles4 ,illustration3 ,,fig4 #aci4--;,gerrish ,drive on #bd inch ,reflector4 ,an admirable example of the application of this drive is shown in ,fig4 #aci1 the #bd inch reflector at the ,harvard ,observatory4 ,the mount is a massive open fork1 and the motor drive is seen on the right of the mount4 ,there are here two motors1 ordinary fan motors in size4 ,the right hand motor carries the fly-wheel and runs steadily on under the pendulum control4 ,the other1 connected to the same differential gear as the driving motor1 serves merely for independent regulation and can be run in either direction by the observer to speed or slow the motion in ,r4 ,a4 ,these examples of clock drive are merely typical of those which have proved to be successful in use for various service1 light and heavy4 ,there are almost innumerable variations on clocks constructed on one or another of the general lines here indicated1 so many variations in fact that one almost might say there are few driving clocks which are not in some degree special4 ,the tendency at present is for large instruments very distinctly toward a motor-driven mechanism operating on the right ascension axis1 and governed in one of a considerable variety of ways by an actual clock pendulum4 ,for smaller instruments the old mechanical clock1 often fitted with electric brake gear and now and then pendulum regulated1 is capable of very excellent work4 ,the principle of the spectroscope is rudimentarily simple1 in the familiar decomposition of white light into rainbow colors by a prism4 ,one gets the phenomena neatly by holding a narrow slit in a large piece of cardboard at arms length and looking at it through a prism held with its edge parallel to the slit4 ,if the light were not white but of a mixture of definite colors each color present would be represented by a separate image of the slit instead of the images being merged into a continuous colored band4 ,with the sun as source the continuous spectrum is crossed by the dark lines first mapped by ,fraunhofer1 each representing the absorption by a relatively cool exterior layer of some substance that at a higher temperature below gives a bright line in exactly the same position4 ,the actual construction of the astronomical spectroscope varies greatly according to its use4 ,in observations on the sun the distant slit is brought nearer for convenience by placing it in the focus of a small objective pointed toward the prisms 7the collimator7 and the spectrum is viewed by a telescope of moderate magnifying power to disclose more of detail4 ,also1 since there is extremely bright light available1 very great dispersion can be used1 obtained by several or many prisms1 so that the spectrum is both fairly wide1 7the length of the slit7 and extremely long4 ,in trying to get the spectrum of a star the source is a point1 equivalent to an extremely minute length of a very narrow slit4 ,therefore no actual slit is necessary and the chief trouble is to get the spectrum wide enough and bright enough to examine4 ,the simplest form of stellar spectroscope and the one in most common use with small telescopes is the ocular spectroscope arranged much like ,fig4 #adj4 ,this fits into the eye tube of a telescope and the ,mc,clean form made by ,browning of ,london consists of an ordinary casing with screw collar ,b1 a cylindrical lens ,c1 a direct vision prism c1 f1 c1 and an eye-cap ,a4 ,the draw tube is focussed on the star image as with any other ocular1 and the light is delivered through ,c to the prism face nearly parallel1 and thence goes to the eye1 after dispersion by the prism4 ,this consists of a central prism1 f1 of large angle1 made of extremely dense flint1 to which are cemented a pair of prisms of light crown c1 c1 with their bases turned away from that of f4 ,we have already seen that the dispersions of glasses vary very much more than their refractions so that with proper choice of materials and angles the refraction of f is entirely compensated for some chosen part of the spectrum1 while its dispersion quite overpowers that of the crown prisms and gives a fairly long available spectrum4 ,the cylindrical lens ,c merely serves to stretch out the tiny round star image into a short line thereby giving the resulting spectrum width enough to examine comfortably4 ,the weak cylindrical lens is sometimes slipped over the eye end of the prisms to give the needed width of spectrum instead of putting it ahead of the prisms4 ,a small instrument of this kind used with a telescope of #c inches to #e inches aperture gives a fairly good view of the spectra of starts above second or third magnitude1 the qualities of tolerably bright comets and nebul and so forth4 ,the visibility of stellar spectra varies greatly according to their type1 those with heavy broad bands being easy to observe1 while for the same stellar magnitude spectra with many fine lines may be quite beyond examination4 ,nevertheless a little ocular spectroscope enables one to see many things well worth the trouble of observing4 ,illustration3 ,,fig4 #adj4--,mc,clean ,ocular ,spectroscope4 ,with the larger instruments1 say #f or #h inches1 one can well take advantage of the greater light to use a spectroscope with a slit1 which gives somewhat sharper definition and also an opportunity to measure the spectrum produced4 ,an excellent type of such an instrument is that shown in ,fig4 #ada1 due to ,professor ,abb4 ,the construction is analogous to ,fig4 #adj4 ,the ocular is a ,huyghenian one with the slit mechanism 7controlled by a milled head7 at ,a in the usual place of the diaphragm4 ,the slit is therefore in the focus of the eye lens1 which serves as collimating lens4 ,above is the direct vision system ,j with the usual prisms which are slightly adjustable laterally by the screw ,p and spring ,q4 ,at ,n is a tiny transparent scale of wave lengths illuminated by a faint light reflected from the mirror ,o1 and in the focus of the little lens ,r1 which transfers it by reflection from the front face of the prism to the eye1 alongside the edge of the spectrum4 ,one therefore sees the spectrum marked off by a bright line wave-length scale4 ,illustration3 ,,fig4 #ada4--;,abb ,ocular ,spectroscope4 ,the pivot ,k and clamp ,l enable the whole to be swung side-wise so that one can look through the widened slit1 locate the star1 close the slit accurately upon it and swing on the prisms4 ,m is the clamp in position angle4 ,sometimes a comparison prism is added1 together with suitable means for throwing in spectra of gases or metals alongside that of the star1 though these refinements are more generally reserved for instruments of higher dispersion4 ,to win the advantage of accurate centering of the star in the field gained by the swing-out of the spectroscope in ,fig4 #ada simple instruments like ,fig4 #adj are sometimes mounted with an ordinary ocular in a double nose-piece like that used for microscope objectives1 so that either can be used at will4 ,any ordinary pocket spectroscope1 with or without scale or a comparison prism over part of the slit1 can in fact be fitted to an adapter and used with the star focussed on the slit and a cylindrical lens1 if necessary1 as an eye-cap4 ,such slit spectroscopes readily give the characteristics of stellar spectra and those of the brighter nebul or of comets4 ,they enable one to identify the more typical lines and compare them with terrestrial sources1 and save for solar work are about all the amateur observer finds use for4 ,for serious research a good deal more of an instrument is required1 with a large telescope to collect the light1 and means for photographing the spectra for permanent record4 ,the cumulative effect of prolonged exposures makes it possible easily to record spectra much too faint to see with the same aperture1 and exposures are often extended to many hours4 ,spectroscopes for such use commonly employ dense flint prisms of about #fj refracting angle and refractive index of about #a4fe1 one1 two1 or three of these being fitted to the instrument as occasion requires4 ,a fine example by ,brashear is shown in ,fig4 #adb1 arranged for visual work on the #bd inch ,lowell refractor4 ,here ,a is the slit1 ,b the prism box1 ,c the observing telescope1 ,d the micrometer ocular with electric lamp for illuminating the wires1 and ,e the link motion that keeps the prism faces at equal angles with collimator and observing telescope when the angle between these is changed to observe different parts of the spectrum4 ,this precaution is necessary to maintain the best of definition4 ,when photographs are to be taken the observing telescope is unscrewed and a photographic lens and camera put in its place4 ,if the brightness of the object permits1 three prisms are installed1 turning the beam #ahj into a camera braced to the same frame alongside the slit4 ,for purely photographic work1 too1 the objective prism used by ,fraunhofer for the earliest observation of stellar spectra is in wide use4 ,it is a prism fitted in front of the objective with its refracting faces making equal angles with the telescope and the region to be observed1 respectively4 ,its great advantages are small loss of light and the ability to photograph many spectra at once1 for all the stars in the clear field of the instrument leave their images spread out into spectra upon the photographic plate4 ,figure #adc shows such an objective prism mounted in front of an astrographic objective4 ,the prism is rotatable into any azimuth about the axis of the objective and by the scale i and clamping screw r can have its refracting face adjusted with respect to that axis to the best position for photographing any part of the spectrum4 ,such an arrangement is typical of those used for small instruments say from #c inches to #f inches aperture4 ,illustration3 ,,fig4 #adb4--,typical ,stellar ,spectroscope4 ,for larger objectives the prism is usually of decidedly smaller angle1 and1 if the light warrants high dispersion1 several prisms in tandem are used4 ,the objective prism does its best work when applied to true photographic objectives of the portrait lens type which yield a fairly large field4 ,it is by means of big instruments of such sort that the spectra for the magnificent ,draper ,catalogue have been secured by the ,harvard ,observatory1 mostly at the ,arequipa station4 ,in photographing with the objective prism the spectra are commonly given the necessary width for convenient examination by changing just a trifle the rate of the driving clock so that there is a slight and gradual drift in ,r4 ,a4 ,the refracting edge of the prism being turned parallel to the diurnal motion this drift very gradually and uniformly widens the spectrum to the extent of a few minutes of arc during the whole exposure4 ,when one comes to solar spectroscopy one meets an entirely different situation4 ,in stellar work the difficulty is to get enough light1 and the tendency is toward large objectives of relatively short focal length and spectroscopes of moderate dispersion4 ,in solar studies there is ample light1 and the main thing is to get an image big enough to be scrutinized in detail with very great dispersion4 ,illustration3 ,,fig4 #adc4--,simple ,objective ,prism4 ,especially is this true in the study of the chromospheric flames that rim the solar disc and blaze over its surface4 ,to examine these effectively the spectroscope should have immense dispersion with a minimum amount of stray light in the field to interfere with vision of delicate details4 ,in using a spectroscope like ,fig4 #adb1 if one turned the slit toward the landscape1 the instrument being removed from the telescope and the slit opened wide1 he could plainly see its various features1 refracted through the prism1 and appearing in such color as corresponded to the part of the spectrum in the line of the observing telescope4 ,in other words one sees refracted images quite distinctly in spite of the bending of the rays4 ,with high dispersion the image seen is practically monochromatic4 ,now if one puts the spectroscope in place1 brings the solar image tangent to the slit and then cautiously opens the slit1 he sees the bright continuous spectrum of the sky close to the sun1 plus any light of the particular color for which the observing telescope is set1 which may proceed from the edge of the solar disc4 ,thus1 if the setting is for the red line of hydrogen 7,c71 one sees the hydrogen glow that plays in fiery pillars of cloud about the sun's limb quite plainly through the opened slit1 on a background of light streaming from the adjacent sky4 ,to see most clearly one must use great dispersion to spread this background out into insignificance1 must keep other stray light out of the field1 and limit his view to the opened slit4 ,illustration3 ,,fig4 #add4--;,diagram of ,evershed ,solar ,spectroscope4 ,to these ends early solar spectroscopes had many prisms in tandem1 up to a dozen or so1 kept in proper relation by complicated linkages analogous to the simple one shown in ,fig4 #adb4 ,details can be found in almost any astronomical work of #dj years ago4 ,they were highly effective in giving dispersion but neither improved the definition nor cut out light reflected back and forth from their many surfaces4 ,of late simpler constructions have come into use of which an excellent type is the spectroscope designed by ,mr4 ,evershed and shown in diagram in ,fig4 #add4 ,here the path of the rays is from the slit through the collimator objective1 then through a very powerful direct vision system1 giving a dispersion of #cj through the visible spectrum1 then by reflection from the mirror through a second such system1 and thence to the observing telescope4 ,the mirror is rotated to get various parts of the spectrum into view1 and the micrometer screw that turns it gives means for making accurate measurement of wave lengths4 ,there are but five reflecting surfaces in the prism system 7for the cemented prism surfaces do not count for much7 as against more than #bj in one of the older instruments of similar power1 and as in other direct vision systems the spectrum lines are substantially straight instead of being strongly curved as with multiple single prisms4 ,the result is the light1 compact1 and powerful spectroscope shown complete in ,fig4 #ade1 equally well fitted for observing the sun's prominences and the detailed spectrum from his surface4 ,illustration3 ,,fig4 #ade4--;,evershed ,solar ,spectroscope4 ,in most of the solar spectroscopes made at the present time the prisms are replaced by a diffraction grating4 ,the original gratings made by ,fraunhofer were made of wire4 ,two parallel screws of extremely fine thread formed two opposite sides of a brass frame4 ,a very fine wire was then wound over these screws1 made fast by solder on one side of each1 and then cut away on the other1 so as to leave a grating of parallel wires with clear spaces between4 ,today the grating is generally ruled by an automatic ruling engine upon a polished plate of speculum metal4 ,the diamond point carried by the engine cuts very smooth and fine parallel furrows1 commonly from #aj1jjj to #bj1jjj to the inch4 ,the spaces between the furrows reflect brilliantly and produce diffraction spectra4#bb #bb ,for the principle of diffraction spectra see ,baly1 ,spectroscopy2 ,kayser1 ,handbuch d4 ,specktroskoie or any of the larger textbooks of physics4 ,when a grating is used instead of prisms the instrument is commonly set up as shown in ,fig4 #adf4 ,here ,a is the collimator with slit upon which the solar image light falls1 ,b is the observing telescope1 and ,c the grating set in a rotatable mount with a fine threaded tangent screw to bring any line accurately upon the cross wires of the ocular4 ,illustration3 ,,fig4 #adf4--;,diagram of ,grating ,spectroscope4 ,the grating gives a series of spectra on each side of the slit1 violet ends toward the slit1 and with deviations proportional to #a1 #b1 #c1 #d1 etc41 times the wave length of the line considered4 ,the spectra therefore overlap1 the ultra violet of the second order being superimposed on the extreme red of the first order and so on4 ,colored screens over the slit or ocular are used to get the overlying spectra out of the way4 ,the grating spectroscopes are very advantageous in furnishing a wide range of available dispersions1 and in giving less stray light than a prism train of equal power4 ,the spectra moreover are very nearly 8normal10 i4e41 the position of each line is proportional to its wave length instead of the blue being disproportionately long as in prismatic spectra4 ,in examining solar prominences the widened slit of a grating spectroscope shows them foreshortened or stretched to an amount depending on the angular position of the grating1 but the effect is easily reckoned4#bc #bc ,the effect on the observed height of a prominence is h h sin c_/sin t1 where h is the real height1 h the apparent height1 c the angle made by the grating face with the collimator1 and t that with the telescope 7,fig4 #adf74 ,if the slit is nearly closed one sees merely a thin line1 irregularly bright according to the shape of the prominence2 a shift of the slit with respect to the solar image shows a new irregular section of the prominence in the same monochromatic light4 ,these simple phenomena form the basis of one of the most important instruments of solar study--the spectro-heliograph4 ,this was devised almost simultaneously by ,g4 ,e4 ,hale and ,m4 ,deslandres about #cj years ago1 and enables photographs of the sun to be taken in monochromatic light1 showing not only the prominences of the limb but glowing masses of gas scattered all over the surface4 ,the principle of the instrument is very simple4 ,the collimator of a powerful grating spectroscope is provided with a slit the full length of the solar diameter1 arranged to slide smoothly on a ball-bearing carriage clear across the solar disc4 ,just in front of the photographic plate set in the focus of the camera lens is another narrow sliding slit1 which1 like a focal plane shutter1 exposes strip after strip of the plate4 ,the two slits are geared together by a system of levers or otherwise so that they move at exactly the same uniform rate of speed4 ,thus when the front slit is letting through a monochromatic section of a prominence on the sun's limb the plate-slit is at an exactly corresponding position4 ,when the front slit is exactly across the sun's center so is the plate slit1 at each element of movement exposing a line of the plate to the monochromatic image from the moving front slit4 ,the grating can of course be turned to put any required line into action but it usually is set for the ,k line 7calcium71 which is photographically very brilliant and shows bright masses of floating vapor all over the sun's surface4 ,figure #adg shows an early and simple type of ,professor ,hale's instrument4 ,here ,a is the collimator with its sliding slit1 ,b the photographic telescope with its corresponding slide and ,c the lever system which connects the slides in perfectly uniform alignment4 ,the source of power is a very accurately regulated water pressure cylinder mounted parallel with the collimator4 ,the result is a complete photograph of the sun taken in monochromatic light of exactly defined wave length and showing the precise distribution of the glowing vapor of the corresponding substance4 ,since the spectro-heliograph of ,fig4 #adg1 which shows the principle remarkably well1 there have been made many modifications1 in particular for adapting the scheme to the great horizontal and vertical fixed telescopes now in use4 7,for details of these see ,cont4 from the ,solar ,obs4 ,mt4 ,wilson1 ,nos4 #c1 #d1 #bc1 and others74 ,the chief difficulty always is to secure entirely smooth and uniform motion of the two moving elements4 ,illustration3 ,,fig4 #adg4--;,hale's ,spectro-heliograph 7,early ,form74 ,so great and interesting a branch of astronomy is the study of variable stars that some form of photometer should be part of the equipment of every telescope in serious use for celestial observation4 ,an immense amount of useful work has been done by ,argelander's systematic method of eye observation1 but it is far from being precise enough to disclose many of the most important features of variability4 ,the conventional way of reckoning by stellar magnitudes is conducive to loose measurements1 since each magnitude of difference implies a light ratio of which the log is #j4d1 i4e41 each magnitude is #b4eab times brighter than the following one4 ,as a result of this way of reckoning the light of a star of mag4 #i4i differs from one of mag4 #aj4j not by one per cent but by about nine4 ,hence to grasp light variations of small order one must be able to measure far below #j4am4 ,illustration3 ,,fig4 #adh4-;,double ,image ,stellar ,photometer4 ,the ordinary laboratory photometer enables one to compare light sources of anywhere near similar color to a probable error of well under #j4a per cent1 but it allows a comparison between sharply defined juxtaposed fields from the two illuminants1 a condition much more favorable to precision than the comparison of two points of light1 even if fairly near together4 ,stellar photometers may in principle be divided into three classes4 7#a7 ,those in which two actual stars are brought into the same field and compared by varying the light from one or both in a known degree4 7#b7 ,those which bring a real star into the field alongside an artificial star1 and again bring the two to equality by a known variation1 usually comparing two or more stars via the same artificial star2 7#c7 those which measure the light of a star by a definite method of extinguishing it entirely or just to the verge of disappearance in a known progression4 ,of each class there are divers varieties4 ,the type of the first class may be taken as the late ,professor ,e4 ,c4 ,pickering's polarizing photometer4 ,its optical principle is shown in ,fig4 #adh4 ,here the brightness of two neighboring objects is compared by polarizing at #ij apart the light received from each and reducing the resulting images to equality by an analyzing ,nicol prism4 ,the photometer is fully described1 with1 several other polarizing instruments1 in ,h4 ,a4 ,vol4 ,,ii from which ,fig4 #adh is taken4 ,a is a ,nicol prism inserted in the ocular ,b1 which revolves carrying with it a divided circle ,c read against the index ,d4 ,in the tube ,e which fits the eye end of the telescope1 is placed the double image quartz prism ,f capable of sliding either way without rotation by pulling the cord ,g4 ,with the objects to be compared in the same field1 two images of each appear4 ,by turning the analyzing ,nicol the fainter image of the brighter can always be reduced to equality with the brighter image of the fainter1 and the amount of rotation measures the required ratio of brightness4#bd ,this instrument works well for objects near enough to be in the same field of view4 ,the distance between the images can be adjusted by sliding the prism ,f back and forth1 but the available range of view is limited to a small fraction of a degree in ordinary telescopes4 #bd ,if ,a be the brightness of one object and ,b that of the other1 the reading of the index when one image disappears and the reading when the two images are equal then ,a_/,b tan7-74 ,there are four positions of the ,nicol1 #ij apart1 for which equality can be established1 and usually all are read and the mean taken4 7,h4 ,a4 ,,ii1 #a47 ,the meridian photometer was designed to avoid this small scope4 ,the photometric device is substantially the same as in ,fig4 #adh4 ,the objects compared are brought into the field by two exactly similar objectives placed at a small angle so that the images1 after passing the double image prism1 are substantially in coincidence4 ,in front of each of the objectives is a mirror4 ,the instrument points in the east and west line and the mirrors are at #de with its axis4 ,one brings ,polaris into the field1 the other by a motion of rotation about the telescope axis can bring any object in or close to the meridian into the field alongside ,polaris4 ,the images are then compared precisely as in the preceding instance4#be ,there are suitable adjustments for bringing the images into the positions required4 #be ,for full description and method see ,h4 ,a4 ,vol4 #ad1 also ,miss ,furness' admirable 8,introduction to the ,study of ,variable ,stars10 p4 #abb1 et seq4 ,some modifications are described in ,h4 ,a4 ,vol4 #bc4 ,these direct comparison photometers give results subject to some annoying small corrections1 but a vast amount of valuable work has been done with them in the ,harvard ,photometry4 ,the various forms of photometer using an artificial star as intermediary in the comparison of real stars differ chiefly in the method of varying the light in a determinate measure4 ,rather the best known is the ,zllner instrument shown in diagram in ,fig4 #adi4 ,here ,a is the eye end of the main telescope tube4 ,across it at an angle of #de is thrown a piece of plane parallel glass ,b which serves to reflect to the focus the beam from down the side tube1 ,c1 forming the artificial star4 ,illustration3 ,,fig4 #adi4--,zllner ,photometer ,diagram4 ,at the end of this tube is a small hole or more often a diaphragm perforated with several very small holes any of which can be brought into the axis of the tube4 ,beyond at ,d1 is the source of light1 originally a lamp flame1 now generally a small incandescent lamp1 with a ground glass disc or surface uniformly to diffuse the light4 ,within the tube ,c lie three ,nicol prisms n1 n#a1 n#b4 ,of these n1 is fixed with respect to the mirror ,b and forms the analyser1 which n#a and n#b turn together forming the polarizing system4 ,between n#a and n#b is a quartz plate e cut perpendicular to the crystal axis4 ,the color of the light transmitted by such a plate in polarized light varies through a wide range4 ,by turning the ,nicol n#b therefore1 the color of the beam which forms the artificial star can be made to match the real star under examination1 and then by turning the whole system n#b1 ,e1 n#a1 reading the rotation on the divided circle at ,f1 the real star can be matched in intensity by the artificial one4 ,illustration3 ,,fig4 #aej4--,wedge ,photometer4 ,this is viewed via the lens ,g and two tiny points of light appear in the field of the ocular due respectively to reflection from the front and back of the mirror ,b1 the latter slightly fainter than the former4 ,alongside or between these the real star image can be brought for a comparison1 and by turning the polarizer through an angle the images can be equalized with the real image4 ,then a similar comparison is made with a reference star4 ,if ,a be the brightness of the former and ,b of the latter then ,a_/,b sin_/sin ,the ,zllner photometer was at first set up as an alt-azimuth instrument with a small objective and rotation in altitude about the axis ,c4 ,since the general use of electric lamps instead of the inconvenient flame it is often fitted to the eye end of an equatorial4 ,another very useful instrument is the modern wedge photometer1 closely resembling the ,zllner in some respects but with a very different method of varying the light2 devised by the late ,professor ,e4 ,c4 ,pickering4 ,it is shown somewhat in diagram in ,fig4 #aej4 ,here as before ,o is the eye end of the tube1 ,b the plane parallel reflector1 ,c the side tube1 ,l the source of light ,d the diaphragm and ,a the lens forming the artificial star by projecting the hole in the diaphragm4 ,in actual practice the diameter of such hole is #a_/ajj inch or less4 ,illustration3 ,,fig4 #aea4--,simple ,polarizing ,photometer4 ,the light varying device ,w is a 8photographic wedge0 set in a frame which is graduated on the edge and moved in front of the aperture by a rack and pinion at ,r4 ,there are beside colored and shade glasses for use as occasion requires4 ,the 8photographic wedge0 is merely a strip of fine grained photographic plate given an evenly graduated exposure from end to end1 developed1 and sealed under a cover glass4 ,its absorption is permanent1 non-selective as to color1 and it can be made to shade off from a barely perceptible density to any required opacity4 ,sometimes a wedge of neutral tinted glass is used in its stead4 ,before using such a 8wedge photometer0 the wedge must be accurately calibrated by observation of real or artificial stars of known difference in brightness4 ,this is a task demanding much care and is well described1 together with the whole instrument by ,parkhurst 7,ap4 ,j4 #ac1 #bdi74 ,the great difficulty with all instruments of this general type is the formation of an artificial star the image of which shall very closely resemble the image of the real star in appearance and color4 ,obviously either the real or artificial star1 or both1 may be varied in intensity by wedge or ,nicols1 and a very serviceable modification of the ,zllner instrument1 with this in mind was recently described by ,shook 7,pop4 ,ast4 #bg1 #eie7 and is shown in diagram in ,fig4 #aea4 ,here ,a is the tube which fits the ordinary eyepiece sleeve4 ,e is a side tube into which is fitted the extension ,d with a fitting ,h at its outer end into which sets the lamp tube ,g4 ,this carries on a base plug ,f a small flash light bulb run by a couple of dry cells4 ,at ,o is placed a little brass diaphragm perforated with a minute hole4 ,between this and the lamp is a disc of diffusing glass or paper4 ,a ,nicol prism is set a little ahead of ,o1 and a lens ,l focusses the perforation at the principal focus of the telescope after reflection from the diagonal glass ,m1 as in the preceding examples4 ,i is an ordinary eyepiece over which is a rotatable ,nicol ,n with a position circle ,k4 ,at ,p is a third ,nicol in the path of the rays from the real star1 thereby increasing the convenient range of the instrument4 ,the original paper gives the details of construction as well as the methods of working4 ,obviously the same general arrangement could be used for a wedge photometer using the wedge on either real or artificial star or both4 ,the third type of visual photometer depends on reducing the light of the star observed until it just disappears4 ,this plan was extensively employed by ,professor ,pritchard of ,oxford some #dj years ago4 ,he used a sliding wedge of dark glass1 carefully calibrated1 and compared two stars by noting the point on the wedge at which each was extinguished4 ,a photographic wedge may be used in exactly the same way4 ,another device to the same end depends on reducing the aperture of the telescope by a 8cat's eye10 an iris diaphragm1 or similar means until the star is no longer visible or just disappearing4 ,the great objection to such methods is the extremely variable sensitivity of the eye under varying stimulus of light4 ,the most that can be said for the extinction photometer is that in skillful and experienced hands like ,pritchard's it has sometimes given much more consistent readings than would be expected4 ,it is now and then very convenient for quick approximation but by no courtesy can it be considered an instrument of precision either in astronomical or other photometry4#bf #bf ,the general order of precision attained by astronomical photometers is shown in the discovery1 photographically1 by ,hertzsprung in #aiaa1 that ,polaris1 used as a standard magnitude for many years1 is actually a variable4 ,its period is very near to four days1 its photographic amplitude #j4ag and its visual amplitude about #j4a1 i4e41 a variation of #e per cent in the light was submerged in the observational uncertainties1 although once known it was traced out in the accumulated data without great difficulty4 ,the photometer question should not be closed without referring the reader to the methods of physical photometry as developed by ,stebbins1 ,guthnick and others4 ,the first of these depends on the use of the selenium cell in which the electrical resistance falls on exposure of the selenium to light4 ,the device is not one adapted to casual use1 and requires very careful nursing to give the best results1 but these are of an order of precision beyond anything yet reached with an astronomical visual photometer4 ,settings come down to variations of something like #b per cent1 and variations in stellar light entirely escaping previous methods become obvious4 ,the photoelectric cell depends on the lowering of the apparent electric resistance of a layer of rarified inert gas between a platinum grid and an electrode of metallic potassium or other alkali metal when light falls on that electrode4 ,the rate of transmission of electricity is very exactly proportional to the illumination1 and can be best measured by a very sensitive electrometer4 ,the results are extraordinarily consistent1 and the theoretical 8probable error0 is very small1 though here1 as elsewhere1 8probable error0 is a rather meaningless term apt to lead to a false presumption of exactness4 ,again the apparatus is somewhat intricate and delicate1 but gives a precision of working if anything a little better than that of the selenium cell1 quite certainly below #a per cent4 ,neither instrument constitutes an attachment to the ordinary telescope of modest size which can be successfully used for ordinary photometry1 and both require reduction of results to the basis of visual effect4#bg ,but both offer great promise in detecting minute variations of light and have done admirable work4 ,for a good fundamental description of the selenium cell photometer see ,stebbins1 ,ap4 ,j4 #cb1 #ahe and for the photoelectric method see ,guthnick ,a4 ,n4 #aif1 #ceg also ,a4 ,f4 and ,f4 ,a4 ,lindemann1 ,m4 ,n4 #ci1 #cdc4 ,the volume by ,miss ,furness already referred to gives some interesting details of both4 #bg ,such apparatus is essentially appurtenant to large instruments only1 say of not less than #ab aperture and preferably much more4 ,the eye is enormously more sensitive as a detector of radiant energy than any device of human contrivance1 and thus small telescopes can be well used for visual photometry1 the bigger instruments having then merely the advantage of reaching fainter stars4 ,,chapter ,,ix ,,the ,,care ,,and ,,testing ,,of ,,telescopes ,a word at the start concerning the choice and purchase of telescopes4 ,the question of refractors vs4 reflectors has been already considered4 ,the outcome of the case depends on how much and how often you are likely to use the instrument1 and just what you want it for4 ,for casual observations and occasional use--all that most busy buyers of telescopes can expect--the refractor has a decided advantage in convenience4 ,if one has leisure for frequent observations1 and particularly if he can give his telescope a permanent mount1 and is going in for serious work1 he will do well not to dismiss the idea of a reflector without due deliberation4 ,in any case it is good policy to procure an instrument from one of the best makers4 ,and if you do not buy directly of the actual maker it is best to deal with his accredited agents4 ,in other words avoid telescopes casually picked up in the optical trade unless you chance to have facilities for thorough testing under competent guidance before purchase4 ,no better telescopes are made than can be had from the best ,american makers4 ,a few ,british and ,german makers are quite in the same class4 ,so few high grade ,french telescopes reach this country as to cause a rather common1 but actually unjust1#bh belief that there are none4 #bh ,e4 g41 the beautiful astrographic and other objectives turned out by the brothers ,henry4 ,if economy must be enforced it is much wiser to try to pick up a used instrument of first class manufacture than to chance a new one at a low price4 ,now and then a maker of very ordinary repute may turn out a good instrument1 but the fact is one to be proved--not assumed4 ,age and use do not seriously deteriorate a telescope if it has been given proper care4 ,some of ,fraunhofer's are still doing good service after a century1 and occasionally an instrument from one of the great makers comes into the market at a real bargain4 ,it may drift back to the maker for resale1 or turn up at any optician's shop1 and in any case is better worth looking at than an equally cheap new telescope4 ,the condition of the tube and stand cuts little figure if they are mechanically in good shape4 ,most of the older high grade instruments were of brass1 beautifully finished and lacquered1 and nothing looks worse after hard usage4 ,it is essential that the fitting of the parts should be accurate and that the focussing rack should work with the utmost smoothness4 ,a fault just here1 however1 can be remedied at small cost4 ,the mount1 whatever its character1 should be likewise smooth working and without a trace of shakiness1 unless one figures on throwing it away4 ,as to the objective1 it demands very careful examination before a real test of its optical qualities4 ,the objective with its cell should be taken out and closely scrutinized in a strong light after the superficial dust has been removed with a camel's hair brush or by wiping very gently with the soft ,japanese 8lens paper0 used by opticians4 ,one is likely to find plenty to look at2 spots1 finger marks1 obvious scratches1 and what is worse a network of superficial scratches1 or a surface with patches looking like very fine pitting4 ,these last two defects imply the need of repolishing the affected surface1 which means also more or less refiguring4 ,ordinary brownish spots and finger marks can usually be removed with little trouble4 ,the layman1 so to speak1 is often warned never to remove the cell from a telescope but he might as well learn the simpler adjustments first as last4 ,in taking off a cell the main thing is to see what one is about and to proceed in an orderly manner4 ,if the whole cell unscrews1 as often is the case in small instruments1 the only precaution required is to put a pencil mark on the cell and its seat so that it can be screwed back to where it started4 ,if as is more usual the cell fits on with three pairs of screws1 one of each pair will form an abutment against which its mate pulls the cell4 ,a pencil mark locating the position of the head of each of the pulling screws enables one to back them out and replace them without shifting the cell4 ,the first inspection will generally tell whether the objective is worth further trouble or not4 ,if all surfaces save the front are in good condition it may pay to send the objective to the maker for repolishing4 ,if more than one surface is in bad shape reworking hardly pays unless the lens can be had for a nominal figure4 ,in buying a used instrument from its original source these precautions are needless as the maker can be trusted to stand back of his own and to put it in first class condition4 ,however1 granted that the objective stands well the inspection for superficial defects1 it should then be given a real test for figure and color correction1 bearing in mind that objectives1 even from first class makers1 may now and then show slightly faulty corrections1 while those from comparatively unknown sources may now and then turn out well4 ,in this matter of necessary testing old and new glasses are quite on all fours save that one may safely trust the maker with a well earned reputation to make right any imperfections4 ,cleansing other than dusting off and cautiously wiping with damp and then dry lens paper requires removal of the lenses from their cell which demands real care4 ,with a promising looking objective1 old or new1 the first test to be applied is the artificial star--artificial rather than natural since the former stays put and can be used by day or by night4 ,for day use the 8star0 is merely the bright reflection of the sun from a sharply curved surface--the shoulder of a small round bottle1 a spherical flask silvered on the inside1 a small silvered ball such as is used for ,christmas tree decoration1 a bicycle ball1 or a glass 8alley0 dear to the heart of the small boy4 ,the object1 whatever it is1 should be set up in the sun against a dark background distant say #dj or #ej times the focal length of the objective to be tested4 ,the writer rather likes a silvered ball cemented to a big sheet of black cardboard4 ,at night a pin hole say #a_/cb inch or less in diameter through cardboard or better1 tinfoil1 with a flame1 or better a gas filled incandescent lamp behind it1 answers well4 ,the latter requires rather careful adjustment that the projected area of the closely coiled little filament may properly fill the pinhole just in front of it4 ,now if one sets up the telescope and focusses it approximately with a low power the star can be accurately centered in the field4 ,then if the eyepiece is removed1 the tube racked in a bit1 and the eye brought into the focus of the objective1 one can inspect the objective for stri4 ,if these are absent the field will be uniformly bright all over4 ,not infrequently however one will see a field like ,fig4 #aeb or ,fig4 #aec4 ,the former is the appearance of a #d inch objective that the author recently got his eye upon4 ,the latter shows typical stri of the ordinary sort4 ,an objective of glass as bad as shown in ,fig4 #aeb gives no hope of astronomical usefulness1 and should be relegated to the porch of a seashore cottage4 ,figure #aec may represent a condition practically harmless though undesirable4 ,the next step is a really critical examination of the focal image4 ,using a moderately high power ocular1 magnifying say #ej to the inch of aperture1 the star should be brought to the sharpest focus possible and the image closely examined4 ,if the objective is good and in adjustment this image should be a very small spot of light1 perfectly round1 softening very slightly in its brilliancy toward the edge1 and surrounded by two or three thin1 sharp1 rings of light1 exactly circular and with well defined dark spaces separating them4 ,illustration3 ,,fig4 #aeb4--;,a ,bad ,case of ,stri4 ,illustration3 ,,fig4 #aec4--,ordinary ,stri4 ,often from the trembling of the air the rings will seem shaky and broken1 but still well centered on the star-disc4 ,the general appearance is that shown in ,fig4 #aed4bi #bi ,this and several of the subsequent figures are taken from quite the best account of testing objectives3 8,on the ,adjustment and ,testing of ,telescope ,objectives40 ,t4 ,cooke ,sons1 ,york1 #ahia1 a little brochure unhappily long since out of print4 ,a new edition is just now1 #aibb1 announced4 ,illustration3 ,,fig4 #aed4--;,a ,first ,class ,star ,image4 ,instead1 several very different appearances may turn up4 ,first1 the bright diffraction rings may be visible only on one side of the central disc1 which may itself be drawn out in the same direction4 ,second1 the best image obtainable may be fairly sharp but angular or irregular instead of round or oval and perhaps with a hazy flare on one side4 ,third1 it may be impossible to get a really sharp focus anywhere1 the image being a mere blob of light with nothing definite about it4 ,one should be very sure that the eyepiece is clean and without fault before proceeding further4 ,as to the first point a bit of lens paper made into a tiny swab on a sliver of soft wood will be of service1 and the surfaces should be inspected with a pocket lens in a good light to make sure that the cleaning has been thorough4 ,turning the ocular round will show whether any apparent defects of the image turn with it4 ,in the first case mentioned the next step is to rack the ocular gently out when the star image will expand into a more or less concentric series of bright interference rings separated by dark spaces1 half a dozen or so resulting from a rather small movement out of focus4 ,if these rings are out of round and eccentric like ,fig4 #aee one has a clear case of failure of the objective to be square with the tube1 so that the ocular looks at the image askew4 ,illustration3 ,,fig4 #aee4--;,effect of ,objective ,askew4 ,in the ordinary forms of objective this means that the side of the objective toward the brighter and less expanded part of the ring system is too near the ocular4 ,this can be remedied by pushing that side of the objective outwards a trifle4 ,easing off the pulling screw on that side and slightly tightening the abutment screw makes the needed correction1 which can be lessened if over done at the first trial1 until the ring system is accurately centered4 ,it is a rather fussy job but not at all difficult if one remembers to proceed cautiously and to use the screw driver gently4 ,illustration3 ,,fig4 #aef4--;,effect of ,flaws in ,objective4 ,in the second case1 racking out the ocular a little gives a ring system which exaggerates just the defects of the image4 ,the faults may be due to mechanical strain of the objective in its cell1 which is easily cured1 or to strains or flaws in the glass itself1 which are irremediable4 ,therefore one should1 with the plane of the objective horizontal1 loosen the retaining ring that holds the lenses1 without disturbing them1 and then set it back in gentle contact and try the out of focus rings once more4 ,if there is no marked improvement the fault lies in the glass and no more time should be wasted on that particular objective4 ,fig4 #aef is a typical example of this fault4 ,in dealing with case three it is well to give the lens a chance by relieving it of any such mechanical strains1 for now and then they will apparently utterly ruin the definition1 but the prognosis is very bad unless the objective has been most brutally mishandled4 ,in any case failure to give a sharply defined focus in a very definite plane is a warning that the lens 7or mirror7 is rather bad4 ,in testing a reflector some pains must be taken at the start with both the main and the secondary mirror4 ,using an artificial star as before1 one should focus and look sharply to the symmetry of the image1 taking care to leave the instrument in observing position and screened from the sun for an hour or two before testing4 ,reflectors are much more sensitive to temperature than refractors and take longer to settle down to stability of figure4 ,with a well mounted telescope of either sort a star at fair altitude on a fine night gives even better testing conditions than an artificial star1 7,polaris is good in northern latitudes7 but one may have a long wait4 ,if the reflector is of good figure and well adjusted1 the star image1 in focus or out1 has quite the same appearance as in a refractor except that with a bright star in focus one sees a thin sharp cross of light centered on the image1 rather faint but perfectly distinct4 ,this is due to the diffraction effect of the four thin strips that support the small mirror1 and fades as the star is put out of focus4 ,the rings then appear as usual1 but also a black disc due to the shadowing of the small mirror4 ,fig4 #aeg shows the extra-focal image of a real or artificial star when the mirror is well centered1 and the star in the middle of the field4 ,there only are the rings round and concentric with the mirror spot4 ,the rings go out of round and the spot out of center for very small departure from the middle of the field when the mirror is of large relative aperture--,f_/#e or ,f_/#f4 ,illustration3 ,,fig4 #aeg4--;,extra-focal ,image from ,reflector4 ,if the star image shows flare or oval out-of-focus rings when central of the field1 one or both mirrors probably need adjustment4 ,before laying the trouble to imperfect figure1 the mirrors should be adjusted1 the small one first as the most likely source of trouble4 ,the side of the mirror toward which the flare or the expanded side of the ring system projects should be slightly pushed away from the ocular4 7,note that owing to the reflection this movement is the reverse of that required with a refractor47 ,if the lack of symmetry persists one may as well get down to first principles and center the mirrors at once4 ,perhaps the easiest plan is to prepare a disc of white cardboard exactly the size of the mirror with concentric circles laid out upon it and an eighth inch hole in the center4 ,taking out the ocular and putting a half inch stop in its place one can stand back1 lining up the stop with the draw tube1 and see whether the small mirror looks perfectly round and is concentric with the reflected circles4 ,if not1 a touch of the adjusting screws will be needed4 ,then with a fine pointed brush dot the center of the mirror itself through the hole1 with white paint4 ,then1 removing the card1 one will see this dot accurately centered in the small mirror if the large one is in adjustment1 and it remains as a permanent reference point4 ,if the dot be eccentric it can be treated as before1 but by the adjusting screws of the large mirror4 ,the final adjustment can then be made by getting a slightly extra-focal star image fairly in the center of the field with a rather high power and making the system concentric as before described4 ,this sounds a bit complicated but it really is not4 ,if the large mirror is not in place1 its counter cell may well be centered and levelled by help of a plumb line from the center of the small mirror and a steel square1 as a starting point1 the small mirror having been centered as nearly as may be by measurement4#cj #cj ,sometimes with ever so careful centering the ring system in the middle of the field is still eccentric with respect to the small mirror1 showing that the axis of the parabola is not perpendicular to the general face of the mirror4 ,this can usually be remedied by the adjusting screws of the main mirror as described1 but now and then it is necessary actually to move over the small mirror into the real optical axis4 ,draper 7loc4 cit47 gives some experiences of this sort4 ,so much for the general adjustment of the objective or mirror4 ,its actual quality is shown only on careful examination4 ,as a starting point one may take the extra-focal system of rings given by an objective or mirror after proper centering4 ,if the spherical aberration has thoroughly removed the appearance of the rings when expanded so that six or eight are visible should be like ,fig4 #aeh4 ,the center should be a sharply defined bright point and surrounding it1 and exactly concentric1 should be the interference rings1 truly circular and gradually increasing in intensity outwards1 the last being very noticeably the strongest4 ,one can best make the test when looking through a yellow glass screen which removes the somewhat confusing flare due to imperfect achromatism and makes the appearances inside and outside focus closely similar4 ,just inside or outside of focus the appearance should be that of ,fig4 #aei for a perfectly corrected objective or mirror4 ,illustration3 ,,fig4 #aeh4--;,correct ,extra-focal ,image4 ,sometimes an objective will be found in which one edge of the focussed star image is notably red and the opposite one tinted with greenish or bluish1 showing unsymmetrical coloring1 still more obvious when the image is put a little out of focus4 ,this means that the optical centers of crown and flint are out of line from careless edging of the lenses or very bad fitting4 ,the case is bad enough to justify trying the only remedy available outside the optician's workshop--rotating one lens upon the other and thus trying the pair in different relative azimuths4 ,the initial positions of the pair must be marked plainly1 care must be taken not to displace the spacers #abj apart often found at the edges of the lenses1 and the various positions must be tried in an orderly manner4 ,one not infrequently finds a position in which the fault is negligible or disappears altogether1 which point should be at once marked for reference4 ,illustration3 ,,fig4 #aei4--;,correct ,image ,just ,out of ,focus4 ,in case there is uncorrected spherical aberration there is departure from regular gradation of brightness in the rings4 ,if there is a 8short edge10 i4e41 spherical aberration1 so that rays from the outer zone come to a focus too short1 the edge ring will look too strong within focus1 and the inner rings relatively weak2 with this appearance reversed outside focus4 ,a 8long edge0 i4e41 - spherical aberration1 shows the opposite condition1 edge rings too strong outside focus and too weak within4 ,both are rather common faults4 ,the 8long edge0 effect is shown in ,figs4 #afj and #afa1 as taken quite close to focus4 ,it takes a rather sharp eye and considerable experience to detect small amounts of spherical aberration2 perhaps the best way of judging is in quickly passing from just inside to just outside focus and back again1 using a yellow screen and watching very closely for variations in brightness4 ,truth to tell a small amount of residual aberration1 like that of ,fig4 #afj1 is not a serious matter as regards actual performance--it hurts the telescopist's feelings much more than the quality of his images4 ,illustration3 ,,fig4 #afj4--,spherical ,aberration ,just ,inside ,focus4 ,illustration3 ,,fig4 #afa4--,spherical ,aberration ,just ,outside ,focus4 ,a much graver fault is zonal aberration1 where some intermediate zone of objective or mirror comes to a focus too long or too short1 generally damaging the definition rather seriously1 depending on the amount of variation in focus of the faulty zone4 ,a typical case is shown in ,fig4 #afb taken within focus4 ,here two zones are abnormally strong showing1 just as in the case of simple spherical aberration1 too short focus4 ,outside of focus the intensities would change places1 the outer and midway zones and center being heavy1 and the strong zones of ,fig4 #afb weak4 ,these zonal aberrations are easily detected and are rather common both in objectives and mirrors1 though rarely as conspicuous as in ,fig4 #afb4 ,another failing is the appearance of astigmatism1 which1 broadly1 is due to a refracting or reflecting surface which is not a surface of revolution and therefore behaves differently for rays incident in different planes around its optical axis4 ,in its commonest form the surface reflects or refracts more strongly along one plane than along another at right angles to it4 ,hence the two have different foci and there is no point focus at all1 but two line foci at right angles4 ,figs4 #afc and #afd illustrate this fault1 the former being taken inside and the latter outside focus1 under fairly high power4 ,if a star image is oval and the major axis of this oval has turned through #ij when one passes to the other side of focus1 astigmatism is somewhere present4 ,as more than half of humanity is astigmatic1 through fault of the eye1 one should twist the axis of the eyes some #ij around the axis of the telescope and look again4 ,if the axis of the oval has turned with the eyes a visit to the oculist is in order4 ,if not1 it is worth while rotating the ocular4 ,if the oval does not turn with it that particular telescope requires reworking before it can be of much use4 ,this astigmatism due to fault of figure must not be confused with the astigmatic difference of the image surfaces referred to in ,chapter ,,iv which is zero on the axis and not of material importance in ordinary telescopes4 ,astigmatism of figure on the contrary is bad everywhere and always4 ,it should be especially looked out for in reflecting surfaces1 curved or plane1 since it is a common result of flexure4 ,passing on now from these simple tests for figure1 chromatic aberration has to be examined4 ,nothing is better than an artificial star formed by the sun in daylight1 for the preliminary investigation4 ,at night ,polaris is advantageous for this as for other tests4 ,illustration3 ,,fig4 #afb4--;,a ,case of ,zonal ,aberration4 ,illustration3 ,,fig4 #afc4--;,astigmatism ,inside ,focus4 ,illustration3 ,,fig4 #afd4--;,astigmatism ,outside ,focus4 ,the achromatization curves1 ,fig4 #afc1 really tell the whole story of what is to be seen4 ,when the telescope is carefully focussed for the bright part of the spectrum1 getting the sharpest star image attainable1 the central disc1 small and clean1 should be yellowish white1 seen under a power of #fj or #gj per inch of aperture4 ,but the red and blue rays have a longer focus and hence rim the image with a narrow purplish circle varying slightly in hue according to the character of the achromatization4 ,pushing the ocular a little inside1 focus1 the red somewhat overbalances the blue and the purple shades toward the red4 ,pulling out the ocular very slightly one brings the deep red into focus as a minute central red point1 just as the image begins to expand a little4 ,further outside focus a bluish or purplish flare fills the center of the field1 while around it lies a greenish circle due to the rays from the middle of the secondary spectrum expanding from their shorter focus4 ,in an under-corrected objective this red point is brighter and the fringe about the image1 focussed or within focus1 is conspicuously reddish4 ,heavy overcorrection gives a strong bluish fringe and the red point is dull or absent4 ,with a low power ocular1 unless it be given a color correction of its own1 any properly corrected objective will seem under-corrected as already explained4 ,the color correction can also be well examined by using an ocular spectroscope like ,fig4 #adj1 with the cylindrical lens removed4 ,examining the focussed star image thus1 the spectrum is a narrow line for the middle color of the secondary spectrum1 widening equally at ,f and ,b1 and expanding into a sort of brush at the violet end4 ,conversely1 when moved outside focus until the width is reduced to a narrow line at ,f and ,b1 the widening toward the yellow and green shows very clearly the nature and extent of the secondary spectrum4 ,in this way too1 the actual foci for the several colors can easily be measured4 ,the exact nature of the color correction is somewhat a matter of taste and of the uses for which the telescope is designed1 but most observers agree in the desirability of the ,b-,f correction commonly used as best balancing the errors of eye and ocular4 ,with reflectors1 achromatic or even over-corrected oculars are desirable4 ,the phenomena in testing a telescope for color vary with the class of star observed--the solar type is a good average4 ,trying a telescope on ,lyr emphasizes unduly the blue phases1 while ,orionis would overdo the red4 ,the simple tests on star discs in and out of focus here described are ample for all ordinary purposes1 and a glass which passes them well is beyond question an admirably figured one4 ,the tests are not however quantitative1 and it takes an experienced eye to pick out quickly minor errors1 which are somewhat irregular4 ,one sometimes finds the ring system excellent but a sort of haze in the field1 making the contrasts poor--bad polish or dirt1 but figure good4 ,a test found very useful by constructors or those with laboratory facilities is the knife edge test1 worked out chiefly by ,foucault and widely used in examining specula4 ,it consists in principle of setting up the mirror so as to bring the rays to the sharpest possible focus4 ,for instance in a spherical mirror a lamp shining through a pin hole is placed in the centre of curvature1 and the reflected image is brought just alongside it where it can be inspected by eye or eyepiece4 ,in ,fig4 #afe all the rays which emanate from the pinhole b and fall on the mirror a are brought quite exactly to focus at c4 ,the eye placed close to c will see1 if the mirror surface is perfect1 a uniform disc of light from the mirror4 ,illustration3 ,,fig4 #afe4--,the ,principle of the ,foucault ,test4 ,if now a knife edge like d1 say a safety razor blade1 be very gradually pushed through the focus the light will be cut off in a perfectly uniform manner--no zone or local spot going first4 ,if some error in the surface at any point causes the reflected ray to miss the focus and cross ahead of or behind it as in the ray bef1 then the knife edge will catch it first or last as the case may be1 and the spot e will be first darkened or remain bright after the light elsewhere is extinguished4 ,illustration3 ,,fig4 #aff4--;,foucault ,test of ,parabolic ,mirror4 ,one may thus explore the surface piecemeal and detect not only zones but slight variations in the same zone with great precision4 ,in case of a parabolic mirror as in ,fig4 #aff the test is made at the focus by aid of the auxiliary plane mirror1 and a diagonal as shown1 the pinhole and knife edge being arranged quite as before4 ,a very good description of the practical use of the knife edge test may be found in the papers of ,dr4 ,draper and ,mr4 ,ritchey already cited4 ,it is also applied to refractors1 in which case monochromatic light had better be used1 and enables the experimenter to detect even the almost infinitesimal markings sometimes left by the polishing tool1 to say nothing of slight variations in local figure which are continually lost in the general illumination about the field when one uses the star test in the ordinary manner4 ,the set-up for the knife edge experiments should be very steady and smooth working to secure precise results1 and it therefore is not generally used save in the technique of figuring mirrors1 where it is invaluable4 ,with micrometer motions on the knife edge1 crosswise and longitudinally1 one can make a very exact diagnosis of errors of figure or flexure4 ,a still more delicate method of examining the perfection of figuring is found in the ,hartmann test4 7,zeit4 fur ,instk41 #aijd1 #aiji74 ,this is essentially a photographic test1 comparing the effect of the individual zones of the objective inside and outside of focus4 ,not only are the effects of the zones compared but also the effects of different parts of the same zone1 so that any lack of symmetry in performance can be at once found and measured4 ,the ,hartmann test is shown diagrammatically in ,fig4 #afg4 ,the objective is set up for observing a natural or artificial star4 ,just in front of it is placed an opaque screen perforated with holes1 as shown in section by ,fig4 #afg1 where ,a is the perforated screen4 ,the diameters of the holes are about #a_/bj the diameter of the objective as the test is generally applied1 and there are usually four holes #ij apart for each zone4 ,and such holes are not all in one line1 but are distributed symmetrically about the screen1 care being taken that each zone shall be represented by holes separated radially and also tangentially1 corresponding to the pairs of elements in the two astigmatic image surfaces1 an arrangement which enables the astigmatism as well as figure to be investigated4 ,illustration3 ,,fig4 #afg4--,the ,principle of the ,hartmann ,test4 ,the arrangement of holes actually found useful is shown in ,hartmann's original papers1 and also in a very important paper by ,plaskett 7,ap4 ,j4 #be #aie7 which contains the best account in ,english of ,hartmann's methods and their application4 ,now each hole in the screen transmits a pencil of light through the objective at the corresponding point1 and each pencil comes to a focus and then diverges1 the foci being distributed somewhere in the vicinity of what one may regard as the principal focus1 ,b4 ,for instance in ,fig4 #afg are shown five pairs of apertures a1 a1 b1 b1 etc41 in five different zones4 ,now if a photographic plate be exposed a few inches inside focus as at ,c each pencil from an aperture in the screen will be represented by a dot on the photograph1 at such distance from the axis and from the corresponding dot on the other side of the axis as the respective inclinations of the pencils of light may determine4 ,similarly a plate exposed at approximately equal distance on the other side of the general focus1 as at ,d1 will show a pattern of dots due to the distribution of the several rays at a point beyond focus4 ,now if all the pencils from the several apertures met at a common focus in ,b1 the two patterns on the plates ,c and ,d would be exactly alike and for equal distance away from focus of exactly the same size4 ,in general the patterns will not exactly correspond1 and the differences measured with the micrometer show just how much any ray in question has departed from meeting at an exact common focus with its fellows4 ,for instance in the cut it will be observed that the rays e and a focus barely beyond ,c and by the time they reach ,d are well spread apart4 ,the relative distance of the dots upon these corresponding plates1 with the distance between the plates1 shows exactly at what point between ,c and ,d these particular rays actually did cross and come to a focus4 ,determining this is merely a matter of measuring up similar triangles1 for the path of the rays is straight4 ,similarly inspection will show that the rays d and d meet a little short of ,b1 and measurement of their respective records on the plates ,c and ,d would show the existence of a zone intermediate in focus between the focus of e1e and the general focus at ,b4 ,the exact departure of this zone from correct focus can therefore be at once measured4 ,a little further examination discloses the fact that the outer zone represented by the rays a1b1 and a1b has not quite the same focus at the two extremities of the same diameter of the objective4 ,in other words the lens is a little bit flatter at one end of this diameter than it is at the other1 so that the rays here have considerably longer focus than they should1 a fault by no means unknown although fortunately not very common4 ,it will be seen that the variations between the two screen patterns on ,c and ,d1 together with the difference between them1 give accurately the performance of each point of the objective represented by an aperture in the screen4 ,and similar investigations by substantially the same method may be extended to the astigmatic variations1 to the general color correction1 and to the difference in the aberrations for the several colors4 ,the original papers cited should be consulted for the details of applying this very precise and interesting test4 ,it gives an invaluable record of the detailed corrections of an objective1 and while it is one with which the ordinary observer has little concern there are times when nothing else can give with equal precision the necessary record of performance4 ,there are divers other tests used for one purpose or another in examining objectives and mirrors1 but those here described are ample for nearly all practical purposes1 and indeed the first two commonly disclose all that it is necessary to know4 ,now and then one has to deal with an objective which is unmitigatedly dirty4 ,it can be given a casual preliminary cleaning in the way already mentioned1 but sometimes even this will not leave it in condition for testing4 ,then one must get down to the bottom of things and make a thorough job of it4 ,the chief point to remember in undertaking this is that the thing which one is cleaning is glass1 and very easy to scratch if one rubs dust into it1 but quite easy to clean if one is careful4 ,the second thing to be remembered is that once cleaned it must be replaced as it was before and not in some other manner4 ,the possessor of a dirty objective is generally advised to take it to the maker or some reliable optician4 ,if the maker is handy1 or an optician of large experience in dealing with telescope objectives is available1 the advice is good1 but there is no difficulty whatever in cleaning an objective with the exercise of that ordinary care which the user of a telescope may be reasonably expected to possess4 ,it is a fussy job1 but not difficult1 and the best advice as to how to clean a telescope objective is to 8tub0 it1 literally1 if beyond the stage where the superficial wiping described is sufficient4 ,to go about the task one first sets down the objective in its cell on a horizontal surface and removes the screws that hold in the retaining ring1 or unscrews the ring itself as the case may be4 ,this leaves the cell and objective with the latter uppermost and free to be taken out4 ,prepare on a table a pad of anything soft1 a little smaller than the objective1 topping the pad with soft and clean old cloth2 then1 raising up the cell at an edge1 slip the two thumbs under it and lay the fingers lightly on the outer lens of the objective1 then invert the whole affair upon the pad and lift off the cell1 leaving the objective on its soft bed4 ,before anything else is done the edge of the objective should be marked with a hard lead pencil on the edge of both the component lenses1 making two well defined v's with their points touching4 ,also1 if1 as usual1 there are three small separators between the edges of the flint and crown lenses1 mark the position of each of these #a1 #b1 #c1 with the same pencil4 ,forming another convenient pad of something soft1 lift off the upper lens1 take out the three separators and lay them in order on a sheet of paper without turning them upside down4 ,mark alongside each1 the serial number denoting its position4 ,then when these spacers1 if in good condition1 are put back1 they will go back in the same place rightside up1 and the objective itself will go back into place unchanged4 ,now have at hand a wooden or fibre tub or basin which has been thoroughly washed out with soap and water and wiped dry4 ,half fill it with water slightly lukewarm and with a good mild toilet soap1 shaving soap for example1 with clean hands and very soft clean cloth1 go at one of the lenses and give it a thorough washing4 ,after this it should be rinsed very thoroughly and wiped dry4 ,as to material for wiping1 the main thing is that it must be soft and free from dust that will scratch4 ,old handkerchiefs serve a good turn4 ,dr4 ,brashear years ago in describing this process recommended cheese cloth4 ,the present day material that goes under this name is far from being as soft at the start as it ought to be1 and only the best quality of it should be used1 and then only after very thorough soaking1 rinsing and drying4 ,the very soft towels used for cleaning cut glass1 if washed thoroughly clean and kept free from dust1 answer perfectly well4 ,the cheese cloth has the advantage of being comparatively cheap so that it can be thrown away after use4 ,whatever the cloth1 it should be kept1 after thorough washing and drying1 in a closed jar4 ,rinsing the lens thoroughly and wiping it clean and dry is the main second stage of cleansing4 ,it sometimes will be found to be badly spotted in a way which this washing will not remove4 ,sometimes the spotting will yield to alcohol carefully rubbed on with soft absorbent cotton or a bunch of lens paper4 ,if alcohol fails the condition of the surface is such as to justify trying more strenuous means4 ,nitric acid of moderate strength rubbed on with a swab of absorbent cotton will sometimes clear up the spotting4 ,if this treatment be used it should be followed up with a #aj per cent solution of pure caustic potash or moderately strong c4p4 ammonia and then by very thorough rinsing4 ,glass will stand without risk cautious application of both acid and alkali1 but the former better than the latter4 ,then a final rinsing and drying is in order4 ,many operators use a final washing with alcohol of at least #ij per cent strength which is allowed to evaporate with little or no wiping4 ,alcohol denatured with methyl alcohol serves well if strong enough but beware denatured alcohol of unknown composition4 ,others have used petroleum naphtha and things of that sort4 ,at the present time these commercial petroleum products are extremely uncertain in quality1 like gasoline1 being obtained1 ,heaven knows how1 from the breaking down of heavier petroleum products4 ,if pure petroleum ether can be obtained it answers quite as well as alcohol1 but unless the volatile fluid is pure it may leave streaks4 ,ordinarily neither has to be used1 as after the proper wiping the glass comes perfectly clean4 ,this done the glass can be replaced on the pad whence it came and its mate put through the same process4 ,flint glass is more liable to spot than the crown1 but the crown is by no means immune against the deterioration of the surface1 perhaps incipient devitrification1 and during the war many objectives 8went blind0 from unexplained action of this character4 ,as a rule the soap and water treatment applied with care leaves even a pretty hard looking specimen of objective in fairly good condition except for the scratches which previous users have put upon it4 ,then if the spacing pieces1 usually of tinfoil1 are not torn or corroded they can be put back into place1 the one lens superimposed upon the other1 and the pair put back into the cell by dropping it gently over them and re-inverting the whole1 taking care this time to have soft cloth or lens paper under the fingers4 ,then the retaining ring can be put into place again and the objective is ready for testing or use as the case may be4 ,if the spacers are corroded or damaged it may be necessary to replace them with very thin tinfoil cut the same size and shape1 leaving however a little extra length to turn down over the edge of the lower lens4 ,they are fastened in place on the extreme edge only by the merest touch of mucilage1 shellac or ,canada balsam1 whichever comes to hand4 ,the one important thing is that the spacers should be entirely free of the sticky material where they lap over the edge of the lens to perform the separation4 ,this lap is generally not over #a_/af of an inch1 not enough to show at the outside of the objective when it is in its cell4 ,when the upper lens is lightly pressed down into place1 after the gum or shellac is dry1 all the projecting portion can be trimmed away with a sharp pen-knife leaving simply the spacers in the appointed places from which the original ones were removed4 ,some little space has been given to this matter of cleaning objectives1 as in many situations objectives accumulate dirt rather rapidly and it is highly desirable for the user to learn how to perform the simple but careful task of cleansing them4 ,in ordinary use1 when dirt beyond the reach of mere dusting with a camel's hair brush has stuck itself to the exterior of an objective1 a succession of tufts of absorbent cotton or wads of lens paper at first dampened with pure water or alcohol and then followed lightly1 after the visible dirt has been gently mopped up1 by careful wiping with the same materials1 will keep the exterior surface in good condition1 the process being just that suggested in the beginning of this chapter as the ordinary cleaning up preparatory to a thorough examination4 ,the main thing to be avoided in the care of a telescope1 aside from rough usage generally1 is getting the objective wet and then letting it take its chances of drying4 ,in many climates dew is a very serious enemy and the customary dew cap three or four diameters long1 bright on the outside and blackened within1 is of very great service in lessening the deposit of dew upon the glass4 ,also the dew cap keeps out much stray light that might otherwise do mischief by brightening the general field4 ,in fact its function as a light-trap is very important especially if it is materially larger in diameter than the objective and provided with stops4 ,the finder should be similarly protected1 otherwise it will mysteriously go blind in the middle of an evening's work due to a heavy deposit of moisture on the objective4 ,the effect is an onset of dimness and bad definition which is altogether obnoxious4 ,as regards the metal parts of a telescope they should be treated like the metal parts of any other machine1 while the moving parts require from time to time a little touch of sperm or similar oil like every other surface where friction may occur4 ,the old fashioned highly polished and lacquered brass tube was practically impossible to keep looking respectably well provided it was really used to any considerable extent4 ,about the most that could be done to it was dusting when dusty1 and cautiously and promptly wiping off any condensed moisture4 ,the more modern lacquered tubes require very little care and if they get in really bad condition can be relacquered without much expense or difficulty4 ,wooden tubes1 occasionally found in old instruments1 demand the treatment which is accorded to other highly finished wooden things1 occasional rubbing with oil or furniture polish according to the character of the original surface4 ,painted tubes may occasionally require a fresh coat1 which it does not require great skill to administer4 ,if the surface of wooden tripods comes to be in bad shape it needs the oil or polish which would be accorded to other well finished wooden articles4 ,mountings are usually painted or lacquered and either surface can be renewed eventually at no great trouble4 ,bright parts may be lightly touched with oil as an ordinary rust preventive4 ,reflecting telescopes are considerably more troublesome to keep in order than refractors owing to the tender nature of the silvered surface4 ,it may remain in good condition with fairly steady use for several years or it may go bad in a few months or a few weeks4 ,the latter is not an unusual figure in telescopes used about a city where smoke is plentiful4 ,the main thing is to prevent the deposit of dew on the mirror1 or getting it wet in any other way1 for in drying off the drops almost invariably leave spots4 ,many schemes have been proposed for the prevention of injury to the mirror surface4 ,a close fitting metal cover1 employed whenever the mirror is not in use1 has given good results in many places4 ,where conditions are extreme this is sometimes lined with a layer of dry absorbent cotton coming fairly down upon the mirror surface1 and if this muffler is dry1 clean1 and a little warmer than the mirror when put on1 it seems to be fairly effective4 ,preferably the mirror should be kept1 when not in use1 at a little higher temperature than the surrounding air so that dew will not tend to deposit upon it4 ,as to actual protective measures the only thing that seems to be really efficient is a very thin coating of lacquer1 first tried by ,perot at the ,paris ,observatory4 ,the author some ten years since took up the problem in protecting some laboratory mirrors against fumes and moisture and found that the highest grade of white lacquer1 such as is used for the coating of fine silverware in the trade1 answered admirably if diluted with six or eight volumes of the thinner sold with such commercial lacquers4 ,it is best to thin the lacquer to the requisite amount and then filter4 ,if now a liberal amount of the mixture is poured upon the mirror surface after careful dusting1 swished quickly around1 and the mirror is then immediately turned up on edge to drain and dry1 a very thin layer of lacquer will be left upon it1 only a fraction of a wave length thick1 so that it shows broad areas of interference colors4 ,treated in this way and kept dry the coating will protect the brilliancy of the silver for a good many months even under rather unfavorable circumstances4 ,after trying out the scheme rather thoroughly the treatment was applied to the #bd inch reflector of the ,harvard ,observatory and has been in use ever since4 ,the author applied the first coating in the spring of #aiac1 and since that time it has only been necessary to resilver perhaps once in six months as against about as many weeks previously4 ,the lacquer used in this case was the so-called 8,lastina0 lacquer made by the ,egyptian ,lacquer ,company of ,new ,york1 but there are doubtless others of similar grade in the market4 ,it is a collodion lacquer and in recent years it has proved desirable to use as a thinner straight commercial amylacetate rather than the thinner usually provided with the lacquer1 perhaps owing to the fact that difficulty of obtaining materials during the war may have caused1 as in so many other cases1 substitutions which1 while perfectly good for the original purpose did not answer so well under the extreme conditions required in preserving telescope mirrors4 ,the lacquer coating when thinned to the extent here recommended does not apparently in any way deteriorate the definition as some years of regular work at ,harvard have shown4 ,some experimenters have1 however1 found difficulty1 quite certainly owing to using too thick a lacquer4 ,the endurance of a lacquer coating where the mirror is kept free from moisture1 and its power to hold the original brilliancy of the surface is very extraordinary4 ,the writer took out and tested one laboratory mirror coated seven years before1 and kept in a dry place1 and found the reflecting power still a little above 4#gj1 despite the fact that the coating was so dry as to be almost powdery when touched with a tuft of cotton4 ,at the start the mirror had seen some little use unprotected and its reflection coefficient was probably around 4#hj4 ,if the silver coating is thick as it can be conveniently made1 on a well coated mirror1 the coat of lacquer1 when tarnish has begun1 can be washed off with amylacetate and tufts of cotton until the surface is practically clear of it1 and the silver itself repolished by the ordinary method and relacquered4 ,there are many silvering processes in use and which one should be chosen for re-silvering a mirror1 big or little1 is quite largely a matter of individual taste1 and more particularly experience4 ,the two most used in this country are those of ,dr4 ,brashear and ,mr4 ,lundin1 head of the ,alvan ,clark ,corporation1 and both have been thoroughly tried out by these experienced makers of big mirrors4 ,the two processes differ in several important particulars but both seem to work very successfully4 ,the fundamental thing in using either of them is that the glass surface to be silvered should be chemically clean4 ,the old silver1 if a mirror is being resilvered1 is removed with strong nitric acid which is very thoroughly rinsed off after every trace of silver has been removed4 ,sometimes a second treatment with nitric acid may advantageously follow the first with more rinsing4 ,the acid should be followed by a #aj per cent solution of c4p4 caustic potash 7some operators use c4p4 ammonia as easier to clear away7 rinsed off with the utmost thoroughness4 ,on general principles the last rinsing should be with distilled water and the glass surface should not be allowed to dry between this rinsing and starting the silvering process1 but the whole mirror should be kept under water until the time for silvering4 ,in ,dr4 ,brashear's process the following two solutions are made up2 first the reducing solution as follows3 ,rock candy1 #bj parts by weight4 ,strong nitric acid 7spec4 gr4 #a4bb71 #a part4 ,alcohol1 #bj parts4 ,distilled water1 #bjj parts4 ,this improves by keeping and if this preparation has to be hurried the acid1 sugar and distilled water should be boiled together and then the alcohol added after the solution is cooled4 ,second1 make up the silvering solution in three distinct portions2 first the silver solution proper as follows3 #a4 #b parts silver nitrate4 #bj parts distilled water4 ,second1 the alkali solution as follows3 #b4 #a parts c4p4 caustic potash4 #bj parts distilled water4 ,third1 the reserve silver solution as follows3 #c4 part silver nitrate4 #af parts distilled water4 ,the working solution of silver is then prepared thus3 ,gradually add to the silver solution ,no4 #a the strongest ammonia1 slowly and with constant stirring4 ,at first the solution will turn dark brown and then it will gradually clear up4 ,ammonia should be added only just to the point necessary to clear the solution4 ,then add ,no4 #b1 the alkali solution4 ,again the mixture will turn dark brown and must be cautiously cleared once more with ammonia until it is straw colored but clear of precipitate4 ,finally add ,no4 #c1 the reserve solution1 very cautiously with stirring until the solution grows darker and begins to show traces of suspended matter which will not stir out4 ,then filter the whole through absorbent cotton to free it of precipitate and it is ready for use4 ,one is then ready for the actual silvering4 ,now there are two ways of working the process1 with the mirror face up1 or face down4 ,the former is advantageous in allowing better inspection of the surface as it forms1 and also it permits the mirror of a telescope to be silvered without removing it from the cell1 as was in fact done habitually in case of the big reflector of the ,alleghany ,observatory where the conditions were such as to demand re-silvering once a month4 ,the solution was kept in motion during the process by rocking the telescope as a whole4 ,when silvering face up the mirror is made to form the bottom of the silvering vessel1 being fitted with a wrapping of strong paraffined or waxed paper or cloth1 wound several times around the rim of the mirror and carried up perhaps half the thickness of the mirror to form a retainer for the silvering solution4 ,this band is firmly tied around the edge of the mirror making a water tight joint4 ,ritchey uses a copper band fitted to the edge of the mirror and drawn tight by screws1 and finishes making tight with paraffin and a warm iron4 ,in silvering face down the mirror is suspended a little distance above the bottom of a shallow dish1 preferably of earthen ware1 containing the solution4 ,various means are used for supporting it4 ,thus cleats across the back cemented on with hard optician's pitch answer well for small mirrors1 and sometimes special provision is made for holding the mirror by the extreme edge in clamps4 ,silvering face down is in some respects less convenient but does free the operator from the very serious trouble of the heavy sediment which is deposited from the rather strong silver solution4 ,this is the essential difficulty of the ,brashear process in silvering face up4 ,the trouble may be remedied by very gentle swabbing of the surface under the liquid with absorbent cotton1 from the time when the silver coating begins fairly to form until it is completed4 ,the ,brashear process is most successfully worked at a temperature between #fe and #gj ,f4 and some experience is required to determine the exact proportion of the reducing solution to be added to the silvering solution4 ,ritchey advises such quantity of the reducing solution as contains of sugar one-half the total weight of the silver nitrate used4 ,the total amount of solution after mixing should cover the mirror about an inch deep4 ,too much increases the trouble from sediment and fails to give a clean coating4 ,the requisite quantity of reducing solution is poured into the silvering solution and then immediately1 if the mirror is face up1 fairly upon it1 without draining it of the water under which it has been standing4 ,if silvering face down the face will have been immersed in a thin layer of distilled water and the mixed solutions are poured into the dish4 ,in either case the solution is rocked and kept moving pretty thoroughly until the process is completed which will take about five minutes4 ,if silvering is continued too long there is likelihood of an inferior whitish outer surface which will not polish well1 but short of this point the thicker the coat the better1 since a thick coat stands reburnishing where a thin one does not and moreover the thin one may be thin enough to transmit some valuable light4 ,when the silvering is done the solution should be rapidly poured off1 the edging removed or the mirror lifted out of the solution1 rinsed off first with tap water and then with distilled1 and swabbed gently to clear the remaining sediment4 ,then the mirror can be set up on edge to dry4 ,a final flowing with alcohol and the use of a fan hastens the process4 ,in ,lundin's method the initial cleaning process is the same but after the nitric acid has been thoroughly rinsed off the surface is gently but thoroughly rubbed with a saturated solution of tin chloride1 applied with a wad of absorbent cotton4 ,after the careful rubbing the tin chloride solution must be washed off with the utmost thoroughness1 preferably with moderately warm water4 ,it is just as important to get off the tin chloride completely1 as it is to clean completely the mirror surface by its use4 ,otherwise streaks may be left where the silvering will not take well4 ,when the job has been properly done one can wet the whole surface with a film of water and it will stay wet even when the surface is slightly tilted4 ,as in the ,brashear process the mirror must be kept covered with water4 ,mr4 ,lundin always silvers large mirrors face up1 and forms the dish by wrapping around the edge of the mirror a strip of bandage cloth soaked in melted beeswax and smoothed off by pulling it while still hot between metal rods to secure even distribution of the wax so as to make a water tight joint4 ,this rim of cloth is tied firmly around the edge of the mirror and the strings then wet to draw them still tighter4 ,meanwhile the water should cover the mirror by of an inch or more4 ,it is to be noted that in the ,lundin process ordinary water is usually found just as efficient as distilled water1 but it is hardly safe to assume that such is the case1 without trying it out on a sample of glass4 ,there are then prepared two solutions1 a silver solution1 #b4af parts silver nitrate 7see ,king1 ,pop4 ,ast #cj1 #ic7 #ajj parts water4 and a reducing solution1 #d parts ,merck's formaldehyde #bj parts water4 ,this latter quantity is used for each #ajj parts of the above silver solution1 and the whole quantity made up is determined by the amount of liquid necessary to cover the mirror as just described4 ,the silver solution is cautiously and completely cleared up by strong ammonia as in the ,brashear process4 ,the silver and reducing solutions are then mixed1 the water covering the mirror poured quickly off1 and the silvering solution immediately poured on4 ,the mirror should then be gently rocked and the silver coating carefully watched as it forms4 ,as the operation is completed somewhat coarse black grains of sediment will form and when these begin to be in evidence the solution should be poured off1 the mirror rinsed in running water1 the edging removed while the mirror is still rinsing and finally the sediment very gently swabbed off with wet absorbent cotton4 ,then the mirror can be set up to dry4 ,the ,lundin process uses a considerably weaker silver solution than the ,brashear process1 is a good deal more cleanly while in action1 and is by experienced workers said to perform best at a materially lower temperature than the ,brashear process1 with the mirror1 however1 always slightly warmer than the solution4 ,some workers have had good results by omitting the tin chloride solution and cleaning up the surface by the more ordinary methods4 ,in the ,lundin process the solution is sufficiently clear for the density acquired by the silver coating to be roughly judged by holding an incandescent lamp under the mirror4 ,a good coating should show at most only the faintest possible outline of the filament1 even of a gas filled lamp4 ,whichever process of silvering is employed1 and both work well1 the final burnishing of the mirror after it is thoroughly dry is performed in the same way1 starting by tying up a very soft ball of absorbent cotton in the softest of chamois skin4 ,this burnisher is used at first without any addition1 simply to smooth and condense the film by going over it with quick1 short1 and gentle circular strokes until the entire surface has been thoroughly cleaned and begins to show a tendency to take polish4 ,then a very little of the finest optical rouge should be put on to the same1 or better another1 rubber1 and the mirror gone steadily over in a similar way until it comes to a brilliant polish4 ,a good deal of care should be taken in performing this operation to avoid the settling of dust upon the surface since scratches will inevitably result4 ,great pains should also be taken not to take any chance of breathing on the mirror or in any other way getting the surface in the slightest degree damp4 ,otherwise it will not come to a decent polish4 ,numerous other directions for silvering will be found in the literature1 and all of them have been successfully worked at one time or another4 ,the fundamental basis of the whole process is less in the particular formula used than in the most scrupulous care in cleaning the mirror and keeping it clean until the silvering is completed4 ,also a good bit of experience is required to enable one to perform the operation so as to obtain a uniform and dense deposit4 ,,chapter ,x ,,setting ,,up ,,and ,,housing ,,the ,,telescope ,in regard to getting a telescope into action and giving it suitable protection1 two entirely different situations present themselves4 ,the first relates to portable instruments or those on temporary mounts1 the second to instruments of position4 ,as respects the two1 the former ordinarily implies general use for observational purposes1 the latter at least the possibility of measurements of precision1 and a mount usually fitted with circles and with a driving clock4 ,portable telescopes may have either alt-azimuth or equatorial mounting1 while those permanently set up are now quite universally equatorials4 ,portable telescopes are commonly small1 ranging from about #b inches to about #e inches in aperture4 ,the former is the smallest that can fairly be considered for celestial observations4 ,if thoroughly good and well mounted even this is capable of real usefulness1 while the five inch telescope if built and equipped in the usual way1 is quite the heaviest that can be rated as portable1 and deserves a fixed mount4 ,setting up an alt-azimuth is the simplest possible matter4 ,if on a regular tripod it is merely taken out and the tripod roughly levelled so that the axis in azimuth is approximately vertical4 ,now and then one sets it deliberately askew so that it may be possible to pass quickly between two objects at somewhat different altitudes by swinging on the azimuth axis4 ,if one is dealing with a table tripod like ,fig4 #fi it should merely be set on any level and solid support that may be at hand1 the main thing being to get it placed so that one may look through it conveniently4 ,this is a grave problem in the case of all small refractors1 which present their oculars in every sort of unreachable and uncomfortable position4 ,of course a diagonal eyepiece promises a way out of the difficulty1 but with small apertures one hesitates to lose the light1 and often something of definition1 and the observer must pretty nearly stand on his head to use the finder4 ,with well adjusted circles1 such are commonly found on a fixed mount1 location of objects is easy4 ,on a portable set-up perhaps the easiest remedy is a pair of well aligned coarse sights near the objective end of the tube and therefore within reach when it is pointed zenith-ward4 ,the writer has found a low1 armless1 cheap splint rocker1 such as is sold for piazza use1 invaluable under these painful circumstances1 and can cordially recommend it4 ,even better is an observing box and a flat cushion4 ,the box is merely a coverless affair of any smooth inch stuff firmly nailed or screwed together1 and of three unequal dimensions1 giving three available heights on which to sit or stand4 ,the dimensions originally suggested by ,chambers 7,handbook of ,astronomy1 ,,ii1 #bae7 were #ba #ab #ae inches1 but the writer finds #ah #aj #ad inches a better combination4 ,the fact is that the ordinary stock telescope tripod is rather too high for sitting1 and too low for standing1 comfortably4 ,a somewhat stubby tripod is advantageous both in point of steadiness and in accessibility of the eyepiece when one is observing within #cj of the zenith1 where the seeing is at its best2 and a sitting position gives a much greater range of convenient upward vision than a standing one4 ,when an equatorial mount is in use one faces the question of adjustment in its broadest aspect4 ,again two totally different situations arise in using the telescope4 ,first is the ordinary course of visual observation for all general purposes1 in which no precise measurements of position or dimensions are involved4 ,here exact following is not necessary1 a clock drive is convenient rather than at all indispensable1 and even circles one may get along without at the cost of a little time4 ,such is the usual situation with portable equatorials4 ,one does not then need to adjust them to the pole with extreme precision1 but merely well enough to insure easy following2 otherwise one is hardly better off than with an alt-azimuth4 ,in a totally different class falls the instrument with which one undertakes regular micrometric work1 or enters upon an extended spectroscopic program or the use of precise photometric apparatus1 to say nothing of photography4 ,in such cases a permanent mount is almost imperative1 the adjustments must be made with all the exactitude practicable1 one finds great need of circles1 and the lack of a clock drive is a serious handicap or worse4 ,moreover in this latter case one usually has1 and needs1 some sort of timepiece regulated to sidereal time1 without which a right ascension circle is of very little use4 ,in broad terms1 then1 one has to deal1 first2 with a telescope on a portable mount1 with or without position circles1 generally lacking both sidereal clock and driving clock1 and located where convenience dictates2 second1 with a telescope on a fixed mount in a permanent location1 commonly with circles and clock1 and with some sort of permanent housing4 ,let us suppose then that one is equipped with a #e inch instrument like ,fig4 #afh1 having either the tripod mount1 or the fixed pillar mount shown alongside it2 how shall it be set up1 and1 if on the fixed mount1 how sheltered8 ,in getting an equatorial into action the fundamental thing is to place the optical axis of the telescope exactly parallel to the polar axis of the mount and to point the latter as nearly as possible at the celestial pole4 ,the conventional adjustments of an equatorial telescope are as follows3 #a4 ,adjust polar axis to altitude of pole4 #b4 ,adjust index of declination circle4 #c4 ,adjust polar axis to the meridian4 #d4 ,adjust optical axis perpendicular to declination axis4 #e4 ,adjust declination axis perpendicular to polar axis4 #f4 ,adjust index of right ascension circle1 and #g4 ,adjust optical axis of finder parallel to that of telescope4 ,now let us take the simplest and commonest case1 the adjustment of a portable equatorial on a tripod mount1 when the instrument has a finder but neither circles nor driving clock4 ,adjustments #b and #f automatically drop out of sight1 #e vanishes for lack of any means to make the adjustment1 and on a mount made with high precision1 like the one before us1 #d is negligible for any purpose to which our instrument is applicable4 ,adjustments #a1 #c and #g are left and these should be performed in the order #g1 #a1 #c1 for sake of simplicity4 ,to begin with the finder has cross-wires in the focus of its eyepiece1 and the next step is to provide the telescope itself with similar cross-wires4 ,these can readily be made1 if not provided1 by cutting out a disc of cardboard to fit snugly either the spring collar just in front of a positive eyepiece or the eyepiece itself at the diaphragm1 if an ordinary ,huygenian4 ,rule two diametral lines on the circle struck for cutting the cardboard1 crossing at the center1 cut out the central aperture1 and then very carefully stretch over it1 guided by the diametral lines1 two very fine threads or wires made fast with wax or shellac4 ,illustration3 ,,fig4 #afh4--;,clark #e-;inch with ,tripod and ,pier4 ,now pointing the telescope at the most distant well defined object in view1 rotate the spring collar or ocular1 when1 if the crossing of the threads is central1 their intersection should stay on the object4 ,if not shift a thread cautiously until the error is corrected4 ,keeping the intersection set on the object by clamping the tube1 one turns attention to the finder4 ,either the whole tube is adjustable in its supports or the cross-wires are capable of adjustment by screws just in front of the eyepiece4 ,in either case finder tube or cross-wires should be shifted until the latter bear squarely upon the object which is in line with the cross threads of the main telescope4 ,then the adjusting screws should be tightened1 and the finder is in correct alignment4 ,as to adjustments #a and #c1 in default of circles the ordinary astronomical methods are not available1 but a pretty close approximation can be made by levelling4 ,a good machinist's level is quite sensitive and reliable4 ,the writer has one picked out of stock at a hardware shop that is plainly sensitive to #b of arc1 although the whole affair is but four inches long4 ,most mounts like the one of ,fig4 #afh have a mark ruled on the support of the polar axis and a latitude scale on one of the cheek pieces4 ,adjustment of the polar axis to the correct altitude is then made by placing the level on the declination axis1 or any other convenient place1 bringing it to a level1 and then adjusting the tripod until the equatorial head can be revolved without disturbing this level4 ,then set the polar axis to the correct latitude and adjustment number #a is complete for the purpose in hand4 ,lacking a latitude scale1 it is good judgment to mark out the latitude by the help of the level and a paper protractor4 ,to do this level the polar axis to the horizontal1 level the telescope tube also1 and clamp it in declination to maintain it parallel4 ,then fix the protractor to a bit of wood tied or screwed to the telescope support1 drop a thin thread plumb line from a pin driven into the wood1 the declination axis being still clamped1 note the protractor reading1 and then raise the polar axis by the amount of the latitude4 ,next1 with a knife blade scratch a conspicuous reference line on the sleeve of the polar axis and its support so that when the equatorial head is again levelled carefully you can set approximately to the latitude at once4 ,now comes adjustment #c1 the alignment of the polar axis to the meridian4 ,one can get it approximately by setting the telescope tube roughly parallel with the polar axis and1 sighting along it1 shifting the equatorial head in azimuth until the tube points to the pole star4 ,then several methods of bettering the adjustment are available4 ,at the present date ,polaris is quite nearly #a #jg from the true pole and describes a circle of that radius about it every #bd hours4 ,to get the correct place of the pole with reference to ,polaris one must have at least an approximate knowledge of the place of that star in its little orbit1 technically its hour-angle4 ,with a little knowledge of the stars this can be told off in the skies almost as easily as one reckons time on a clock4 ,fig4 #afi is1 in fact1 the face of the cosmic clock1 with a huge sweeping hour hand that he who runs may read4 ,illustration3 ,,fig4 #afi4--,the ,cosmic ,clock4 ,it is a clock in some respects curious2 it has a twenty-four hour face like some clocks and watches designed for ,continental railway time2 the hour hand revolves backward1 78counter-clockwise07 and it stands in the vertical not at noon1 but at #a4bj ,star ,time4 ,the two stars which mark the tip and the reverse end of the hour hand are delta ,cassiope and zeta ,urs ,majoris respectively4 ,the first is the star that marks the bend in the back of the great 8chair10 the second 7,mizar71 the star which is next to the end of the 8dipper0 handle4 ,one or the other is above the horizon anywhere in the northern hemisphere4 ,further1 the line joining these two stars passes almost exactly through the celestial pole1 and also very nearly through ,polaris1 which lies between the pole and ,cassiope4 ,consequently if you want to know the hour-angle of ,polaris just glance at the clock and note where on the face ,cassiope stands1 between the vertical which is ,,xxiv o'clock1 and the horizontal1 which is ,,vi 7east7 or ,,xviii 7west7 o'clock4 ,you can readily estimate its position to the nearest half hour1 and knowing that the great hour hand is vertical 7 ,cassiope up7 at ,ih #bjm or 7 ,urs ,majoris up7 at ,,xiiih #bjm1 you can make a fairly close estimate of the sidereal time4 ,a little experience enables one to make excellent use of the clock in locating celestial objects1 and knowledge of the approximate hour angle of ,polaris thus observed can be turned to immediate use in making adjustment #c4 ,to this end slip into the plane of the finder cross wires a circular stop of metal or paper having a radius of approximately #a #ae which means a diameter of #j4eb inch per foot of focal length4 ,then1 leaving the telescope clamped in declination as it was after adjustment #a1 turn it in azimuth across the pole until the pole star enters the field which1 if the finder inverts it will do on the other side of the center2 i4e4 if it stands at ,,iv to the naked eye it will enter the field apparently from the ,,xvi o'clock quarter4 ,when just comfortably inside the field1 the axis of the telescope is pointing substantially at the pole4 ,it is better to get ,polaris in view before slipping in the stop and if it is clearly coming in too high or too low shift the altitude of the polar axis a trifle to correct the error4 ,this approximate setting can be made even with the smallest finder and on any night worth an attempt at observation4 ,with a finder of an inch or more aperture a very quick and quite accurate setting to the meridian can be made by the use of ,fig4 #agj1 which is a chart of all stars of #h mag4 or brighter within #a #cj of the pole4 ,there are only three stars besides ,polaris at all conspicuous in this region1 one quite close to ,polaris1 the other two forming with it the triangle marked on the chart4 ,these two are1 to the left1 a star of magnitude #f4d designated ,b4 ,d4 #hh #aab1 and to the right one of magnitude #g4j1 ,b4 ,d4 #hi #ac4 ,the position of the pole for the rest of the century is marked on the vertical arrow and with the stars in the field of the finder one can set the cross wires on the pole1 the instrument remaining clamped in declination1 within a very few minutes of arc1 quite closely enough for any ordinary use of a portable mount4 ,all this could be done even better with the telescope itself1 but it is very rare to find an eyepiece with sufficient field4 ,illustration3 ,,fig4 #agj4--,the ,pole among the ,stars4 ,at all events the effect of any error likely to be made in these adjustments is not serious for the purpose in hand1 since if one makes an error of a minute of arc in the setting the resulting displacement of a star in the field will even in the most unfavorable case reach this full amount only after #f hours following4 ,i4e4 with any given eyepiece an error of adjustment equal to the radius of the field will still permit following a star for an hour or two before it drifts inconveniently wide of the center4 ,considerable space has been devoted to these easy approximations in setting up1 since the directions commonly given require circles and often a clock drive4 ,in some cases one has to set up a portable equatorial where from necessity for clear sky space1 ,polaris is not visible4 ,the best plan then is to set up with great care where ,polaris can be seen1 paying especial attention to the levelling4 ,then establish two meridian marks on stakes at a convenient distance by turning the telescope #ahj on its declination axis and sighting through it in both directions4 ,now with a surveyor's tape transfer the meridian line ,east or ,west as the case may be until it can be used where there is clear sky room4 ,few observers near a city can get good sky room1 from the interference of houses1 trees or blazing street lamps1 and the telescope must often be moved from one site to another to reach different fields4 ,in such case it is wise to take the very first step toward giving the telescope a local habitation by establishing a definite placement for the tripod4 ,to this end the three legs should be firmly linked together by chains that will not stretch--leg directly to leg1 and not to a common junction4 ,then see to it that each leg has a strong and moderately sharp metal point1 and1 the three points of support being thus definitely fixed1 establish the old reliable point-slot-plane bearing as follows3 ,lay out at the site 7or sites7 giving the desired clear view1 a circle scratched on the ground of such size that the three legs of your tripod may rest approximately on its periphery4 ,then lay out on the circle three points #abj apart4 ,at each point sink a short post #ab to #ah inches long and of any convenient diameter1 well tarred1 and firmly set with the top levelled off quite closely horizontal4 ,to the top of each bolt a square or round of brass or iron about half an inch thick4 ,the whole arrangement is indicated in diagram in ,fig4 #aga4 ,in a sink a conical depression such as is made by drilling nearly through with a #a inch twist drill4 ,the angle here should be a little broader than the point on the tripod leg4 ,in b have planed a ,v shaped groove of equally broad angle set with its axis pointing to the conical hole in a4 ,leave the surface of c a horizontal plane4 ,now if you set a tripod leg in a1 another in the slot at b and the third on c1 the tripod will come in every instance to the same level and orientation4 ,so1 if you set up your equatorial carefully in the first place and leave the head clamped in azimuth1 you can take it in and replace it at any time still in adjustment as exact as at the start4 ,and if it is necessary to shift from one location to another you can do it without delay still holding accurate adjustment of the polar axis to the pole1 and avoiding the need of readjustment4 ,in case the instrument has a declination circle the original set-up becomes even simpler4 ,one has only to level the tripod1 either with or without the equatorial head in place1 and then to set the polar axis either vertical or horizontal1 levelling the tube with it either by placing the level across the objective cell perpendicular to the declination axis1 or laying it along the tube when horizontal4 ,illustration3 ,,fig4 #aga4--;,a ,permanent ,foothold for the ,tripod4 ,then1 reading the declination circle1 one can set off the co-atitude or latitude as the case may be and1 leaving the telescope clamped in declination1 lower or raise the polar axis until the tube levels to the horizontal4 ,when the mount does not permit wide adjustment and has no latitude scale one is driven to laying out a latitude templet and1 placing a straight edge under the equatorial head1 or suspending a plumb line from the axis itself1 setting it mechanically to latitude4 ,now suppose we are dealing with the same instrument1 but are planning to plant it permanently in position on its pillar mount4 ,it is now worth while to make the adjustments quite exactly1 and to spend some time about it4 ,the pillar is commonly assembled by well set bolts on a brick or concrete pier4 ,the preliminary steps are as already described4 ,the pillar is levelled across the top1 the equatorial head1 which turns upon it in azimuth1 is levelled as before1 the adjustment being made by metal wedges under the pillar or by levelling screws in the mount if there are any4 ,then the latitude is set off by the scale1 or by the declination circle1 and the polar axis turned to the approximate meridian as already described4 ,there is likely to be an outstanding error of a few minutes of arc which should in a permanent mount be reduced as far as practicable4 ,at the start adjust the declination of the optical axis of the telescope to that of the polar axis4 ,this is done in the manner suggested by ,fig4 #agb4 ,here p is the polar axis and d the declination axis4 ,now if one sights1 using the cross wires1 through the telescope a star near the meridian1 i4e41 one that is changing in declination quite slowly1 starting from the position ,a with the telescope ,e4 of the polar axes1 and turns it over #ahj into the position ,b1 ,w4 of the polar axis1 the prolongation of the line of sight1 b1 will fall below a1 when as here the telescope points too high in the ,a position4 ,illustration3 ,,fig4 #agb4--;,aligning the ,optical ,axis4 ,in other words the apparent altitude of the star will change by twice the angle between ,a and p4 ,read both altitudes on the declination circle and split the difference with the slow motion as precisely as the graduation of the declination circle permits4 ,the telescope will probably not now point exactly at the star1 but as the tube is swung from the ,a to the ,b position and back the visible stars will describe arcs of circles which should be nearly concentric with the field as defined by the stop in the eyepiece4 ,if not1 a very slight touch on the declination slow motion one way or the other will make them do so to a sufficient exactness1 especially if a rather high power eyepiece is used4 ,the optical axis of the telescope is now parallel to the polar axis1 but the latter may be slightly out of position in spite of the preliminary adjustment4 ,now reverting to the polar field of ,fig4 #agj1 swing from position ,a to ,b and back again1 correcting any remaining eccentricity of the star arcs around the pole by cautious shifting of the polar axis1 leaving the telescope clamped in declination4 ,the first centering is around the pole of the instrument1 the second around the celestial pole by help of a half dozen small stars within a half degree on both sides of it1 magnitudes #i and #aj1 easily visible in a #c0 or #d0 telescope1 using the larger field of the finder for the coarse adjustment4 ,if the divided circles read to single minutes or closer1 which they generally do not on instruments of moderate size1 one can use the readings to set the polar axis and the declination circle1 and to make the other adjustments as well4 ,in default of this help1 the declination circle adjustment may be set to read #ij when the optical axis is brought parallel to the polar axis1 and after the adjustment of the latter is complete1 the ,r4 ,a4 circle can be set by swinging up the telescope in the meridian and watching for the transit of any star of known ,r4 ,a4 over the central cross wire1 at which moment the circle should be clamped to the ,r4 ,a4 thus defined4 ,two possible adjustments are left1 the perpendicularity of the polar and declination axes1 and that of the optical axis to the declination axis4 ,as a rule there is no provision for either of these1 which are supposed to have been carried out by the maker4 ,the latter adjustment if of any moment will disclose itself as a lateral wobble in trying to complete the adjustment of optical axis to polar axis4 ,it can be remedied by a liner of tinfoil or even paper under one end of the tube's bearing on its cradle4 ,adjustment of the former is strictly a job for the maker4 ,for details of the rigorous adjustments on the larger instruments the reader will do well to consult ,loomis' ,practical ,astronomy page #bh and following4#ca ,the adjustments here considered are those which can be effectively made without driving clock1 finely divided circles1 or exact knowledge of sidereal time4 ,the first and last of these auxiliaries1 however1 properly belong with an instrument as large as ,fig4 #afh1 on a fixed mount4 #ca ,see also two valuable papers by ,sir ,howard ,grubb1 ,the ,observatory1 ,vol4 ,,vii1 pp4 #i1 #dc4 ,also in ,jour4 ,roy4 ,ast4 ,soc4 ,canada1 ,dec41 #aiba1 ,jan4 #aibb4 ,there are several rather elegant methods of adjusting the polar axis to the pole which depend on the use of special graticules in the eyepiece1 or on auxiliary devices applied to the telescope1 the general principle being automatically to provide for setting off the distance between ,polaris and the pole at the proper hour angle4 ,a beautifully simple one is that of ,gerrish 7,pop4 ,ast4 #bi1 #bhc74 ,the simple plan here outlined will generally1 however1 prove sufficient for ordinary purposes and where high precision is necessary one has to turn to the more conventional astronomical methods4 ,if one gives his telescope a permanent footing such as is shown in ,fig4 #aga adjustment has rarely to be repeated4 ,with a pillar mount such as we have just now been considering the instrument itself can be taken in doors and replaced with very slight risk of disturbing its setting1 but some provision must be made for sheltering the mount4 ,a tarpaulin is sometimes recommended and indeed answers well1 particularly if a bag of rubber sheeting is drawn loosely over the mount first4 ,better still is a box cover of copper or galvanized iron set over the mount and closely fitting well down over a base clamped to the pillar with a gasket to close the joint4 ,but the fact is when one is dealing with a fine instrument like ,fig4 #afh of as much as #e inches aperture1 the question of a permanent housing 7call it observatory if you like7 at once comes up and will not down4 ,it is of course always more convenient to have the telescope permanently in place and ready for action4 ,some observers feel that working conditions are better with the telescope in the open1 but most prefer a shelter from the wind1 even if but partial1 and the protection of a covering1 however slight1 in severe weather4 ,in the last resort the question is mainly one of climate4 ,where nights1 otherwise of the best seeing quality1 are generally windless or with breezes so slight that the tube does not quiver a telescope in the open1 however protected between times1 works perfectly well4 ,in other regions the clearest nights are apt to be those of a steady gentle wind producing great uniformity of conditions at the expense of occasional vibration of the instrument and of discomfort to the observer4 ,hence one finds all sorts of practice1 varied too1 by the inevitable question of expense4 ,the simplest possible housing is to provide for the fixed instrument a moveable cover which can be lifted or slid quite out of the way leaving the telescope in the open air1 exposed to wind1 but free from the disturbing air currents that play around the opening of a dome4 ,shelters of this cheap and simple sort have been long in use both for small and large instruments4 ,illustration3 ,,fig4 #agc4--,the ,simplest of ,telescope ,housings4 ,for example several small astrographic instruments in the ,harvard equipment are mounted as shown in ,fig4 #agc4 ,here are two fork mounts1 each on a short pier1 and covered in by galvanized iron hoods made in two parts1 a vertical door which swings down1 as in the camera of the foreground1 and the hood proper1 hinged to the base plate and free to swing down when the rear door is unlocked and opened4 ,a little to the rear is a similar astrographic camera with the hood closed4 ,it is all very simple1 cheap1 and effective for an instrument not exceeding say two or three feet in focal length4 ,a very similar scheme has been successfully tried on reflectors as shown in ,fig4 #agd4 ,the instrument shown is a ,browning equatorial of #h inches aperture4 ,the cover is arranged to open after the manner of ,fig4 #agc and the plan proved very effective1 preserving much greater uniformity of conditions and hence permitting better definition than in case of a similar instrument peering through the open shutter of a dome4 ,such a contrivance gets unwieldly in case of a refractor on account of the more considerable height of the pier and the length of the tube itself4 ,but a modification of it may be made to serve exceedingly well in climates where working in the open is advantageous4 ,a good example is the equatorial of the ,harvard ,observatory station at ,mandeville1 ,jamaica1 which has been thus housed for some twenty years1 as shown in ,fig4 #age4 ,this #aa inch refractor1 used mainly on planetary detail1 is located alongside the polar telescope of #ab inches aperture and #ace feet #d inches focal length used for making a photographic atlas of the moon and on other special problems4 ,the housing1 just big enough to take in the equatorial with the tube turned low1 opens on the south side and then can be rolled northward on its track1 into the position shown1 where it is well clear of the instrument1 which is then ready for use4 ,illustration3 ,,fig4 #agd4--;,cover for ,small ,reflector4 ,the climate of ,jamaica1 albeit extremely damp1 affords remarkably good seeing during a large part of the year1 and permits use of the telescope quite in the open without inconvenience to the observer4 ,the success of this and all similar housing plans depends on the local climate more than on anything else--chiefly on wind during the hours of good seeing4 ,an instrument quite uncovered suffers from gusts far more than one housed under a dome1 which is really the sum of the whole matter1 save that a dome to a slight extent does shelter the observer in extremely cold weather4 ,even very large reflectors can be housed in similar fashion if suitably mounted4 ,for example in ,fig4 #agf is shown the #cf inch aperture reflector of the late ,dr4 ,common1 which was fitted with an open fork equatorial mounting4 ,here the telescope itself1 with its short pier and forked polar axis1 is shown in dotted lines4 ,illustration3 ,,fig4 #age4--,sliding ,housing for #aa-;inch ,refractor4 ,built about it is a combined housing and observing stand rotatable on wheels ,t about a circular track ,r4 ,the housing consists of low corrugated metal sides and ends1 here shown partly broken away1 of dimensions just comfortably sufficient to take in the telescope when the housing is rotated to the north and south position1 and the tube turned down nearly flat southward4 ,a well braced track ,,ww extends back along the top of the side housing and well to the rear4 ,on this track rolls the roof of the housing ,x1,x1,x1 with a shelter door at the front end4 ,illustration3 ,,fig4 #agf4--,sliding ,housing for a ,big ,reflector4 ,the members ,u constitute a framing which supports at once the housing and the observing platform1 to which access is had by a ladder1 ,z1 provided with a counterbalanced observing seat4 ,the instrument is put into action by clearing the door at the end of the roof1 running the roof back to the position shown in the dotted lines1 raising the tube1 and then revolving the whole housing into whatever position is necessary to permit the proper setting of the tube4 ,illustration3 ,,fig4 #agg4--,sliding ,roof ,observatory4 ,this arrangement worked well but was found a bit troublesome owing to wind and weather4 ,with a skeleton tube and in a favorable climate the plan would succeed admirably providing an excellent shelter for a large telescope at very low cost4 ,since a fork mount allows the tube to lie flat1 such an instrument1 up to say #h or #aj inches aperture can be excellently protected by covers fitting snugly upon a base and light enough to lift off as a whole4 ,the successful use of all these shelters however depends on climatic conditions4 ,they require circumstances allowing observation in the open1 as with tripod mounts1 and afford no protection from wind or cold4 ,complete protection for the observer cannot be had1 except by some of the devices shown in ,chapter ,v1 but conditions can be improved by permanent placement in an observatory1 simple or elaborate1 as the builder may wish4 ,the word observatory may sound formidable1 but a modest one can be provided at less expense than a garage for the humblest motor car4 ,the chief difference in the economic situation is that not even the most derided car can be picked up and carried into the back hall for shelter1 and it really ought not to be left out in the weather4 ,the next stage of evolution is the telescope house with a sliding roof in one or more sections--ordinarily two4 ,in this case the building itself is a simple square structure large enough to accommodate the instrument with maneuvering room around it4 ,the side walls are carried merely high enough to give clearance to the tube when turned nearly flat and to give head room to the observer4 ,the roof laps with a close joint in the middle and each half rolls on a track supported beyond the ends of the building by an out-rigger arranged in any convenient manner4 ,when the telescope is in use the roof sections are displaced enough to give an ample clear space for observing1 often wide open as shown in ,fig4 #agg1 which is the house of the #af inch ,metcalf photographic doublet at the ,harvard ,observatory4 ,this instrument is in an open fork mount like that shown in ,fig4 #aci4 ,the sliding roof type is on the whole the simplest structure that can be regarded as an observatory in the sense of giving some shelter to the observer as well as the instrument4 ,it gives ample sky room for practical purposes even to an instrument with a fork mount1 since in most localities the seeing within #cj or so of the horizon is decidedly bad4 ,if view nearer the horizon is needed it can readily be secured by building up the pier a bit4 ,numberless modifications of the sliding roof type will suggest themselves on a little study4 ,one rather interesting one is used in the housing of the #bd inch reflector of the ,harvard ,observatory1 #aa feet #c inches in focal length1 the same of which the drive in its original dome is shown in ,fig4 #aci4 ,as now arranged the lower part of the observatory remains while the upper works are quite similar in principle to the housing of ,dr4 ,common's #c foot reflector of ,fig4 #agf4 ,the cover open is shown in ,fig4 #agh4 ,it will be seen that on the north side of the observatory there is an out-rigger on which the top housing slides clear of the low revolving turret which gives access to the ocular fitting used generally to carry the plate holder1 and the eyepiece for following when required4 ,the tube cannot be brought to the horizontal1 but it easily commands all the sky-space that can advantageously be used in this situation1 and the protection given the telescope when not in use is very complete4 ,to close the observatory the tube is brought north and south and turned low and the sliding roof is then run back into its fixed position4 ,the turret is very easily turned by hand4 ,illustration3 ,,fig4 #agh4--,turret ,housing of the #bd-;inch ,harvard ,reflector4 ,of course for steady work with the maximum shelter for observer obtainable without turning to highly special types of housing1 the familiar dome is the astronomer's main reliance4 ,it is in the larger sizes usually framed in steel and covered with wood1 externally sheathed in copper or steel4 ,sometimes in smaller domes felt covered with rubberoid serves a good purpose1 and painted canvas is now and then used1 with wooden framing4 ,but even the smallest dome of conventional construction is heavy and rather expensive1 and for home talent offers many difficulties1 especially with respect to the shutter and shutter opening4 ,a hemisphere is neither easy to frame nor to cover1 and the curved sliding shutter is especially troublesome4 ,illustration3 ,,fig4 #agi4--,the ,original 8,romsey0 ,observatory4 ,hence for small observatories other forms of revolving roof are desirable1 and quite the easiest and cheapest contrivance is that embodied in the 8,romsey0 type of observatory1 devised half a century ago by that accomplished amateur the ,rev4 ,e4 ,l4 ,berthon1 vicar of ,romsey4 ,the feature of his construction is an unsymmetrical peak in the revolving roof which permits the ordinary shutter to be replaced by a hinged shutter like the skylight in a roof1 exposing the sky beyond the zenith when open1 and closing down over a coaming to form a water tight joint4 ,berthon's original description of his observatory1 which accommodated a #i inch reflector1 may be found in ,vol4 #ad of the ,english ,mechanic and ,world of ,science whence ,fig4 #agi is taken4 ,in this plate ,fig4 #a shows the complete elevation and ,fig4 #b the ground plan1 each to a scale of a eighth of an inch to the foot4 ,in the plan1 ,a1,a1 are the main joists1 ,p the pier for the telescope1 ,t that for the transit1 and ,c the clock4 ,figs4 #c1 #d1 and #e are of details4 ,in the last named ,a is a rafter1 b the base ring1 c the plate1 d one of the sash rollers carrying the roof1 and e a lateral guide roller holding the roof in place4 ,the structure can readily be built without the transit shelter1 and in fact now-a-days most observers find it easier to pick up their time by wireless4 ,the main bearing ring is cut out of ordinary inch board1 in ten or a dozen1 or more1 sections according to convenience1 done in duplicate1 joints lapping1 and put very firmly together with screws set up hard4 ,sometimes #c layers are thus used4 ,the roof in the original 8,romsey0 observatory was of painted canvas1 but rubberoid or galvanized iron lined with roofing paper answers well4 ,the shutter can be made single or double in width1 and counterbalanced if necessary4 ,the framing may be of posts set in the ground as here shown1 or with sills resting on a foundation1 and the walls of any construction--matched boards of any kind1 cement on wire lath1 hollow tile1 or concrete blocks4 ,chambers' ,handbook of ,astronomy ,vol4 ,,ii contains quite complete details of the 8,romsey0 type of observatory and is easier to get at than the original description4 ,a very neat adaptation of the plan is shown in ,fig4 #ahj1 of which a description may be found in ,popular ,astronomy #bh1 #ahc4 ,this observatory was about #i feet in diameter1 to house a #d inch telescope1 and was provided with a rough concrete foundation on which was built a circular wall #f feet high of hollow glazed tile1 well levelled on top4 ,to this was secured a ring plate built up in two layers1 carrying two circles of wooden strips with a couple of inches space between them for a runway4 ,in this ran #f two-inch truck castors secured to a similar ring plate on which was built up the frame of the 8dome0 arranged as shown4 ,altogether a very neat and workmanlike affair1 in this case built largely by the owner but permitting construction at very small expense almost anywhere4 ,another interesting modification of the same general plan in the same volume just cited is shown in ,fig4 #aha4 ,this is also for a #d inch refractor and the dome proper is but #h feet #d inches in diameter4 ,like the preceding structure the foundation is of concrete but the walls are framed in spruce and sheathed in matched boards with a 8beaver-board0 lining4 ,illustration3 ,,fig4 #ahj4--;,a ,more ,substantial 8,romsey0 ,type4 ,the ring plate is three-ply1 #ab sections to the layer1 and its mate on which the dome is assembled is similarly formed1 though left with the figure of a dodecagon to match the dome4 ,the weight is carried on four rubber tired truck rollers1 and there are lateral guide rollers on the plan of those in ,fig4 #agi4 ,the dome itself however1 is wholly of galvanized iron1 in #ab gores joined with standing seams1 turned1 riveted1 and soldered4 ,there is a short shutter at the zenith sliding back upon a frame1 while the main shutter is removed from the outside by handles4 ,illustration3 ,,fig4 #aha4--;,detail of ,light ,metal ,dome for ,small ,observatory4 ,observatories of the ,romsey or allied types can be erected at very moderate cost1 varying considerably from place to place1 but running at present say from #bjj to #fjj1 and big enough to shelter refractors of #d to #f inches aperture4 ,the revolving roofs will range from #i to #ab feet in diameter4 ,if reflectors are in use1 those of about double these apertures can be accommodated since the reflector is ordinarily much the shorter for equal aperture4 ,the sliding roof1 not to say the sliding shelter1 forms of housing cost somewhat less1 depending on the construction adopted4 ,going to brick may double the figures quoted1 but such solidity is generally quite needless1 though it is highly desirable that the cover of a valuable instrument should be fire-proof and not easily broken open4 ,the stealing of objectives and accessories is not unknown1 and vandalism is a risk not to be forgotten4 ,but to even the matter up1 housing a telescope is rather an easy thing to accomplish1 and as a matter of fact for the price of a very modest motor car one can both buy and house an instrument big enough to be of genuine service4 ,,chapter ,,xi ,,seeing ,,and ,,magnification ,few things are more generally disappointing than one's first glimpse of the ,heavens through a telescope4 ,the novice is fed up with maps of ,mars as a great disc full of intricate markings1 and he generally sees a little wriggling ball of light with no more visible detail than an egg4 ,it is almost impossible to believe that1 at a fair opposition1 ,mars under the power of even the smallest astronomical telescope really looks as big as the full moon4 ,again1 one looks at a double star to see not two brilliant little discs resplendent in color1 but an indeterminate flicker void of shape and hue4 ,the fact is1 that most of the time over most of the world seeing conditions are bad1 so that the telescope does not have a fair chance1 and on the whole the bigger the telescope the worse the chance4 ,one famous ,english astronomer1 possessed of a fine refractor that would be reckoned large even now-a-days1 averred that he had seen but one first class night in fifteen years past4 ,the case is really much less bad than this implies1 for even in rather unfavorable climates many a night1 at some o'clock or other1 will furnish an hour or two of pretty good seeing1 while now and then1 without any apparent connection with the previous state of the weather1 a night will turn up when the pictures in the popular astronomies come true1 the stars shrink to steady points set in clean cut rings1 and no available power seems too high4 ,one can get a good idea of the true inwardness of bad seeing by trying to read a newspaper through an opera glass across a hot stove4 ,if the actual movements in the atmosphere could be made visible they would present a strange scene of turbulence--rushing currents taking devious courses up and around obstacles1 slowly moving whirlpools1 upward slants such as gulls hug on the quarter of a liner1 great downward rushes dreaded by the aviator1 and over it all incessant ripples in every direction4 ,and movements of air are usually associated with changes of temperature1 as over the stove1 varying the refraction and contorting the rays that come from a distant star until the image is quite ruined4 ,the condition for excellence of definition is that the atmosphere through which we see shall be homogeneous1 whatever its temperature1 humidity1 or general trend of movement4 ,irregular refraction is the thing to be feared1 particularly if the variations are sudden and frequent4 ,hence the common troubles near the ground and about buildings1 especially where there are roofs and chimneys to radiate heat--even in and about an observatory dome4 ,professor ,w4 ,h4 ,pickering1 who has had a varied experience in climatic idiosyncrasies1 gives the ,northern ,atlantic seaboard the bad preminence of having the worst observing conditions of any region within his knowledge4 ,the author cheerfully concurs1 yet now and then1 quite often after midnight1 the air steadies and1 if the other conditions are good1 definition becomes fairly respectable1 sometimes even excellent4 ,temperature and humidity as such1 seem to make little difference1 and a steady breeze unless it shakes the instrument is relatively harmless4 ,hence we find the most admirable definition in situations as widely different as the ,harvard station at ,mandeville1 ,jamaica2 ,flagstaff1 ,arizona #gjjj feet up and snow bound in winter2 ,italy1 and ,egypt4 ,the first named is warm and with very heavy rainfall and dew1 the second dry with rather large seasonal variation of temperature1 and the others temperate and hot respectively4 ,perhaps the most striking evidence of the importance of uniformity was noted by ,evershed at an ,indian station where good conditions immediately followed the flooding of the rice fields with its tendency to stabilize the temperature4 ,mountain stations may be good as at ,flagstaff1 ,mt4 ,hamilton1 or ,mt4 ,wilson1 or very bad as ,pike's ,peak proved to be1 probably owing to local conditions4 ,in fact much of the trouble comes from nearby sources1 atmospheric waves and ripples rather than large movements1 ripples indeed often small compared with the aperture of the telescope and sometimes in or not far outside of the tube itself4 ,aside from these difficulties1 there are still others which have to do with the transparency of the atmosphere with respect to its suspended matter4 ,this does not affect the definition as such1 but it cuts down the light to a degree that may interfere seriously with the observation of faint stars and nebul4 ,the smoke near a city aggravates the situation1 but in particular it depends on general weather conditions which may be persistent or merely temporary4 ,often seeing conditions may be admirable save for this lack of transparency in the atmosphere1 so that study of the moon1 of planetary markings and even of double stars1 not too faint1 may go on quite unimpeded4 ,the actual loss of light may reach however a magnitude or more1 while the sky is quite cloudless and without a trace of fog or noticeable haziness by day4 ,there have been a good many nights the past year 7#aiba7 when ,alcor 7#hj ,urs ,majoris7 the tiny neighbor of ,mizar1 very nearly of the #dth magnitude1 has been barely or not at all visible while the seeing otherwise was respectably good4 ,ordinarily stars of #fm should be visible in a really clear night1 and in a brilliant winter sky in the temperate zones1 or in the clear air of the tropics1 a good many eyes will do better than this1 reaching #fm4#e or even #gm1 occasionally a bit more4 ,the relation of air waves and such like irregularities to telescopic vision was rather thoroughly investigated by ,douglass more than twenty years ago 7,pop4 ,ast4 #f1 #aic7 with very interesting results4 ,in substance1 from careful observation with telescopes from #d inches up to #bd inches aperture1 he found that the real trouble came from what one may call ripples1 disturbances from say #d inches wave length down to inch or less4 ,long waves are rare and relatively unimportant since their general effect is to cause shifting of the image as a whole rather than the destruction of detail which accompanies the shorter waves4 ,this rippling of the air is probably associated with the contact displacements in air currents such as on a big scale become visible in cloud forms4 ,clearly ripples1 marked as they are by difference of refraction1 located in front of a telescope objective1 produce different focal lengths for different parts of the objective and render a clean and stable image quite out of the question4 ,in rough terms ,douglass found that waves of greater length than half the aperture did not materially deteriorate the image1 although they did shift it as a whole1 while waves of length less than one third the aperture did serious mischief to the definition1 the greater as the ripples were shorter1 and the image itself more minute in dimension or detail4 ,hence there are times when decreasing the aperture of an objective by a stop improves the seeing considerably by increasing the relative length of the air waves4 ,such is in fact found to be the case in practical observing1 especially when the seeing with a large aperture is decidedly poor4 ,in other words one may often gain more by increased steadiness than he loses by lessened 8resolving power10 the result depending somewhat on the class of observation which chances to be under way4 ,and this brings us1 willy-nilly1 to the somewhat abstruse matter of resolving power1 depending fundamentally upon the theory of diffraction of light1 and practically upon a good many other things that modify the character of the diffraction pattern1 or the actual visibility of its elements4 ,when light shines through a hole or a slit the light waves are bent at the margins and the several sets1 eventually overlapping1 interfere with each other so as to produce a pattern of bright and dark elements depending on the size and shape of the aperture1 and distributed about a central bright image of that aperture4 ,one gets the effect well in looking through an open umbrella at a distant street light4 ,the outer images of the pattern are fainter and fainter as they get away from the central image4 ,without burdening the reader for the moment with details to be considered presently1 the effect in telescopic vision is that a star of real angular diameter quite negligible1 perhaps #j4jja of arc1 is represented by an image under perfect conditions like ,fig4 #aed1 of quite perceptible diameter1 surrounded by a system of rings1 faint but clear-cut1 diminishing in intensity outwards4 ,when the seeing is bad no rings are visible and the central disc is a mere bright blur several times larger than it ought to be4 ,the varying appearance of the star image is a very good index of the quality of the seeing1 so that1 having a clear indication of this appearance1 two astronomers in different parts of the world can gain a definite idea of each other's relative seeing conditions4 ,to this end a standard scale of seeing1 due largely to the efforts of ,prof4 ,w4 ,h4 ,pickering1 has come into rather common use4 7,h4 ,a4 #fa #bi74 ,it is as follows1 based on observations with a #e inch telescope4 ,,standard ,,scale ,,of ,,seeing #a4 ,image usually about twice the diameter of the third ring4 #b4 ,image occasionally twice the diameter of the third ring4 #c4 ,image of about the same diameter as the third ring1 and brighter at the centre4 #d4 ,disc often visible1 arcs 7of rings7 sometimes seen on brighter stars4 #e4 ,disc always visible1 arcs frequently seen on brighter stars4 #f4 ,disc always visible1 short arcs constantly seen4 #g4 ,disc sometimes sharply defined1 7a7 long arcs4 7b7 ,rings complete4 #h4 ,disc always sharply defined1 7a7 long arcs4 7b7 ,rings complete all in motion4 #i4 ,rings1 7a7 ,inner ring stationary1 7b7 ,outer rings momentarily stationary4 #aj4 ,rings all stationary1 7a7 ,detail between the rings sometimes moving4 7b7 ,no detail between the rings4 ,the first three scale numbers indicate very bad seeing2 the next two1 poor2 the next two1 good2 and the last three1 excellent4 ,one can get some idea of the extreme badness of scale divisions #a1 #b1 #c1 in realizing that the third bright diffraction ring is nearly #d times the diameter of the proper star-disc4 ,it must be noted that for a given condition of atmosphere the seeing with a large instrument ranks lower on the scale than with a small one1 since as already explained the usual air ripples are of dimensions that might affect a #e inch aperture imperceptibly and a #ae inch aperture very seriously4 ,douglass 7loc4 cit47 made a careful comparison of seeing conditions for apertures up to #bd inches and found a systematic difference of #b or #c scale numbers between #d or #f inches aperture1 and #ah or #bd inches4 ,with the smallest aperture the image showed merely bodily motion due to air waves that produced serious injury to the image in the large apertures1 as might be expected4 ,there is likewise a great difference in the average quality of seeing as between stars near the zenith and those toward the horizon1 due again to the greater opportunity for atmospheric disturbances in the latter case4 ,pickering's experiments 7loc4 cit47 show a difference of nearly #c scale divisions between say #bj and #gj elevation4 ,this difference1 which is important1 is well shown in ,fig4 #ahb1 taken from his report4 ,the three lower curves were from ,cambridge observations1 the others obtained at various ,jamaica stations4 ,they clearly show the systematic regional differences1 as well as the rapid falling off in definition below altitude #dj1 which points the importance of making provision for comfortable observing above this altitude4 ,illustration3 ,,fig4 #ahb4--,variation of ,seeing with ,altitude4 ,illustration3 ,,fig4 #ahc4--;,airy's ,diffraction ,pattern4 ,the relation of the diffraction pattern as disclosed in the moments of best seeing to its theoretical form is a very interesting one4 ,the diffraction through a theoretically perfect objective was worked out many years ago by ,sir ,george ,airy who calculated the exact distribution of the light in the central disc and the surrounding rings4 ,this is shown from the centre outwards in ,fig4 #ahc1 in which the ordinates of the curve represent relative intensities while the absciss represent to an arbitrary scale the distances from the axis4 ,it will be at once noticed that the star image1 brilliant at its centre1 sinks1 first rapidly and then more slowly1 to a minimum and then very gradually rises to the maximum of the first bright ring1 then as slowly sinks again to increase for the second ring and so on4 ,illustration3 ,,fig4 #ahd4--;,diffraction ,solid for a ,star4 ,for unity brightness in the centre of the star disc the maximum brightness of the first ring is #j4jag1 of the second #j4jjd and the third #j4jjaf4 ,the rings are equidistant and the star disc has a radius substantially equal to the distance between rings4 ,one's vision does not follow down to zero the intensities of the rings or of the margin of the disc1 so that the latter has an apparent diameter materially less than the diameter to the first diffraction minimum1 and the rings themselves look sharper and thinner than the figure would show1 even were the horizontal scale much diminished4 ,the eye does not descend in the presence of bright areas to its final threshold of perception4 ,one gains a somewhat vivid idea of the situation by passing to three dimensions as in ,fig4 #ahd1 the 8diffraction solid0 for a star1 a conception due to ,m4 ,andr 7,mem4 de l',acad4 de ,lyon #cj1 #di74 ,here the solid represents in volume the whole light received and the height taken at any point1 the intensity at that point4 ,a cross section at any point shows the apparent diameter of the disc1 its distance to the apex the remaining intensity1 and the volume above the section the remaining total light4 ,substantially #he of the total light belongs to the central cone1 for the theoretical distribution4 ,granting that the eye can distinguish from the background of the sky1 in presence of a bright point1 only light above a certain intensity1 one readily sees why the discs of faint stars look small1 and why shade glasses are sometimes useful in wiping out the marginal intensities of the solid4 ,there are physiological factors that alter profoundly the appearance of the actual star image1 despite the fact that the theoretical diffraction image for the aperture is independent of the star's magnitude4 ,practically the general reduction of illumination in the fainter stars cuts down the apparent diameters of their discs1 and reduces the number of rings visible against the background of the sky4 ,the scale of the diffraction system determines the resolving power of the telescope4 ,this scale is given in ,airy's original paper 7,cambr4 ,phil4 ,trans4 #ahcd p4 #bhc71 from which the angle to any maximum or minimum in the ring system is defined by sin n_/,r in which is numerically the wave length of any light considered and ,r is the radius of the objective4 ,we therefore see that the ring system varies in dimension inversely with the aperture of the objective and directly with the wave length considered4 ,hence the bigger the objective the smaller the disc and its surrounding ring system2 and the greater the wave length1 i4e4 the redder the light1 the bigger the diffraction system4 ,evidently there should be color in the rings but it very seldom shows on account of the faintness of the illumination4 ,now the factor n is for the first dark ring #j4fa1 and for the first bright ring #j4ha1 as computed from ,airy's general theory1 and therefore if we reckon that two stars will be seen as separate when the central disc of one falls on the first dark ring of the other the angular distance will be ,sin #j4fa _/,r and1 taking at the brightest part of the spectrum i4e41 about #efj 1 in the yellow green1 with taken for sin 1 we can compute this assumed separating power for any aperture4 ,thus #efj being very nearly #a_/de1ejj inch1 and assuming a #e inch telescope1 the instrument should on this basis show as double two stars whose centres are separated by #a4a of arc4 ,in actual fact one can do somewhat better than this1 showing that the visible diameter of the central disc is in effect less than the diameter indicated by the diffraction pattern1 owing to the reasons already stated4 ,evidently the brightness of the star is a factor in the situation since if very bright the disc gains apparent size1 and when very faint there is sufficient difficulty in seeing one star1 let alone a pair4 ,the most thorough investigation of this matter of resolving power was made by the ,rev4 ,w4 ,r4 ,dawes many years ago 7,mem4 ,r4,a4,s4 #ce1 #aeh74 ,his study included years of observation with telescopes of different sizes1 and his final result was to establish what has since been known as 8,dawes' ,limit40 ,to sum up ,dawes' results he established the fact that on the average a one inch aperture would enable one to separate two #fth magnitude stars the centers of which were separated by #d4ef4 ,or1 to generalize from this basis1 the separating power of any telescope is for very nearly equal stars1 moderately bright1 #d4ef_/;,a where ,a is the aperture of the telescope in inches4 ,many years of experience have emphasized the usefulness of this approximate rule1 but that it is only approximate must be candidly admitted4 ,it is a limit decidedly under that just assigned on the basis of the theory of diffraction for the central bright wave-lengths of the spectrum4 ,attempts have been made to square the two figures by assuming in the diffraction theory a wave length of #a_/ee1jjj inch1 but this figure corresponds to a point well up into the blue1 of so low luminosity that it is of no importance whatever in the visual use of a telescope4 ,the fact is that the visibility of two neighboring bright points as distinct1 depends on a complex of physical and physiological factors1 the exact relations of which have never been unravelled4 ,to start with we have the principles of diffraction as just explained1 which define the relation of the stellar disc to the center of the first dark ring1 but we know that under no circumstances can one see the disc out to this limit1 since vision fails to take cognizance of the faint rim of the image4 ,the apparent diameter of the diffraction solid therefore corresponds to a section taken some distance above the base1 the exact point depending on the sensitiveness of the particular observer's eye1 the actual brilliancy of the center of the disc1 and the corresponding factors for the neighboring star4 ,illustration3 ,,fig4 #ahe4--;,diffraction ,solid for a ,disc4 ,under favorable circumstances one would not go far amiss in taking the visible diameter of the disc at about half that reckoned to the center of the first dark ring4 ,this figure in fact corresponds to what has been shown to be within the grasp of a good observer under favorable conditions1 as we shall presently see4 ,on the other hand1 if the stars are decidedly bright there is increase of apparent diameter of the disc due to the phenomenon known as irradiation1 the spreading of light about its true image on the retina which corresponds quite closely to the halation produced by a bright spot on a photographic plate4 ,if1 on the contrary1 the stars are very faint the total amount of light available is not sufficient to make contrast over and above the background sufficient to disclose the two points as separate1 while if the pair is very unequal the brighter one will produce sufficient glare to quite over-power the light from the smaller one so that the eye misses it entirely4 ,a striking case of this is found in the companion to ,sirius1 an extremely difficult object for ordinary telescopes although the distance to the companion is about #aj4f and its magnitude is #h4d1 making a superlatively easy double for the very smallest telescope save for the overpowering effect of the light of the large star4 ,another notoriously difficult object for small telescopes is ,cygni1 a beautiful double of which the smaller component falls unpleasantly near the first diffraction maximum of the primary in which it is apt to be lost4 8,dawes' ,limit0 is therefore subject to many qualifying factors4 ,lewis1 in the papers already referred to 7,obs4 #cg1 #cgh7 did an admirable piece of investigation in going through the double star work of about two score trained observers working with telescopes all the way from #d inches to #cf inches aperture4 ,from this accumulation of data several striking facts stand out4 ,first there is great difference between individual observers working with telescopes of similar aperture as respects their agreement with 8,dawes' ,limit10 showing the effect of variation in the physiological factors as well as instrumental ones4 ,second1 there is also a very large difference between the facility of observing equal bright pairs and equal faint pairs1 or unequal pairs of any kind1 again emphasizing the physiological as well as the physical factors4 ,finally1 there is most unmistakable difference between small and large apertures in their capacity to work up to or past the standard of 8,dawes',limit40 ,the smaller telescopes are clearly the more efficient as would be anticipated from the facts just pointed out regarding the different effect of the ordinary and inescapable atmospheric waves on small and large instruments4 ,the big telescopes are unquestionably as good optically speaking as the small ones but under the ordinary working conditions1 even as good as those a double star observer seeks1 the smaller aperture by reason of less disturbance from atmospheric factors does relatively much the better work1 however good the big instrument may be under exceptional conditions4 ,this is admirably shown by the discussion of the beautiful work of the late ,mr4 ,burnham1 than whom probably no better observer of doubles has been known to astronomy4 ,his records of discovery with telescopes of #f1 #i4d1 #ab1 #ah and #cf inches show the relative ease of working to the theoretical limit with instruments not seriously upset by ordinary atmospheric waves4 ,with the #f inch aperture ,burnham reached in the average #j4ec of ,dawes' limit1 quite near the rough figure just suggested1 and he also fell well inside ,dawes' limit with the #i4d inch instrument4 ,with none of the others did he reach it and in fact fell short of it by #ae to #fj4 ,all observations being by the same notably skilled observer and representing discoveries of doubles1 so that no aid could have been gained by familiarity1 the issue becomes exceedingly plain that size with all its advantages in resolving power brings serious countervailing limitations due to atmosphere4 ,but a large aperture has besides its possible separating power one advantage that can not be discounted in 8light grasp10 the power of discerning faint objects4 ,this is the thing in which a small telescope necessarily fails4 ,the 8light grasp0 of the telescope obviously depends chiefly on the area of the objective1 and visually only in very minor degree on the absorption of the thicker glass in the case of a large lens4 ,according to the conventional scale of star magnitudes as now in universal use1 stars are classified in magnitudes which differ from each other by a light ratio of #b4eab4 a number the logarithm of which is #j4d1 a relation suggested by ,pogson some forty years ago4 ,a second magnitude star therefore gives only about #dj of the light of a first magnitude star1 while a third magnitude star gives again a little less than #dj of the light of a second magnitude star and so on4 ,but doubling the aperture of a telescope increases the available area of the objective four times and so on1 the 8light grasp0 being in proportion to the square of the aperture4 ,thus a #aj inch objective will take in and deliver nearly #ajj times as much light as would a #a inch aperture4 ,if one follows ,pogson's scale down the line he will find that this corresponds exactly to #e stellar magnitudes1 so that if a #a inch aperture discloses1 as it readily does1 a #ith magnitude star1 a #aj inch aperture should disclose a #adth magnitude star4 ,such is substantially in fact the case1 and one can therefore readily tabulate the minimum visible for an aperture just as he can tabulate the approximate resolving power by reference to ,dawes' limit4 ,fig4 #ahf shows in graphic form both these relations for ready reference1 the variation of resolving power with aperture1 and that of 8light grasp10 reckoned in stellar magnitudes4 ,it is hardly necessary to state that considerable individual and observational differences will be found in each of these cases1 in the latter amounting to not less than #j4e to #a4j magnitude either way4 ,the scale is based on the #ith magnitude star just being visible with #a inch aperture1 whereas in fact under varying conditions and with various observers the range may be from the #hth to #ajth magnitude4 ,all these things1 however convenient1 must be taken merely at their true value as good working approximations4 ,even the diffraction theory can be taken only as an approximation since no optical surface is absolutely perfect and in the ordinary refracting telescope there is a necessary residual chromatic aberration beside whatever may remain of spherical errors4 ,illustration3 ,,fig4 #ahf4--,light-grasp and ,resolving ,power4 ,it is a fact therefore1 as has been shown by ,conrady 7,m4,n4 #gi #ege7 following up a distinguished investigation by ,lord ,rayleigh 7,sci4 ,papers #a #dae71 that a certain small amount of aberration can be tolerated without material effect on the definition1 which is very fortunate considering that the secondary spectrum represents aberrations of about #a_/b1jjj of the focal length1 as we have already seen4 ,the chief effect of this1 as of very slight spherical aberration1 is merely to reduce the maximum intensity of the central disc of the diffraction pattern and to produce a faint haze about it which slightly illuminates the diffraction minima4 ,the visible diameter of the disc and the relative distribution of intensity in it is not however materially changed so that the main effect is a little loss and scattering of light4 ,with larger aberrations these effects are more serious but where the change in length of optical path between the ray proceeding through the center of the objective and that from the margin does not exceed the injury to the definition is substantially negligible and virtually disappears when the image is focussed for the best definition1 the loss of maximum intensity in the star disc amounting to less than #bj4 ,even twice this error is not a very serious matter and can be for the most part compensated by a minute change of focus as is very beautifully shown in a paper by ,buxton7,m4 ,n4 #ha1 #edg71 which should be consulted for detail of the variations to be effected4 ,conrady finds a given change dp in the difference in lengths of the optical paths1 related to the equivalent linear change of focus1 df1 as follows3-- df #h;dp7f_/,a7 ,a being the aperture and f the focal length1 which indicates for telescopes of ordinary focal ratio a tolerance of the order of #j4ja inch before getting outside the limit for variation of path4 ,for instruments of greater relative aperture the precision of focus and in general the requirements for lessened aberration are far more severe1 proportional in fact to the square of this aperture4 ,hence the severe demands on a reflector for exact figure4 ,an instrument working at ,f_/#e or ,f_/#f is extremely sensitive to focus and demands great precision of figure to fall within permissible values1 say to 1 for dp4 ,further1 with a given value of dp and the relation established by the chromatic aberration1 i4e41 about f_/#bjjj1 a relation is also determined between f and ,a1 required to bring the aberration within limits4 ,the equation thus found is f #b4h;,a ,this practically amounts to the common ,f_/#ae ratio for an aperture of approximately #e inches4 ,for smaller apertures a greater ratio can be well used1 for larger1 a relatively longer focus is indicated1 the penalty being light spread into a halo over the diffraction image and reducing faint contrasts somewhat seriously4 ,this is one of the factors aside from atmosphere1 interfering with the full advantage of large apertures in refractors4 ,while as already noted small amounts of spherical aberration may be to a certain extent focussed out1 the sign of df must change with the sign of the residual aberration1 and a quick and certain test of the presence of spherical aberration is a variation in the appearance of the image inside and outside focus4 ,to emphasize the importance of exact knowledge of existing aberrations note ,fig4 #ahg1 which shows the results of ,hartmann tests on a typical group of the world's large objectives4 ,all show traces of residual zones1 but differing greatly in magnitude and position as the attached scales show4 ,the most conspicuous aberrations are in the big ,potsdam photographic refractor1 the least are in the #bd inch ,lowell refractor4 ,the former has since been refigured by ,schmidt and revised data are not yet available2 the latter received its final figure from the ,lundins after the last of the ,clarks had passed on4 ,now a glance at the curves shows that the bad zone of the ,potsdam glass was originally near the periphery1 7,i71 hence both involved large area and1 from ,conrady's equation1 seriously enlarged df due to the large relative aperture at the zone4 ,an aberrant zone near the axis as in the stage 7,,iii7 of the ,potsdam objective or in the ,ottawa #ae inch objective is much less harmful for corresponding reasons4 ,such differences have a direct bearing on the use of stops1 since these may do good in case of peripheral aberration and harm when the faults are axial4 ,unless the aberrations are known no general conclusions can be drawn as to the effect of stops4 ,even in the ,lowell telescope shown as a whole in ,fig4 #ahh1 the late ,dr4 ,lowell found stops to be useful in keeping down atmospheric troubles and reducing the illumination although they could have had no effect in relation to figure4 ,fig4 #ahh shows at the head of the tube a fitting for a big iris diaphragm1 controlled from the eye-end1 the value of which was well demonstrated by numerous observers4 ,there are1 too1 cases in which a small instrument1 despite intrinsic lack of resolving power1 may actually do better work than a big one4 ,such are met in instances where extreme contrast of details is sought1 as has been well pointed out by ,nutting 7,ap4 ,j4 #dj1 #cc7 and the situation disclosed by him finds amplification in the extraordinary work done by ,barnard with a cheap lantern lens of #a inch diameter and #e inches focus 7,pop4 ,ast41 #f1 #deb74 ,illustration3 ,,fig4 #ahg4--;,hartmann ,tests of ,telescopes ,from ,hartmann's ,measures4 ,the fact is that every task must seek its own proper instrument4 ,and in any case the interpretation of observed results is a matter that passes far beyond the bounds of geometrical optics1 and involves physiological factors that are dominant in all visual problems4 ,with respect to the visibility of objects the general diffraction theory again comes into play4 ,for a bright line1 for example1 the diffraction figure is no longer chiefly a cone like ,fig4 #ahc1 but a similar long wedge-shaped figure1 with wave-like shoulders corresponding to the diffraction rings4 ,the visibility of such a line depends not only on the distribution of intensity in the theoretical wedge but on the sensitiveness of the eye and the nature of the background and so forth1 just as in the case of a star disc4 ,if the eye is from its nature or state of adaptation keen enough on detail but not particularly sensitive to slight differences of intensity1 the line will very likely be seen as if a section were made of the wedge near its thin edge4 ,in other words the line will appear thin and sharp as the diffraction rings about a star frequently do4 ,with an eye very sensitive to light and small differences of contrast the appearance of absolutely the same thing may correspond to a section through the wedge near its base1 in other words to a broad strip shading off somewhat indistinctly at the edges1 influenced again by irradiation and the character of the background4 ,if there be much detail simultaneously visible the diffraction patterns may be mixed up in a most intricate fashion and one can readily see the confusion which may exist in correlating the work of various observers on things like planetary and lunar detail4 ,in the planetary case the total image is a complex of illuminated areas of diffraction at the edges1 which may be represented as the diffraction solid of ,fig4 #ahe1 in which the dotted lines show what may correspond fairly to the real diameter of the planet1 the edge shading off in a way again complicated by irradiation4 ,illustration3 ,,fig4 #ahh4--,the ,lowell ,refractor ,fitted with ,iris ,diaphragm4 ,fancy detail superimposed on a disc of this sort and one has a vivid idea of the difficulty of interpreting observations4 ,it would be an exceedingly good thing if everyone who uses his telescope had the advantage of at least a brief course in microscopy1 whereby he would gain very much in the practical understanding of resolving power1 seeing conditions1 and the interpretation of the image4 ,the principles regarding these matters are in fact very much the same with the two great instruments of research4 ,aperture1 linear in the case of the telescope and the so-called numerical in the case of the microscope1 bear precisely the same relation to resolution1 the minimum resolvable detail being in each case directly proportional to aperture in the senses here employed4 ,further1 although the turbulence of intervening atmosphere does not interfere with the visibility of microscopic detail1 a similar disturbing factor does enter in the form of irregular and misplaced illumination4 ,it is a perfectly easy matter to make beautifully distinct detail quite vanish from a microscopic image merely by mismanagement of the illumination1 just as unsteady atmosphere will produce substantially the same effect in the telescopic image4 ,in the matter of magnification the two cases run quite parallel1 and magnification pushed beyond what is justified by the resolving power of the instrument does substantially little or no good4 ,it neither discloses new detail nor does it bring out more sharply detail which can be seen at all with a lower power4 ,the microscopist early learns to shun high power oculars1 both from their being less comfortable to work with1 and from their failing to add to the efficiency of the instrument except in some rare cases with objectives of very high resolving power4 ,furthermore in the interpretation of detail the lessons to be learned from the two instruments are quite the same1 although one belongs to the infinitely little and the other to the infinitely great4 ,nothing is more instructive in grasping the relation between resolving power1 magnification1 and the verity of detail1 than the study under the microscope of some well known objects4 ,for example1 in ,fig4 #ahi is shown a rough sketch of a common diatom1 ,navicula ,lyra4 ,the tiny siliceous valve appears thus under an objective of slightly insufficient resolving power4 ,the general form of the object is clearly perceived1 as well as the central markings1 standing boldly out in the form which suggests the specific name4 ,no trace of any finer detail appears and no amount of dexterity in arranging the illumination or increase of magnifying power will show any more than here appears1 the drawing being one actually made with the camera lucida1 using an objective of numerical aperture just too small to resolve the details of the diatoms on this particular slide4 ,figure #ahi;a shows what happens when1 with the same magnifying power1 an objective of slightly greater aperture is employed4 ,here the whole surface of the valve is marked with fine striations1 beautifully sharp and distinct like the lines of a steel engraving4 ,there is a complete change of aspect wrought by an increase of about #bj in the resolving power4 ,again nothing further can be made out by an increase of magnification1 the only effect being to make the outlines a little hazier and the view therefore somewhat less satisfactory4 ,illustration3 ,,fig4 #ahi4--,the ,stages of ,resolution4 ,finally in ,fig4 #ahi;b we have again the same valve under the same magnifying power1 but here obtained from an objective of numerical aperture #fj above that used for the main figure4 ,the sharp stri now show their true character4 ,they had their origin in lines of very clearly distinguished dots1 which are perfectly distinct1 and are due to the resolving power at last being sufficient to show the detail which previously merely formed a sharp linear diffraction pattern entirely incapable of being resolved into anything else by the eye1 however much it might be magnified4 ,here one has1 set out in unmistakable terms1 the same kind of differences which appear in viewing celestial detail through telescopes of various aperture4 ,what cannot be seen at all with a low aperture may be seen with higher ones under totally different aspects2 while in each case the apparent sharpness and clarity of the image is somewhat extraordinary4 ,further in ,fig4 #ahi;b in using the resolving power of the objective of high numerical aperture1 the image may be quite wrecked by a little carelessness in focussing1 or by mismanagement of light1 so that one would hardly know that the valve had markings other than those seen with the objectives of lower aperture1 and under these circumstances added magnification would do more harm than good4 ,in precisely the same way mismanagement of the illumination in ,fig4 #ahi;a would cause the stri to vanish and with ,navicula ,lyra1 as with many other diatoms1 the resolution into stri is a thing which often depends entirely on careful lighting1 and the detail flashes into distinctness or vanishes with a suddenness which is altogether surprising4 ,for 8lighting0 read 8atmosphere10 and you have just the sort of conditions that exist in telescope vision4 ,with respect to magnifying powers what has already been said is sufficient to indicate that on the whole the lowest power which discloses to the eye the detail within the reach of the resolving power of the objective is the most satisfactory4 ,every increase above this magnifies all the optical faults of the telescope and the atmospheric difficulties as well1 beside decreasing the diameter of the emergent pencil which enters the eye1 and thereby causing serious loss of acuity4 ,for the eye like any other optical instrument loses resolving power with decrease of effective aperture1 and1 besides1 a very narrow beam entering it is subject to the interference of entoptic defects1 such as floating motes and the like1 to a serious extent4 ,figure #aij shows from ,cobb's experiments 7,am4 ,jour4 of ,physiol41 #ce1 #cce7 the effect of reduction of ocular aperture upon acuity4 ,the curve shows very plainly that for emergent pencils below a millimeter 7#a_/be inch7 in diameter1 visual acuity falls off almost in direct proportion to the decreasing aperture4 ,below this figure there can be only incidental gains1 such as may be due to opening up double stars and simultaneously so diminishing the general illumination as to render the margins of the star discs a little less conspicuous4 ,an emergent pencil of this diameter is not quite sufficient for the average eye to utilize fully the available resolving power and some excess of magnification even though it actually diminishes visual acuity materially1 may be of some service4 ,illustration3 ,,fig4 #aij4--,resolving ,power of the ,eye4 ,increased acuity will of course be gained for the same magnification in using an objective of greater diameter1 to say nothing of increased resolving power1 at the cost1 of course1 of relatively greater atmospheric troubles4 ,to come down to figures as to the resolving power of the eye1 often repeated experiments have shown that two points offering strong contrast with the background can be noted as separate by the normal eye when at an angular separation of about #c of arc4 ,people1 as we have seen1 differ considerably in acuity so that now and then individuals will considerably better this figure1 while others1 far less keen sighted1 may require a separation of #d or even #e4 ,the pair of double stars #a1 #b1 ,lyr1 separated by #c #bg mags4 nearly #d and #e respectively1 can be seen as separate by those of fairly keen vision1 while ,mizar and ,alcor1 #aa apart1 seem thrown wide to nearly every one4 ,on the other hand the writer has never known anybody who could separate the two components of ,asterope of the ,pleiades1 distant a scant #b but of mags4 #f4e and #g4j only1 while ,pleione and ,atlas1 distance about #e1 mags4 #f4e and #d1 are very easy4 ,assuming for liberality that the separation constant is in the neighborhood of #e one can readily estimate the magnification that for any telescope will take full advantage of its resolving power4 ,as we have already seen this resolving power is practically #d4ef_/;,a for equal stars moderately bright4 ,an objective of #d4ef inches aperture has a resolving constant of #a and to develop this should take a magnification of say #cjj1 about #fe to the inch of aperture1 requiring a focal length of ocular about #j4bj to #j4be inch for telescopes of normal relative aperture1 and pushing the emergent pencil down to little more than #j4jb inch1--rather further than is physiologically desirable4 ,except for these extreme stunts of separation1 half to two thirds this power is preferable and conditions under which one can advantageously go above this limit are very rare indeed4 ,a thoroughly good objective or mirror will stand quite #ajj magnification to the inch without1 as the microscopist would say1 8breaking down the image10 but in at least nine cases out of ten the result will be decidedly unsatisfactory4 ,as the relative aperture of the instrument increases1 other things being equal1 one is driven to oculars of shorter and shorter focus to obtain the same magnification and soon gets into trouble4 ,very few oculars below #j4bj inch in focus are made1 and such are rarely advisable1 although occasionally in use down to #j4ae inch or thereabouts4 ,the usual ,f_/#ae aperture is a figure quite probably as much due to the undesirability of extremely short focus oculars as to the easier corrections of the objective4 ,in the actual practice of experienced observers the indications of theory are well borne out4 ,data of the habits of many observers of double stars are of record and the accomplished veteran editor of ,the ,observatory1 ,mr4 ,t4 ,lewis1 took the trouble in one of his admirable papers on 8,double ,star ,astronomy0 7,obs4 #cf1 #dbf7 to tabulate from the original sources the practice of a large group of experts4 ,the general result was to show the habitual use with telescopes of moderate size of powers around #ej per inch of aperture1 now and then on special occasions raised to the neighborhood of #gj per inch4 ,but the data showed unequivocally just what has been already indicated1 that large apertures1 suffering severely as they generally do from turbulence of the air1 will not ordinarily stand their due proportion of magnification4 ,with the refractors of #bd inches aperture and upwards the records show that even in this double star work1 where1 if anywhere1 high power counts1 the general practice ran in the vicinity of #cj per inch of aperture4 ,analyzing the data more completely in this respect ,mr4 ,lewis found that the best practise of the skilled observers studied was approximately represented by the empirical equation m #adj ,a ,of course the actual figures must vary with the conditions of location and the general quality of the seeing1 as well as the work in hand4 ,for other than double star work the tendency will be generally toward lower powers4 ,the details which depend on shade perception rather than visual acuity are usually hurt rather than helped when magnified beyond the point at which they are fairly resolved1 quite as in the case of the microscope4 ,now and then they may be made more distinct by the judicious use of shade glasses4 ,quite apart from the matter of the high powers which can advantageously be used on a telescope1 one must for certain purposes consider the lowest powers which are fairly applicable4 ,this question really turns on the largest utilizable emergent pencil from the eye piece4 ,it used to be commonly stated that inch for the emergent pencil was about a working maximum1 leading to a magnification of #h per inch of aperture of the objective4 ,this in view of our present knowledge of the eye and its properties is too low an estimate of pupillary aperture4 ,it is a fact which has been well known for more than a decade that in faint light1 when the eye has become adapted to its situation1 the pupil opens up to two or three times this diameter and there is no doubt that a fifth or a fourth of an inch aperture can be well utilized1 provided the eye is properly dark-adapted4 ,for scrutinizing faint objects1 comet sweeping and the like1 one should therefore have one ocular of very wide field and magnifying power of #d or #e per inch of aperture1 the main point being to secure a field as wide is practicable4 ,one may use for such purposes either a very wide field ,huyghenian1 or1 if cross wires are to be used1 a ,kellner form4 ,fifty degrees of field is perfectly practicable with either4 ,as regards the rest of the eyepiece equipment the observer may well suit his own convenience and resources4 ,usually one ocular of about half the maximum power provided will be found extremely convenient and perhaps oftener used than either the high or low power4 ,oculars of intermediate power and adapted for various purposes will generally find their way into any telescopic equipment4 ,and as a last word do not expect to improve bad conditions by magnifying4 ,if the seeing is bad with a low power1 cap the telescope and await a better opportunity4 ,,appendix ,,work ,,for ,,the ,,telescope ,to make at first hand the acquaintance of the celestial bodies is1 in and of itself1 worth the while1 as leading the mind to a new sense of ultimate values4 ,to tell the truth the modern man on the whole knows the ,heavens less intimately than did his ancestors4 ,he glances at his wrist-watch to learn the hour and at the almanac to identify the day4 ,the rising and setting of the constellations1 the wandering of the planets among the stars1 the seasonal shifting of the sun's path--all these are a sealed book to him1 and the intricate mysteries that lie in the background are quite unsuspected4 ,the telescope is the lifter of the cosmic veil1 and even for merely disclosing the spectacular is a source of far-reaching enlightenment4 ,but for the serious student it offers opportunities for the genuine advancement of human knowledge that are hard to underestimate4 ,it is true that the great modern observatories can gather information on a scale that staggers the private investigator4 ,but in this matter fortune favors the pertinacious1 and the observer who settles to a line of deliberate investigation and patiently follows it is likely to find his reward4 ,there is so much within the reach of powerful instruments only1 that these are in the main turned to their own particular spheres of usefulness4 ,for modest equipment there is still plenty of work to do4 ,the study of variable stars offers a vast field for exploration1 most fruitful perhaps with respect to the irregular and long-period changes of which our own ,sun offers an example4 ,even in solar study there are transient phenomena of sudden eruptions and of swift changes that escape the eye of the spectro-heliograph1 and admirable work can be done1 and has been done1 with small telescopes in studying the spectra of sun spots ,temporary stars visible to the naked eye or to the smallest instruments turn up every few years and their discovery has usually fallen to the lot of the somewhat rare astronomer1 professional or amateur1 who knows the field of stars as he knows the alphabet4 ,the last three important nov fell to the amateurs--two to the same man4 ,comets are to be had for the seeking by the persistent observer with an instrument of fair light-grasp and field2 one distinguished amateur found a pair within a few days1 acting on the theory that small comets are really common and should be looked for--most easily by one who knows his nebul1 it should be added4 ,and within our small planetary system lies labor sufficient for generations4 ,we know little even about the superficial characters of the planets1 still less about their real physical condition4 ,we are not even sure about the rotation periods of ,venus and ,neptune4 ,the clue to many of the mysteries requires eternal vigilance rather than powerful equipment1 for the appearance of temporary changes may tell the whole story4 ,the old generation of astronomers who believed in the complete inviolability of celestial order has been for the most part gathered to its fathers1 and we now realize that change is the law of the universe4 ,within the solar system there are planetary surfaces to be watched1 asteroids to be scanned for variability or change of it1 meteor swarms to be correlated with their sources1 occultations to be minutely examined1 and when one runs short of these1 our nearest neighbor the ,moon offers a wild and physically unknown country for exploration4 ,it is suspected with good reason of dynamic changes1 to say nothing of the possible last remnants of organic life4 ,much of this work is well within the useful range of instruments of three to six inches aperture4 ,the strategy of successful investigation is in turning attention upon those things which are within the scope of one's equipment1 and selecting those which give promise of yielding to a well directed attack4 ,and to this end efforts correlated with those of others are earnestly to be advised4 ,it is hard to say too much of the usefulness of directed energies like those of the ,variable ,star ,association and similar bodies4 ,they not only organize activities to an important common end1 but strengthen the morale of the individual observer4 ,,index ,a ,abb1 roof prism1 #afb ,aberration1 compensated by minute change of focus1 #bff illuminates the diffraction minima1 #bfe relation determines of focus and aperture1 #bff ,achromatic long relief ocular1 #adf objective1 #gg ,achromatism1 condition for1 #gh determination of1 #gh imperfection of1 #hg ,adjustment where ,polaris invisible1 #bce ,air waves1 length of1 #bee ,alt-azimuth mount for reflector1 #ajb mounts1 with slow motions1 #ajb setting up an1 #bbh ,anastigmats1 #hd ,annealing1 pattern of strain1 #fh ,astigmatism1 #hd1 #bji of figure1 #baj ,astronomy1 dawn of popular1 #ai ,b ,bacon1 ,roger1 alleged description of telescopes1 #f ,barlow lens1 #aeb 8,bent10 objective1 #hf ,binocular1 #b advantage of1 exaggerated1 #aea for strictly astronomical use1 #aeb telescopes for astronomical use1 #afc ,c ,camouflage1 in optical patents1 #ig ,cassegrain1 design for reflecting telescope1 #bb ,cassegrain1 sculptor and founder of statues1 #bb ,cell1 taking off from a telescope1 #bjb ,chromatic aberration1 #aa1 #gf investigation of1 #baj correction1 differences in1 #ia error of the eye1 #ij ,clairault's condition1 #ha two cemented forms for1 #ha ,clarks1 portable equatorial mounting1 #aji terrestrial prismatic eyepiece1 #aeh ,clock1 the cosmic1 #bcc ,clock drive1 #aaj1 #agd ,clock mechanism1 regulating rate of motor1 #agi ,coddington lens1 #acg ,clostat constructions1 #abf tower telescopes1 #abg ,color correction1 commonly used1 #baa examined by spectroscope1 #baa of the great makers1 #ij ,coma-free1 condition combined with ,clairault's1 #hc ,comet seeker1 ,caroline ,herschel's #aah seekers with triple objective1 #aai ,crowns distinguished from flints1 #fd ,curves1 struggle for non-spherical1 #ah ,d ,davon micro-telescope1 #adh ,dawes' ,limit1 #bfa in physiological factors1 #bfc ,declination circle1 #ajh adjustment of1 #bci ,declination circle1 adjustment by1 #bcg facilitates setting up instrument1 #aaj ,definition condition for excellence of1 #bed good in situations widely different1 #bed ,de,rheita1 #ab constructed binoculars1 #ac terrestrial ocular1 #ac ,descartes' dioptrics1 publication of1 #aa lens with elliptical curvature1 #ab ,dew cap1 #bai ,diaphragms1 importance of1 #dc ,diffraction figure for bright line1 #bfi pattern1 #bef solid1 apparent diameter of1 #bfb solid of planet1 #bfi solid for a star1 #bfj spectra1 #aij system1 scale of1 #bfj varies inversely with aperture1 #bfj through objective1 #beh ,digges1 account suggests camera obscura1 #g ,dimensions1 customary1 telescope of1 #bd ,discs1 inspection of glass1 #ff roughing to form1 #fi ,distortion1 #hf ,dolland1 ,john1 #bh published his discovery of achromatism1 #bi ,peter1 early triple objective1 #bi ,dome wholly of galvanized iron1 #bej ,domes1 #bdf ,driving clock1 a simple1 #agd pendulum controlled1 #agg clocks spring operated1 #age ,e ,english equatorial1 #aaj mounts1 mechanical stability of1 #aac ,equatorial1 adjustments of1 #bcj ,equatorial1 coud1 #abd mount1 different situations in using1 #bbi mount1 first by ,short1 #ajd mount1 pier overhung1 #aae mount in section1 #ajg two motions necessary in1 #ajf ,equilibrating levers1 devised by ,t4 ,grubb1 #ci ,evershed1 direct vision solar spectroscope1 #ahi ,eye lens1 simple1 preferred by ,sir ,w4 ,herschel1 #acf ,eyepiece1 compensating1 #adb ,huygenian1 #aci ,huygenian1 achromatism of1 #adj ,huygenian1 with cross wires1 #adj ,huygenian1 field of1 #ada ,huygenian focal length of1 #adc measuring focus of1 #acf microscope form1 #adg1 #adh monocentric1 #aci a simple microscope1 #acd ,tolles solid1 #ada ,f ,field1 curvature of1 #he glass1 arrangement of parts1 #aea ,galilean1 #aej lens diameter possible1 #aej ,field lens1 #aci ,figuring locally1 #gc process of1 #gc ,filar micrometer1 #agb ,finder1 #ajh1 #acb adjustment of1 #bcj ,fine grinding1 #fi ,fixed eyepiece mounts1 #aah ,flints1 highly refractive due to ,guinand1 #cf ,foucault1 #ci development of silver on glass reflector1 #da knife edge test1 #bab ,foucault1 methods of working and testing1 #da ,fraunhofer1 #cf applied condition of absence of coma1 #hb form of objectives1 #cg long list of notable achievements1 #ch 8,front view0 telescope1 #cb mechanical difficulty of1 #cc ,furnaces1 glass1 classes of1 #ei ,g ,galilean telescope1 small field of1 #i ,galileo1 exhibited telescope to senators of ,venice1 #h grasps the general principles1 #g produces instrument magnifying #cb times1 #h ,gascoigne1 ,william1 first using genuine micrometer1 #ab ,gauss1 ,objective1 #hb ,gerrish1 application of drive1 #aha motor drive1 #agi ,ghosts1 #acg ,glass1 dark1 as sunshade1 #aff forming and annealing1 #fb inspection of raw1 #fa losses by volatilization1 #eh materials of1 #ei origin of1 #eg persistent bubbles in1 #eh a solid solution1 #eg ,grating spectroscopes1 #aij ,gratings1 spectroscope1 #ahi ,gregory1 ,james1 described construction which bears his name1 #ai failed of material success1 #bj ,grubb1 ,sir ,howard1 objectives1 #gd ,guinand1 ,pierre ,louis1 improvements in optical glass1 #cf ,h ,hadley1 disclosed test for true figure1 #bg ,john1 real inventor of reflector1 #be ,hadley's reflector1 tested with satisfactory results1 #bf ,hall1 ,chester ,moor1 designed first achromatic telescope1 #bg had telescopes made as early as #agcc1 #bg ,hand telescope1 magnifying power1 #aej monocular1 #aea ,hartmann test1 #bac on large objectives1 #bfg principle of1 #bad ,hartness1 turret telescope1 #acj1 #aca ,heliometer1 principle of1 #aga ,hensoldt1 prism form1 #afc ,herschel's discovery of ,uranus1 #cb forty foot telescope1 #cd ,sir ,john1 #ce ,sir ,john1 proposed defining condition1 #ha ,sir ,william1 #ca ,herschel's time1 instruments of1 #ce ,hevelius1 construction for objective of #aej feet1 #ag directions for designing ,galilean and ,keplerian telescopes1 #ad invention of first periscope1 #ae ,johannes1 #ac mention of advantage of plano convex lens1 #ad mentions telescope due to ,de,rheita1 #ad ,housing reflector of #cf inch aperture1 #bdc rolling on track1 #bdb simplest instrument for fixed1 #bda ,huygens1 ,christian1 devised methods of grinding polishing1 #af ,huygens' eyepiece1 introduction of1 #bd ,huygens1 sketch of ,mars1 #af ,i ,image1 correct extra focal1 #bjh critical examination of1 #bjd ,image1 curvature of1 #hg seen without eyepiece1 #acd showing unsymmetrical coloring1 #bjh ,interference rings1 eccentric1 #bje ,irradiation1 #bfb ,j ,jansen1 ,zacharius1 #d ,k ,kellner1 ocular1 #ade ,kepler1 astronomical telescope1 #aj differences of from ,galilean form1 #aj ,knife edge test of parabolic mirror1 #bab ,l ,lacquer1 endurance of coating1 #bbc ,latitude scale1 #bcb ,lenses1 determinate forms for1 #hj ,lens1 magnifying power of1 #acd 8crossed10 #bd polishing the fine ground1 #gj power of1 #gh triple cemented1 a useful ocular1 #ach simple achromatic1 #acg single1 has small field1 #acg spotted1 cleaning of1 #bag ,light grasp and resolving power1 #bfe small telescope fails in1 #bfd ,light ratio of star magnitudes1 #bfd ,light transmitted by glass1 #ec ,lippershey1 ,jan1 #b discovery1 when made1 #e retainer to1 #c ,lunette ,napoleon ,troisime1 #aed1 #aee1 #afb ,m ,magnifying power1 directly as ratio of increase in tangent1 #ace powers1 increase of1 #bgc ,marius1 ,simon1 #e used with glasses from spectacles1 #e ,marius1 picked up satellites of ,jupiter1 #e ,meridian photometer1 #aid ,metius1 ,james1 #d ,metius1 tale of1 #d ,micrometer1 double image1 #aga square bar1 #aga ,micrometers1 #afh ,micrometry1 foundations of1 #ab ,mirror's1 aberrations of1 #ib adjustment of1 #bjf concave spherical1 #ib final burnishing of1 #bbf hyperboloidal1 #if lacquer coating for surface1 #bba mounting1 by ,browning1 #di parabolic oblique1 shows aberration1 #ie surface1 prevention of injury to1 #bbj ,mittenzwey ocular1 #ada ,mountain stations1 good or very bad1 #bed ,mounts1 alt-azimuth and equatorial1 #ih ,myopia1 glasses for1 came slowly1 #b ,n ,navicula ,lyra1 stages of resolution of1 #bga ,newton1 abandoned parabolic mirror1 #ba blunder in experiment1 #bj gave little information about material for mirrors1 #bc ,isaac1 attempt at a reflector1 #bj ,normal spectra1 #aij ,o ,objective1 adjustable mount for1 #dd adjusting screws of1 #dd ,clark's form1 #hc cleansing1 #bjc examination of1 #bjb ,objective1 four-part1 #he ,fraunhofer flint-ahead1 #hc how to clean1 #baf spacers1 to take out1 #bag typical stri in1 #bjc ,objective prism1 photographing with1 #ahe1 #ahg ,objectives1 crown glass equiconvex1 #hj over-achromatized1 #ij rated on focal length for green #bd ,observatories1 cost of ,romsey1 #beb ,observatory at small expense1 #bdi ,romsey1 description of1 #bdi with simple sliding roof1 #bde ,observing box1 #bbi ,oblique fork alt-azimuth1 #ajj ,ocular1 apparent angular field of1 #adf terrestrial1 #adg ,tolles terrestrial1 #adg typical form1 #de ,oculars1 radius of curvature of image in1 #adf undesirability of short focus1 #bge ,open fork mount1 #aae well suited to big reflectors1 #aag ,optical axis1 to adjust declination of1 #bch ,optical glass1 classes of1 #fc data and analysis of1 #fd industry1 due to single man1 #cf production of1 #fj ,orthoscopic ocular1 #ade ,p ,parallactic mount1 #ajd ,petition for annulment of ,dolland's patent1 #bi ,photometer1 artificial star ,zllner1 #aid extinction1 #aih photoelectric cell1 #aii precision of astronomical1 #aii selenium cell1 #aii ,zllner1 #aig ,photometers1 three classes in stellar1 #aic 8,photo-visual1 objective10 #hi ,pillar-and-claw stand1 #ih ,pillar mount1 #bdj ,pitch1 optician's1 #ga ,placement for tripod legs1 #bcf ,polar and coud forms of reflector1 #abe axis1 adjustment of by level1 #bcb axis1 alignment to meridian1 #bcb axis1 setting with finder altitude of1 #bcd telescope1 #aai1 #abb ,polaris1 hour angle of1 #bcc a variable star1 #aii ,polarizing photometer1 #aic ,pole1 position1 #bcd ,polishing machine1 #gj surface of tool1 #gb tool1 #ga ,porro's second form1 #aeg work1 original description of1 #aef ,porta1 description unintelligible1 #g ,portable equatorial1 adjustment of1 #bcj telescopes1 mounting of1 #bbh ,porter polar reflector1 #acj ,position angle micrometer of ,lowell ,observatory1 #agc ,powers1 lowest practicable1 #bgf ,prismatic inversion1 ,porro's first form1 #aee ,prismatic inverting system1 the first1 #aed ,prisms1 ,dove's1 #aed ,prism field glasses1 stereoscopic effect of1 #aei ,prism glass1 #aeb loss of light in1 #afj objectives of1 #afa weak points of1 #afj ,r ,resolving constant1 magnification to develop1 #bge power and verity of detail1 #b power of the eye1 #bgd ,reticulated micrometer1 #afi ,reversion prism1 #aec ,right ascension circle1 #ajh ,ring micrometer1 #afi computation of results of1 #agj ,ring system faults due to strain1 #bje 8,romsey0 observatory type1 #bdh ,rack motion in altitude1 #ajj ,ramsden1 ocular1 #add ,reflection1 coefficient of1 from silvered surface1 #ed ,reflector costs1 #ee cover for1 #bdb development in ,england1 #da for astrophysical work1 #ef light-grasp of1 #ec relative aperture of1 #ej section of ,newtonian1 #de skeleton construction1 #di suffers from scattered light1 #ef working field of1 #ee ,refractive index1 #fc ,refractors and reflectors1 relative advantages of1 #eb few made after advent of reflector1 #bg in section1 #dc light transmission of1 #ec ,refractors1 relative equivalent apertures of1 #ed tubes of1 #db ,s ,scheiner1 ,christopher1 use of ,kepler's telescope1 #aa devised parallactic mount1 #aa ,secondary spectrum1 #hg new glasses reducing1 #hh ,seeing1 #beg conditions1 for difference of aperture1 #beg conditions generally bad1 #bec standard scale of1 #bef true inwardness of bad1 #bec ,separating power1 to compute1 #bfa ,short1 ,james1 mastered art of figuring paraboloid1 #bg took up ,gregorian construction with success1 #bg ,shortened telescope1 #aeb ,sights1 on portable mount1 #bbi ,silver films1 condition of1 #ed ,silvering1 ,ludin's process1 #bbe processes1 #bbb process1 ,dr4 ,brashear's1 #bbb ,sine condition1 ,abb's1 #hb ,slit1 spectroscope1 ,abb type1 #ahd ,snow clostat telescope1 #abg ,solar diagonal1 #aff eye piece diaphragms in1 #afh early spectroscopes1 #ahh polarizing eyepiece1 #afg spectroscope1 #ahg ,spacers1 #dd1 #bah ,spectacle lenses1 combination of1 #b ,spectacles for presbyopia1 #b invention of1 #a ,spectra1 visibility of stellar1 #ahc ,spectro-heliograph1 principle of1 #aia simple type of ,hale's1 #aia ,spectroscope1 #ahb construction of astronomical1 #ahb of ,lowell refractor1 #ahe ocular1 ,mc,clean form1 #ahc ,specula1 small1 methods of support1 #di ,speculum metal composition of1 #bd ,sphenoid prisms1 #aeh1 #afc ,spherical aberration1 #aa amount of1 #hj annulling in both directions1 #hd examination for1 #bjg quick test of1 #bfg remedy for1 #gi concave mirror1 errors of1 #bb ,star1 appearance of1 #bjd artificial1 #ff1 #bjc diagonal1 #afe disc1 apparent diameter of1 #bei image of reflector1 #bjf ,steinheil1 achromatic ocular1 #add ,karl ,august1 silvering specula1 #ci ,stri1 location of1 #fg ,surface1 treatment of deterioration of1 #bah ,t ,taylor1 triplets with reduced secondary spectrum1 #hi ,telescopes1 choice and purchase of1 #bja ,early in #afaj made in ,england1 #f first1 #c the first astronomical1 #i improvement of early1 #aa lineage of1 #a name devised1 #i ,telescopes1 portable and fixed1 #ajh #afji1 for sale in ,paris1 #e size and mounting of early1 #ad ,telescopic vision1 discovery of1 #b ,templets1 designed curves of1 #fi ,tests for stri and annealing1 #fh ,transparency1 lack of in atmosphere1 #bee ,triplet1 cemented1 #he ,turret housing of reflector1 #bdd ,v ,variable stars1 #aib ,w ,wedge calibrated by observation1 #aig photographic1 #aig photometer1 #aig ,wind1 shelter from1 #bdj ,z ,zeiss1 binocular of extreme stereoscopic effect1 #afa ,zllner1 photometer modification of1 #aih ,zonal aberration1 #bji 99 99 99 99 99 ,transcriber's ,notes ,obvious typographical errors have been silently corrected4 ,variations in hyphenation and accents have been standardised but all other spelling and punctuation remains unchanged4 ,italics are represented thus italic1 bold thus bold1 subscript thus s and underline thus underline4 ,in caption of ,fig4 #di4--,spherical ,aberration of ,concave ,lens4 ,concave has been changed to ,convex ,in 8,an objective of #d4ef inches aperture has a resolving constant of #a and to develop this should take a magnification of say #cjj10 #a has been hand altered in the original and may be #a4 ,the table 8,characteristics of ,optical ,glasses has been divided to fit within the width restriction4