,,the ,,microscope4 ,,being ,,the ,,article ,,contributed ,,by ,,andrew ,,ross ,,to ,,the 8,,penny ,,cyclop,,dia10 ,,published ,,by ,,the ,,society ,,for ,,the ,,diffusion ,,of ,,useful ,,knowledge4 ,,fully ,,illustrated4 ,,new ,,york3 ,,the ,,industrial ,,publication ,,company4 #ahgg4 ,,the ,,microscope4 ,microscope1 the name of an instrument for enabling the eye to see distinctly objects which are placed at a very short distance from it1 or to see magnified images of small objects1 and therefore to see smaller objects than would otherwise be visible4 ,the name is derived from the two ,greek words1 expressing this property1 ,,mikros1 small1 and ,,skopeo1 to see4 ,so little is known of the early history of the microscope1 and so certain is it that the magnifying power of lenses must have been discovered as soon as lenses were made1 that there is no reason for hazarding any doubtful speculations on the question of discovery4 ,we shall proceed therefore at once to describe the simplest forms of microscopes1 to explain their later and more important improvements1 and finally to exhibit the instrument in its present perfect state4 ,in doing this we shall assume that the reader is familiar with the information contained in the articles 8,light10 8,lens10 8,achromatic10 8,aberration10 and the other sub-divisions of the science of ,optics1 which are treated of in this work4 ,the use of the term magnifying has led many into a misconception of the nature of the effect produced by convex lenses4 ,it is not always understood that the so-called magnifying power of a lens applied to the eye1 as in a microscope1 is derived from its enabling the eye to approach more nearly to its object than would otherwise be compatible with distinct vision4 ,the common occurrence of walking across the street to read a bill is in fact magnifying the bill by approach2 and the observer1 at every step he takes1 makes a change in the optical arrangement of his eye1 to adapt it to the lessening distance between himself and the object of his inquiry4 ,this power of spontaneous adjustment is so unconsciously exerted1 that unless the attention be called to it by circumstances1 we are totally unaware of its exercise4 ,in the case just mentioned the bill would be read with eyes in a very different state of adjustment from that in which it was discovered on the opposite side of the street1 but no conviction of this fact would be impressed upon the mind4 ,if1 however1 the supposed individual should perceive on some part of the paper a small speck1 which he suspects to be a minute insect1 and if he should attempt a very close approach of his eye for the purpose of verifying his suspicion1 he would presently find that the power of natural adjustment has a limit2 for when his eye has arrived within about ten inches1 he will discover that a further approach produces only confusion4 ,but if1 as he continues to approach1 he were to place before his eye a series of properly arranged convex lenses1 he would see the object gradually and distinctly increase in apparent size by the mere continuance of the operation of approaching4 ,yet the glasses applied to the eye during the approach from ten inches to one inch1 would have done nothing more than had been previously done by the eye itself during the approach from fifty feet to one foot4 ,in both cases the magnifying is effected really by the approach1 the lenses merely rendering the latter periods of the approach compatible with distinct vision4 ,a very striking proof of this statement may be obtained by the following simple and instructive experiment4 ,take any minute object1 a very small insect for instance1 held on a pin or gummed to a slip of glass2 then present it to a strong light1 and look at it through the finest needle-hole in a blackened card placed about an inch before it4 ,the insect will appear quite distinct1 and about ten times larger than its usual size4 ,then suddenly withdraw the card without disturbing the object1 which will instantly become indistinct and nearly invisible4 ,the reason is1 that the naked eye cannot see at so small a distance as one inch4 ,but the card with the hole having enabled the eye to approach within an inch1 and to see distinctly at that distance1 is thus proved to be as decidedly a magnifying instrument as any lens or combination of lenses4 ,this description of magnifying power does not apply to such instruments as the solar or gas microscope1 by which we look not at the object itself1 but at its shadow or picture on the wall2 and the description will require some modification in treating of the compound microscope1 where1 as in the telescope1 an image or picture is formed by one lens1 that image or picture being viewed as an original object by another lens4 ,it is nevertheless so important to obtain a clear notion of the real nature of the effect produced by a lens applied to the eye1 that we will adduce the instance of spectacles to render the point more familiar4 ,if the person who has been supposed to cross the street for the purpose of reading a bill had been aged1 the limit to the power of adjustment would have been discovered at a greater distance1 and without so severe a test as the supposed insect4 ,the eyes of the very aged generally lose the power of adjustment at a distance of thirty or forty inches instead of ten1 and the spectacles worn in consequence are as much magnifying glasses to them as the lenses employed by younger eyes to examine the most minute objects4 ,spectacles are magnifying glasses to the aged because they enable such persons to see as closely to their objects as the young1 and therefore to see the objects larger than they could themselves otherwise see them1 but not larger than they are seen by the unassisted younger eye4 ,in saying that an object appears larger at one time1 or to one person1 than another1 it is necessary to guard against misconception4 ,by the apparent size of an object we mean the angle it subtends at the eye1 or the angle formed by two lines drawn from the centre of the eye to the extremities of the object4 ,in ,fig4 #a1 the lines ,a ,e and ,b ,e drawn from the arrow to the eye form the angle ,a ,e ,b1 which1 when the angle is small1 is nearly twice as great as the angle ,c ,e ,d1 formed by lines drawn from a similar arrow at twice the distance4 ,the arrow ,a ,b will therefore appear nearly twice as long as ,c ,d1 being seen under twice the angle1 and in the same proportion for any greater or lesser difference in distance4 ,the angle in question is called the angle of vision1 or the visual angle4 ,illustration3 ,fig4 #a4 ,the angle of vision must1 however1 not be confounded with the angle of the pencil of light by which an object is seen1 and which is explained in ,fig4 #b4 ,here we have drawn two arrows placed in relation to the eye as before1 and from the centre of each have drawn lines exhibiting the quantity of light which each point will send into the eye at the respective distances4 ,illustration3 ,fig4 #b4 ,now if ,e ,f represent the diameter of the pupil1 the angle ,e ,a ,f shows the size of the cone or pencil of light which enters the eye from the point ,a1 and in like manner the angle ,e ,b ,f is that of the pencil emanating from ,b1 and entering the eye4 ,then1 since ,e ,a ,f is double ,e ,b ,f1 it is evident that ,a is seen by four times the quantity of light which could be received from an equally illuminated point at ,b2 so that the nearer body would appear brighter if it did not appear larger2 but as its apparent area is increased four times as well as its light1 no difference in this respect is discovered4 ,but if we could find means to send into the eye a larger pencil of light1 as for instance that shown by the lines ,g ,a ,h1 without increasing the apparent size in the same proportion1 it is evident that we should obtain a benefit totally distinct from that of increased magnitude1 and one which is in some cases of even more importance than size in developing the structure of what we wish to examine4 ,this1 it will be hereafter shown1 is sometimes done2 for the present1 we wish merely to explain clearly the distinction between apparent magnitude1 or the angle under which the object is seen1 and apparent brightness1 or the angle of the pencil of light by which each of its points is seen1 and with these explanations we shall continue to employ the common expressions magnifying glass and magnifying power4 ,illustration3 ,fig4 #c4 ,the magnifying power of a single lens depends upon its focal length1 the object being in fact placed nearly in its principal focus1 or so that the light which diverges from each point may1 after refraction by the lens1 proceed in parallel lines to the eye1 or as nearly so as is requisite for distinct vision4 ,in ,fig4 #c1 ,a ,b is a double convex lens1 near which is a small arrow to represent the object under examination1 and the cones drawn from its extremities are portions of the rays of light diverging from those points and falling upon the lens4 ,these rays1 if suffered to fall at once upon the pupil1 would be too divergent to permit their being brought to a focus upon the retina by the optical arrangements of the eye4 ,but being first passed through the lens1 they are bent into nearly parallel lines1 or into lines diverging from some points within the limits of distinct vision1 as from ,c and ,d4 ,thus altered1 the eye receives them precisely as if they emanated from a larger arrow placed at ,c ,d1 which we may suppose to be ten inches from the eye1 and then the difference between the real and the imaginary arrow is called the magnifying power of the lens in question4 ,from what has been said it will be evident that two persons whose eyes differed as to the distance at which they obtained distinct vision1 would give different results as to the magnifying power of a lens4 ,to one who can see distinctly with the naked eye at a distance of five inches1 the magnifying power would seem and would indeed be only half what we have assumed4 ,such instances are1 however1 rare2 the focal length of the eye usually ranges from six to twelve or fourteen inches1 so that the distance we first assumed of ten inches is very near the true average1 and is a convenient number1 inasmuch as a cipher added to the denominator of the fraction which expresses the focal length of a lens gives its magnifying power4 ,thus a lens whose focal length is one-sixteenth of an inch is said to magnify #afj times4 ,when the focal length of a lens is very small1 it is difficult to measure accurately the distance between its centre and its object4 ,in such cases the best way to obtain the focal length for parallel or nearly parallel rays is to view the image of some distant object formed by the lens in question through another lens of one inch solar focal length1 keeping both eyes open and comparing the image presented through the two lenses with that of the naked eye4 ,the proportion between the two images so seen will be the focal length required4 ,thus if the image seen by the naked eye is ten times as large as that shown by the lenses1 the focal length of the lens in question is one-tenth of an inch4 ,the panes of glass in a window1 or courses of bricks in a wall1 are convenient objects for this purpose4 ,in whichever way the focal length of the lens is ascertained1 the rules given for deducing its magnifying power are not rigorously correct1 though they are sufficiently so for all practical purposes1 particularly as the whole rests on an assumption in regard to the focal length of the eye1 and as it does not in any way affect the actual measurement of the object4 ,to calculate with great precision the magnifying power of a lens with a given focal length of eye1 it is necessary that the thickness of the lens be taken into the account1 and also the focal length of the eye itself4 ,we have hitherto considered a magnifying lens only in reference to its enlargement of the object1 or the increase of the angle under which the object is seen4 ,a further and equally important consideration is that of the number of rays or quantity of light by which every point of the object is rendered visible4 ,the naked eye1 as shown in ,fig4 #b1 admits from each point of every visible object a cone of light having the diameter of the pupil for its base1 and most persons are familiar with that beautiful provision by which in cases of excessive brilliancy the pupil spontaneously contracts to reduce the cone of admitted light within bearable limits4 ,this effect is still further produced in the experiment already described1 of looking at an object through a needle-hole in a card1 which is equivalent to reducing the pupil to the size of a needle-hole4 ,seen in this way the object becomes comparatively dark or obscure2 because each point is seen by means of a very small cone of light1 and a little consideration will suffice to explain the different effects produced by the needle-hole and the lens4 ,both change the angular value of the cone of light presented to the eye1 but the lens changes the angle by bending the extreme rays within the limits suited to distinct vision1 while the needle-hole effects the same purpose by cutting off the rays which exceed those limits4 ,it has been shown that removing a brilliant object to a greater distance will reduce the quantity of light which each point sends into the eye1 as effectually as viewing it through a needle-hole2 and magnifying an object by a lens has been shown to be the same thing in some respects as removing it to a greater distance4 ,we have to see the magnified picture by the light emanating from the small object1 and it becomes a matter of difficulty to obtain from each point a sufficient quantity of light to bear the diffusion of a great magnifying power4 ,we want to perform an operation just the reverse of applying the card with the needle-hole to the eye--we want in some cases to bring into the eye the largest possible pencil of light from each point of the object4 ,referring to ,fig4 #c1 it will be observed that if the eye could see the small arrow at the distance there shown without the intervention of the lens1 only a very small portion of the cones of light drawn from its extremities would enter the pupil2 whereas we have supposed that after being bent by the lens the whole of this light enters the eye as part of the cones of smaller angle whose summits are at ,c and ,d4 ,these cones will further explain the difference between large and small pencils of light2 those from the small arrow are large pencils2 the dotted cones from the large arrow are small pencils4 ,in assuming that the whole of this light could have been suffered to enter the eye through the lens ,a ,b1 we did so for the sake of not perplexing the reader with too many considerations at once4 ,he must now learn that so large a pencil of light passing through a single lens would be so distorted by the spherical figure of the lens1 and by the chromatic dispersion of the glass1 as to produce a very confused and imperfect image4 ,this confusion may be greatly diminished by reducing the pencil2 for instance1 by applying a stop1 as it is called1 to the lens1 which is neither more nor less than the needle-hole applied to the eye4 ,a small pencil of light may be thus transmitted through a single lens without suffering from spherical aberration or chromatic dispersion any amount of distortion which will materially affect the figure of the object2 but this quantity of light is insufficient to bear diffusion over the magnified picture1 which is therefore too obscure to exhibit what we most desire to see--those beautiful and delicate markings by which one kind of organic matter is distinguished from another4 ,with a small aperture these markings are not seen at all3 with a large aperture and a single lens they exhibit a faint nebulous appearance enveloped in a chromatic mist1 a state which is of course utterly valueless to the naturalist1 and not even amusing to the amateur4 ,it becomes therefore a most important problem to reconcile a large aperture with distinctness1 or1 as it is called1 definition2 and this has been done in a considerable degree by effecting the required amount of refraction through two or more lenses instead of one1 thus reducing the angles of incidence and refraction1 and producing other effects which will be shortly noticed4 ,this was first accomplished in a satisfactory manner by-- ,,dr4 ,,wollaston',s ,,doublet1 invented by the celebrated philosopher whose name it bears2 it consists of two plano-convex lenses 7,fig4 #d7 having their focal lengths in the proportion of #a to #c1 or nearly so1 and placed at a distance which can be ascertained best by actual experiment4 ,their plane sides are placed towards the object1 and the lens of shortest focal length next the object4 ,illustration3 ,fig4 #d4 ,it appears that ,dr4 ,wollaston was led to this invention by considering that the ,achromatic ,huyghenean ,eye-piece1 which will be hereafter described1 would1 if reversed1 possess similar good properties as a simple microscope4 ,but it will be evident when the eye-piece is understood1 that the circumstances which render it achromatic are very imperfectly applicable to the simple microscope1 and that the doublet1 without a nice adjustment of the stop1 would be valueless4 ,dr4 ,wollaston makes no allusion to a stop1 nor is it certain that he contemplated its introduction1 although his illness1 which terminated fatally soon after the presentation of his paper1 may account for the omission4 ,the nature of the corrections which take place in the doublet is explained in the annexed diagram 7,fig4 #e71 where ,l ,o ,l is the object1 ,p a portion of the pupil1 and ,d ,d the stop1 or limiting aperture4 ,now1 it will be observed that each of the pencils of light from the extremities ,l ,l of the object is rendered eccentrical by the stop1 and of consequence each passes through the two lenses on opposite sides of their common axis ,o ,p2 thus each becomes affected by opposite errors1 which to some extent balance and correct each other4 ,to take the pencil ,l1 for instance1 which enters the eye at ,r ,b1 ,r ,b2 it is bent to the right at the first lens1 and to the left at the second2 and as each bending alters the direction of the blue rays more than the red1 and1 moreover1 as the blue rays fall nearer the margin of the second lens1 where the refraction1 being more powerful than near the centre1 compensates in some degree for the greater focal length of the second lens1 the blue and red rays will emerge very nearly parallel1 and of consequence colorless to the eye4 ,at the same time the spherical aberration has been diminished by the circumstance that the side of the pencil which passes one lens nearest the axis passes the other nearest the margin4 ,this explanation applies only to the pencils near the extremities of the object4 ,the central pencil1 it is obvious1 would pass both lenses symmetrically2 the same portions of light occupying nearly the same relative places on both lenses4 ,the blue light would enter the second lens nearer to its axis than the red1 and being thus less refracted than the red by the second lens1 a small amount of compensation would take place1 quite different in principle and inferior in degree to that which is produced in the eccentrical pencils4 ,in the intermediate spaces the corrections are still more imperfect and uncertain2 and this explains the cause of the aberrations which must of necessity exist even in the best-made doublet4 ,it is1 however1 infinitely superior to a single lens1 and will transmit a pencil of an angle of from #ce to #ej without any very sensible errors4 ,it exhibits1 therefore1 many of the usual test-objects in a very beautiful manner4 ,illustration3 ,fig4 #e4 ,illustration3 ,fig4 #f4 ,the next step in the improvement of the simple microscope bears more analogy to the eye-piece4 ,this improvement was made by ,mr4 ,holland1 and it consists 7as shown in ,fig4 #f7 in substituting two lenses for the first in the doublet1 and retaining the stop between them and the third4 ,the first bending1 being thus effected by two lenses instead of one1 is accompanied by smaller aberrations1 which are therefore more completely balanced or corrected at the second bending1 in the opposite direction1 by the third lens4 ,this combination1 though called a triplet is essentially a doublet1 in which the anterior lens is divided into two4 ,for it must be recollected that the first pair of lenses merely accomplishes what might have been done1 though with less precision1 by one2 but the two lenses of the doublet are opposed to each other2 the second diminishing the magnifying power of the first4 ,the first pair of lenses in the triplet concur in producing a certain amount of magnifying power1 which is diminished in quantity and corrected as to aberration at the third lens by the change in relation to the position of the axis which takes place in the pencil between what is virtually the first and second lens4 ,in this combination the errors are still further reduced by the close approximation to the object which causes the refractions to take place near the axis4 ,thus the transmission of a still larger angular pencil1 namely #fe1 is rendered compatible with distinctness1 and a more intense image is presented to the eye4 ,every increase in the number of lenses is attended with one drawback1 from the circumstance that a certain portion of light is lost by reflection and absorption each time that the ray enters a new medium4 ,this loss bears no sensible proportion to the gain arising from the increased aperture1 which1 being as the square of the diameter1 multiplies rapidly2 or1 if we estimate by the angle of the admitted pencil1 which is more easily ascertained1 the intensity will be as the square of twice the tangent of half the angle4 ,to explain this1 let ,d ,b 7,fig4 #g7 represent the diameter of the lens1 or of that part of it which is really employed2 ,c ,a the perpendicular drawn from its centre1 and ,a ,b1 ,a ,d1 the extreme rays of the incident pencil of light ,,dab4 ,then the diameter being #b ,c ,b1 the area to which the intensity of vision is proportional will be 7#b ,c ,b71 and ,c ,b is evidently the tangent of the angle ,c ,a ,b1 which is half the angle of the admitted pencil ,d ,a ,b4 ,or1 if a be used to denote the angular aperture1 the expression for the intensity is 7#b tan4 a7 which increases so rapidly with the increase of a as to make the loss of light by reflection and absorption of little consequence4 ,illustration3 ,fig4 #g4 ,the combination of three lenses approaches1 as has been stated1 very close to the object2 so close1 indeed1 as to prevent the use of more than three2 and this constitutes a limit to the improvement of the simple microscope1 for it is called a simple microscope1 although consisting of three lenses1 and although a compound microscope may be made of only three or even two lenses2 but the different arrangement which gives rise to the term compound will be better understood when that instrument is explained4 ,before we proceed to describe the simple microscope and its appendages1 it will be well to explain such other points in reference to the form and materials of lenses as are most likely to be interesting4 ,a very useful form of lens was proposed by ,dr4 ,wollaston1 and called by him the ,periscopic lens4 ,it consisted of two hemispherical lenses1 cemented together by their plane faces1 having a stop between them to limit the aperture4 ,a similar proposal was made ,mr4 ,coddington1 who1 however1 executed the project in a better manner1 by cutting a groove in a whole sphere1 and filling the groove with opaque matter4 ,his lens1 which is the well-known ,coddington lens1 is shown in ,fig4 #h4 ,it gives a large field of view1 which is equally good in all directions1 as it is evident that the pencils ,a ,a and ,b ,b pass through under precisely the same circumstances4 ,its spherical form has the further advantage of rendering the position in which it is held of comparatively little consequence4 ,it is therefore very convenient as a hand-lens1 but its definition is of course not so good as that of a well-made doublet or achromatic lens4 ,illustration3 ,fig4 #h4 ,another very useful form of doublet was proposed by ,sir ,john ,herschel1 chiefly like the ,coddington lens1 for the sake of a wide field1 and chiefly to be used in the hand4 ,it is shown in ,fig4 #i2 it consists of a double convex or crossed lens1 having the radii of curvature as #a to #f1 and of a plane concave lens whose focal length is to that of the convex lens as #ac to #e4 ,various1 indeed innumerable1 other forms and combinations of lenses have been projected1 some displaying much ingenuity1 but few of any practical use4 ,in the ,catadioptric lenses the light emerges at right angles from its entering direction1 being reflected from a surface cut at an angle of #de degrees to the axes of the curved surfaces4 ,illustration3 ,fig4 #i4 ,it was at one time hoped1 as the precious stones are more refractive than glass1 and as the increased refractive power is unaccompanied by a correspondent increase in chromatic dispersion1 that they would furnish valuable materials for lenses1 inasmuch as the refractions would be accomplished by shallower curves1 and consequently with diminished spherical aberration4 ,but these hopes were disappointed2 everything that ingenuity and perseverance could accomplish was tried by ,mr4 ,varley and ,mr4 ,pritchard1 under the patronage of ,dr4 ,goring4 ,it appeared1 however1 that the great reflective power1 the doubly-refracting property1 the color1 and the heterogeneous structure of the jewels which were tried1 much more than counterbalanced the benefits arising from their greater refractive power1 and left no doubt of the superiority of skillfully made glass doublets and triplets4 ,the idea is now1 in fact1 abandoned2 and the same remark is applicable to the attempts at constructing fluid lenses1 and to the projects for giving to glass other than spherical surfaces--none of which have come into extensive use4 ,by the term simple microscope is meant one in which the object is viewed directly through a lens or combination of lenses1 just as we have supposed an arrow or an insect to be viewed through a glass held in the hand4 ,when1 however1 the magnifying power of the glass is considerable1 in other words1 when its focal length is very short1 and its proper distance from its object of consequence equally short1 it requires to be placed at that proper distance with great precision3 it cannot1 therefore1 be held with sufficient accuracy and steadiness by the unassisted hand1 but must be mounted in a frame having a rack or screw to move it towards or from another frame or stage which holds the object4 ,it is then called a microscope1 and it is furnished1 according to circumstances1 with lenses and mirrors to collect and reflect the light upon the object1 and with other conveniences which will now be described4 ,one of the best forms of a stand for a simple microscope is shown in ,fig4 #aj1 where ,a is a brass pillar screwed to a tripod base2 ,b is a broad stage for the objects1 secured to the stem by screws1 whose milled heads are at ,c4 ,by means of the large milled head ,d1 a triangular bar1 having a rack1 is elevated out of the stem ,a1 carrying the lens-holder ,e1 which has a horizontal movement in one direction1 by means of a rack worked by the milled head ,f1 and in the other direction by turning on a circular pin4 ,a concave mirror ,g reflects the light upwards through the hole in the stage1 and a lens may be attached to the stage for the purpose of throwing light on an opaque object1 in the same way that the forceps ,h for holding such objects is attached4 ,this microscope is peculiarly adapted1 by its broad stage and its general steadiness1 for dissecting2 and it is rendered more convenient for this purpose by placing it between two inclined planes of mahogany1 which support the arms and elevate the wrists to the level of the stage4 ,this apparatus is called the dissecting rest4 ,when dissecting is not a primary object1 a joint may be made at the lower end of the stem ,a1 to allow the whole to take an inclined position2 and then the spring clips shown upon the stage are useful to retain the object in its place4 ,numerous convenient appendages may be made to accompany such microscopes1 which it will be impossible to mention in detail2 the most useful are ,mr4 ,varley's capillary cages for containing animalcul in water1 and parts of aquatic plants2 also his tubes for obtaining and separating such objects1 and his phial and phial-holder for preserving and exhibiting small living specimens of the ,chara1 ,nitella1 and other similar plants1 and observing their circulation4 ,the phial-microscope affords facilities for observing the operations of minute vegetable and animal life1 which will probably lead to the most interesting discoveries4 ,the recent volumes of the ,transactions of the ,society of ,arts contain an immense mass of information of this sort1 and to these we refer the reader4 ,illustration3 ,fig4 #aj4 ,the mode of illuminating objects is one on which we must give some further information1 for the manner in which an object is lighted is second in importance only to the excellence of the glass through which it is seen4 ,in investigating any new or unknown specimen1 it should be viewed in turns by every description of light1 direct and oblique1 as a transparent object and as an opaque object1 with strong and with faint light1 with large angular pencils and with small angular pencils thrown in all possible directions4 ,every change will probably develop some new fact in reference to the structure of the object1 which should itself be varied in the mode of mounting in every possible way4 ,it should be seen both wet and dry1 and immersed in fluids of various qualities and densities1 such as water1 alcohol1 oil1 and ,canada balsam1 for instance1 which last has a refractive power nearly equal to that of glass4 ,if the object be delicate vegetable tissue1 it will be in some respects rendered more visible by gentle heating or scorching by a clear fire placed between two plates of glass4 ,in this way the spiral vessels of asparagus and other similar vegetables may be beautifully displayed4 ,dyeing the objects in tincture of iodine will in some cases answer this purpose better4 ,but the principal question in regard to illumination is the magnitude of the illuminating pencil1 particularly in reference to transparent objects4 ,generally speaking the illuminating pencil should be as large as can be received by the lens1 and no larger4 ,any light beyond this produces indistinctness and glare4 ,the superfluous light from the mirror may be cut off by a screen having various-sized apertures placed below the stage2 but the best mode of illumination is that proposed by ,dr4 ,wollaston1 and called the ,wollaston condenser4 ,a tube is placed below the stage of the instrument containing a lens ,a ,b 7,fig4 #aa71 which can be elevated or depressed within certain limits at pleasure2 and at the lower end is a stop with a limited aperture ,c ,d4 ,a plane mirror ,e ,f receives the rays of light ,l ,l from the sky or a white cloud1 which last is the best source of light1 and reflects them upwards through the aperture in ,c ,d1 so that they are refracted1 and form an image of the aperture at ,g1 which is supposed to be nearly the place of the object4 ,the object is sometimes best seen when the image of the aperture is also best seen2 and sometimes it is best to elevate the summit ,g of the cone ,a ,b ,g above the object1 and at others to depress it below3 all which is done at pleasure by the power of moving the lens ,a ,b4 ,if artifical light 7as a lamp or candle7 be employed1 the flame must be placed in the principal focus of a large detached lens on a stand1 so that the rays ,l ,l may fall in parallel lines on the mirror1 or as they would fall from the cloud4 ,this will be found an advantage1 not only when the ,wollaston condenser is employed1 but also when the mirror and diaphragm are used4 ,a good mode of imitating artificially the light of a white cloud opposite the sun has been proposed by ,mr4 ,varley2 he covers the surface of the mirror under the stage with carbonate of soda or any similar material1 and then concentrates the sun's light upon its surface by a large condensing lens4 ,the intense white light diffused from the surface of the soda forms an excellent substitute for the white cloud1 which1 when opposite the sun1 and of considerable size1 is the best daylight1 as the pure sky opposite to the sun is the worst4 ,illustration3 ,fig4 #aa4 ,the ,compound ,microscope may1 as before stated1 consist of only two lenses1 while a simple microscope has been shown to contain sometimes three4 ,in the triplet for the simple microscope1 however1 it was explained that the effect of the two first lenses was to do what might have been accomplished1 though not so well1 by one2 and the third merely effected certain modifications in the light before it entered the eye4 ,but in the compound microscope the two lenses have totally different functions2 the first receives the rays from the object1 and1 bringing them to new foci1 forms an image1 which the second lens treats as an original object1 and magnifies it just as the single microscope magnified the object itself4 ,illustration3 ,fig4 #ab4 ,the annexed figure 7#ab7 shows the course of the rays through a compound microscope of two lenses4 ,the rays proceeding from the object ,a ,b are so acted upon by the lens ,c ,d1 near it1 and thence called the object glass1 that they are converged to foci in ,a ,b1 where they form an enlarged image of the object1 as would be evident if a piece of oiled paper or ground glass were placed there to receive them4 ,they are not so intercepted1 and therefore the image is not rendered visible at that place2 but their further progress is similar to what it would have been had they really proceeded from an object at ,a ,b4 ,they are at length received by the eye-lens ,l ,m1 which acts upon them as the simple microscope has been described to act on the light proceeding from its objects4 ,they are bent so that they may enter the eye at ,e in parallel lines1 or as nearly so as is requisite for distinct vision4 ,when we say that the rays enter the eye in nearly parallel lines1 we mean only those which proceed from one point of the original object4 ,thus the two parallel rays ,m ,e have proceeded from and are part of the cone of rays ,c ,a ,d1 emanating from the point ,a of the arrow2 but they do not form two pictures in the eye1 because any number of parallel rays which the pupil can receive will be converged to a point by the eye1 and will convey the impression of one point to the mind4 ,in like manner the rays ,l ,e are part of the cone of rays emanating from ,b1 and the angle ,l ,e ,m is that under which the eye will see the magnified image of the arrow1 which is evidently many times greater than the arrow could be made to occupy in the naked eye at any distance within the limits of distinct vision4 ,the magnifying power depends on two circumstances3 first1 on the ratio between the anterior distance ,a ,c or ,b ,d and the posterior focal length ,c ,b or ,d ,a2 and secondly1 on the power of the eye-lens ,l ,m4 ,the first ratio is the same as that between the object ,a ,b and the image ,a ,b2 this and the focal length or power of the eye lens are both easily obtained1 and their product is the power of the compound instrument4 ,since the power depends on the ratio between the anterior and posterior foci of the object-glass1 it is evident that by increasing that ratio any power may be obtained1 the same eye-glass being used2 or having determined the first1 any further power may be obtained by increasing that of the eye-glass2 and thus1 by a pre-arrangement of the relative proportions in which the magnifying power shall be divided between the object-glass and the eye-glass1 almost any given distance 7within certain limits7 between the first and its object may be secured4 ,this is one valuable peculiarity of the compound instrument2 and another is the large field1 or large angle of view1 which may be obtained1 every part of which will be nearly equally good2 whereas with the best simple microscopes the field is small1 and is good only in the centre4 ,the field of the compound instrument is further increased by using two glasses at the eye-end2 the first being called1 from its purpose1 the field-glass1 and the two constituting what is called the eye-piece4 ,this will be more particularly explained in the figure of the achromatic compound microscope presently given4 ,for upwards of a century the compound microscope1 notwithstanding the advantages above mentioned1 was a comparatively feeble and inefficient instrument1 owing to the distance which the light had to traverse1 and the consequent increase of the chromatic and spherical aberrations4 ,to explain this we have drawn in ,fig4 #ab a second image near ,a ,b1 the fact being that the object-glass would not form one image1 as has been supposed1 but an infinite number of variously-colored and various-sized images1 occupying the space between the two dotted arrows4 ,those nearest the object-glass would be red1 and those nearest the eye-glass would be blue4 ,the effect of this is to produce so much confusion1 that the instrument was reduced to a mere toy1 although these errors were diminished to the utmost possible extent by limiting the aperture of the object-glass1 and thus restricting the angle of the pencil of light from each point of the object4 ,but this involved the defects1 already explained1 of making the picture obscure1 so that on the whole the best compound instruments were inferior to the simple microscopes of a single lens1 with which1 indeed1 all the important observations of the last century were made4 ,even after the improvement of the simple microscope by the use of doublets and triplets1 the long course of the rays1 and the large angular pencil required in the compound instrument1 deterred the most sanguine from anticipating the period when they should be conducted through such a path free both from spherical and chromatic errors4 ,within twenty years of the present period1 philosophers of no less eminence than ,m4 ,blot and ,dr4 ,wollaston predicted that the compound would never rival the simple microscope1 and that the idea of achromatizing its object-glass was hopeless4 ,nor can these opinions be wondered at when we consider how many years the achromatic telescope had existed without an attempt to apply its principles to the compound microscope4 ,when we consider the smallness of the pencil required by the telescope1 and the enormous increase of difficulty attending every enlargement of the pencil--when we consider further that these difficulties had to be contended with and removed by operations on portions of glass so small that they are themselves almost microscopic objects1 we shall not be surprised that even a cautious philosopher and most able manipulator like ,dr4 ,wollaston should prescribe limits to improvement4 ,fortunately for science1 and especially for the departments of animal and vegetable physiology1 these predictions have been shown to be unfounded4 ,the last fifteen years have sufficed to elevate the compound microscope from the condition we have described to that of being the most important instrument ever bestowed by art upon the investigator of nature4 ,it now holds a very high rank among philosophical implements1 while the transcendant beauties of form1 color and organization1 which it reveals to us in the minute works of nature1 render it subservient to the most delightful and instructive pursuits4 ,to these claims on our attention1 it appears likely to add a third of still higher importance4 ,the microscopic examination of the blood and other human organic matter will in all probability afford more satisfactory and conclusive evidence regarding the nature and seat of disease than any hitherto appealed to1 and will of consequence lead to similar certainty in the choice and application of remedies4 ,we have thought it necessary to state thus at large the claims of the modern achromatic microscope upon the attention of the reader1 as a justification of the length at which we shall give its recent history and explain its construction2 and we are further induced to this course by the consideration that the subject is entirely new ground1 and that there are at this time not more than two or three makers of achromatic microscopes in ,england4 ,soon after the year #ahbj a series of experiments was begun in ,france by ,m4 ,selligues1 which were followed up by ,frauenhofer at ,munich1 by ,amici at ,modena1 by ,m4 ,chevalier at ,paris1 and by the late ,mr4 ,tulley in ,london4 ,in #ahbd the last-named excellent artist1 without knowing what had been done on the ,continent1 made the attempt to construct an achromatic object-glass for a compound microscope1 and produced one of nine-tenths of an inch focal length1 composed of three lenses1 and transmitting a pencil of eighteen degrees4 ,this was the first that had been made in ,england2 and it is due to ,mr4 ,tulley to say1 that as regards accurate correction throughout the field1 that glass has not been excelled by any subsequent combination of three lenses4 ,such an angular pencil1 and such a focal length1 would bear an eye-piece adapted to produce a gross magnifying power of one hundred and twenty4 ,mr4 ,tulley afterwards made a combination to be placed in front of the first mentioned1 which increased the angle of the transmitted pencil to thirty-eight degrees1 and bore a power of three hundred4 ,while these practical investigations were in progress1 the subject of achromatism engaged the attention of some of the most profound mathematicians in ,england4 ,sir ,john ,herschel1 ,professor ,airy1 ,professor ,barlow1 ,mr4 ,coddington1 and others1 contributed largely to the theoretical examination of the subject2 and though the results of their labors were not immediately applicable to the microscope1 they essentially promoted its improvement4 ,for some time prior to #ahbi the subject had occupied the mind of a gentleman1 who1 not entirely practical1 like the first1 nor purely mathematical1 like the last-mentioned class of inquirers1 was led to the discovery of certain properties in achromatic combinations which had been before unobserved4 ,these were afterwards experimentally verified2 and in the year #ahbi a paper on the subject1 by the discoverer1 ,mr4 ,joseph ,jackson ,lister1 was read and published by the ,royal ,society4 ,the principles and results thus obtained enabled ,mr4 ,lister to form a combination of lenses which transmitted a pencil of fifty degrees1 with a large field correct in every part2 as this paper was the foundation of the recent improvements in achromatic microscopes1 and as its results are indispensable to all who would make or understand the instrument1 we shall give the more important parts of it in detail1 and in ,mr4 ,lister's own words4 8,i would premise that the plano-concave form for the correcting flint lens has in that quality a strong recommendation1 particularly as it obviates the danger of error which otherwise exists in centering the two curves1 and thereby admits of correct workmanship for a shorter focus4 ,to cement together also the two surfaces of the glass diminishes by very nearly half the loss of light from reflection1 which is considerable at the numerous surfaces of a combination4 ,i have thought the clearness of the field and brightness of the picture evidently increased by doing this2 it prevents any dewiness or vegetation from forming on the inner surfaces2 and ,i see no disadvantage to be anticipated from it if they are of identical curves1 and pressed closely together1 and the cementing medium permanently homogeneous4 8,these two conditions then1 that the flint lens shall be plano-concave1 and that it shall be joined by some cement to the convex1 seem desirable to be taken as a basis for the microscopic object-glass1 provided they can be reconciled with the destruction of the spherical and chromatic aberrations of a large pencil4 8,now in every such glass that has been tried by me which has had its correcting lens of either ,swiss or ,english glass1 with a double convex of plate1 and has been made achromatic by the form given to the outer curve of the convex1 the proportion has been such between the refractive and dispersive powers of its lenses1 that its figure has been correct for rays issuing from some point in its axis not far from its principal focus on its plane side1 and either tending to a conjugate focus within the tube of a microscope1 or emerging nearly parallel4 8,let ,a ,b 7,fig4 #ac7 be supposed such an object-glass1 and let it be roughly considered as a plano-convex lens1 with a curve ,a ,c ,b running through it1 at which the spherical and chromatic errors are corrected which are generated at the two outer surfaces2 and let the glass be thus free from aberration for rays ,f ,d ,e ,g issuing from the radiant point ,f1 ,h ,e being a perpendicular to the convex surface1 and ,i ,d to the plane one4 ,under these circumstances1 the angle of emergence ,g ,e ,h much exceeds that of incidence ,f ,d ,i1 being probably nearly three times as great4 8,if the radiant is now made to approach the glass1 so that the course of the ray ,f ,d ,e ,g shall be more divergent from the axis1 as the angles of incidence and emergence become more nearly equal to each other1 the spherical aberration produced by the two will be found to bear a less proportion to the opposing error of the single correcting curve ,a ,c ,b2 for such a focus therefore the rays will be over-corrected4 ,illustration3 ,fig4 #ac4 8,but if ,f still approaches the glass1 the angle of incidence continues to increase with the increasing divergence of the ray1 till it will exceed that of emergence1 which has in the meanwhile been diminishing1 and at length the spherical error produced by them will recover its original proportion to the opposite error of the curve of correction4 ,when ,f has reached this point ,f 7at which the angle of incidence does not exceed that of emergence so much as it had at first come short of it71 the rays again pass the glass free from spherical aberration4 8,if ,f be carried from hence towards the glass1 or outwards from its original place1 the angle of incidence in the former case1 or of emergence in the latter1 becomes disproportionately effective1 and either way the aberration exceeds the correction4 8,these facts have been established by careful experiment3 they accord with every appearance in such combinations of the plano-convex glasses as have come under my notice1 and may1 ,i believe1 be extended to this rule1 that in general an achromatic object-glass1 of which the inner surfaces are in contact1 or nearly so1 will have on one side of it two foci in its axis1 for the rays proceeding from which it will be truly corrected at a moderate aperture2 that for the space between these two points its spherical aberration will be over-corrected1 and beyond them either way under-corrected4 8,the longer aplanatic focus may be found1 when one of the plano-convex object-glasses is placed in a microscope1 by shortening the tube1 if the glass shows over-correction2 if under-correction1 by lengthening it1 or by bringing the rays together1 should they be parallel or divergent1 by a very small good telescope4 ,the shorter focus is got at by sliding the glass before another of sufficient length and large aperture that is finely corrected1 and bringing it forwards till it gives the reflection of a bright point from a globule of quicksilver1 sharp and free from mist1 when the distance can be taken between the glass and the object4 8,the longer focus is the place at which to ascertain the utmost aperture that may be given to the glass1 and where1 in the absence of spherical error1 its exact state of correction as to color is seen most distinctly4 8,the correction of the chromatic aberration1 like that of the spherical1 tends to excess in the marginal rays2 so that if a glass which is achromatic1 with a moderate aperture1 has its cell opened wider1 the circle of rays thus added to the pencil will be rather over-corrected as to color4 8,the same tendency to over-correction is produced1 if1 without varying the aperture1 the divergence of the incident rays is much augmented1 as in an object-glass placed in front of another2 but generally in this position a part only of its aperture comes into use2 so that the two properties mentioned neutralize each other1 and its chromatic state remains unaltered4 ,if1 for example1 the outstanding colors were observed at the longer focus to be green and claret1 which show that the nearest practicable approach is made to the union of the spectrum1 they usually continue nearly the same for the whole space between the foci1 and for some distance beyond them either way4 8,the places of these two foci and their proportions to each other depend on a variety of circumstances4 ,in several object-glasses that ,i have had made for trial1 plano-convex1 with their inner surfaces cemented1 their diameters the radius of the flint lens1 and their color pretty well corrected1 those composed of dense flint and light plate have had the rays from the longer focus emerging nearly parallel2 and this focus has been not quite three times the distance of the shorter from the glass3 with ,english flint the rays have had more convergence1 and the shorter focus has borne a rather less proportion to the longer4 8,if the surfaces are not cemented1 a striking effect is produced by minute differences in their curves4 ,it may give some idea of this1 that in a glass of which nearly the whole disk was covered with color from contact of the lenses1 the addition of a film of varnish1 so thin that this color was not destroyed by it1 caused a sensible change in the spherical correction4 8,i have found that whatever extended the longer aplanatic focus1 and increased the convergence of its rays1 diminished the relative length of the shorter4 ,thus by turning to the concave lens the flatter instead of the deeper side of a convex lens1 whose radii were to each other as #ca to #ce1 the pencil of the longer aplanatic focus1 from being greatly divergent1 was brought to converge at a very small distance behind the glass2 and the length of the shorter focus1 which had been one-half that of the longer1 became but one-sixth of it4 8,the direction of the aplanatic pencils appears to be scarcely affected by the differences in the thickness of glasses1 if their state as to color is the same4 8,one other property of the double object-glass remains to be mentioned1 which is1 that when the longer aplanatic focus is used1 the marginal rays of a pencil not coincident with the axis of the glass are distorted1 so that a coma is thrown outwards2 while the contrary effect of a coma directed towards the centre of the field is produced by the rays from the shorter focus4 ,these peculiarities of the coma seem inseparable attendants on the two foci1 and are as conspicuous in the achromatic meniscus as in the plano-convex object-glass4 ,illustration3 ,fig4 #ad4 8,of several purposes to which the particulars just given seem applicable1 ,i must at present confine myself to the most obvious one4 ,they furnish the means of destroying with the utmost ease both aberrations in a large focal pencil1 and of thus surmounting what has hitherto been the chief obstacle to the perfection of the microscope4 ,and when it is considered that the curves of its diminutive object-glasses have required to be at least as exactly proportioned as those of a large telescope to give the image of a bright point equally sharp and colorless1 and that any change made to correct one aberration was liable to disturb the other1 some idea may be formed of what the amount of that obstacle must have been4 ,it will1 however1 be evident that if any object-glass is but made achromatic1 with its lenses truly worked and cemented1 so that their axes coincide1 it may with certainty be connected with another possessing the same requisites and of suitable focus1 so that the combination shall be free from spherical error also in the centre of its field4 ,for this the rays have only to be received by the front glass ,b 7,fig4 #ad7 from its shorter aplanatic focus ,f1 and transmitted in the direction of the longer correct pencil ,f ,a of the other glass ,a4 ,it is desirable that the latter pencil should neither converge to a very short focus nor be more than very slightly if at all divergent2 and a little attention at first to the kind of glass used will keep it within this range1 the denser flint being suited to the glasses of shorter focus and larger angle of aperture4 8,the adjustment of the microscope is then perfected1 if necessary1 by slightly varying the distance between the object-glasses2 and after that is done1 the length of the tube which carries the eye-pieces may be altered greatly without disturbing the correction1 opposite errors which balance each other being produced by the change4 8,if the two glasses which in the diagram are drawn at some distance apart are brought nearer together 7if the place of ,a1 for instance1 is carried to the dotted figure71 the rays transmitted by ,b in the direction of the longer aplanatic pencil of ,a will plainly be derived from some point ,z more distant than ,f1 and lying between the aplanatic foci of ,b2 therefore 7according to what has been stated7 this glass1 and consequently the combination1 will then be spherically over-corrected4 ,if1 on the other hand1 the distance between ,a and ,b is increased1 the opposite effects are of course produced4 8,in combining several glasses together it is often convenient to transmit an under-corrected pencil from the front glass1 and to counteract its error by over-correction in the middle one4 8,slight errors in color may in the same manner be destroyed by opposite ones2 and on the principles described we not only acquire fine correction for the central ray1 but by the opposite effects at the two foci on the transverse pencil1 all coma can be destroyed1 and the whole field rendered beautifully flat and distinct40 ,mr4 ,lister's paper enters into further particulars1 which are not essential to the comprehension of the subject4 ,it is sufficient to say that his investigations and results proved to be of the highest value to the practical optician1 and the progress of improvement was in consequence extremely rapid4 ,the new principles were applied and exhibited by ,mr4 ,hugh ,powell and ,mr4 ,andrew ,ross with a degree of success which had never been anticipated2 so perfect indeed were the corrections given to the achromatic object-glass--so completely were the errors of sphericity and dispersion balanced or destroyed--that the circumstance of covering the object with a plate of the thinnest glass or talc disturbed the corrections1 if they had been adapted to an uncovered object1 and rendered an object-glass which was perfect under one condition sensibly defective under the other4 ,this defect1 if that should be called a defect which arose out of improvement1 was first discovered by ,mr4 ,ross1 who immediately suggested the means of correcting it1 and presented to the ,society of ,arts1 in #ahcg1 a paper on the subject1 which was published in the #east volume of their ,transactions1 and which1 as it is1 like ,mr4 ,lister's essential to a full understanding of the ultimate refinements of the instrument1 we shall extract nearly in full3 8,in the course of a practical investigation 7says ,mr4 ,ross7 with the view of constructing a combination of lenses for the object-glass of a compound microscope1 which should be free from the effects of aberration1 both for central and oblique pencils of great angle1 ,i combined the condition of the greatest possible distance between the object and object-glass2 for in object-glasses of short focal length their closeness to the object has been an obstacle in many cases to the use of high magnifying powers1 and is a constant source of inconvenience4 8,in the improved combination1 the diameter is only sufficient to admit the proper pencil2 the convex lenses are wrought to an edge1 and the concave have only sufficient thickness to support their figure2 consequently the combination is the thinnest possible1 and it follows that there will be the greatest distance between the object and the object-glass4 ,the focal length is one-eighth of an inch1 having an angular aperture of #fj1 with a distance of #a-beth of an inch1 and a magnifying power of #igj times linear1 with perfect definition on the most difficult ,podura scales4 ,i have made object-glasses #a-afth of an inch focal length2 but as the angular aperture cannot be advantageously increased1 if the greatest distance between the object and object-glass is preserved1 their use will be very limited4 8,the quality of the definition produced by an achromatic compound microscope will depend upon the accuracy with which the aberrations1 both chromatic and spherical1 are balanced1 together with the general perfection of the workmanship4 ,now1 in ,wollaston's doublets1 and ,holland's triplets1 there are no means of producing a balance of the aberrations1 as they are composed of convex lenses only2 therefore the best that can be done is to make the aberrations a minimum2 the remaining positive aberration in these forms produces its peculiar effect upon objects 7particularly the detail of the thin transparent class71 which may lead to misapprehension of their true structure2 but with the achromatic object-glass1 where the aberrations are correctly balanced1 the most minute parts of an object are accurately displayed1 so that a satisfactory judgment of their character may be formed4 ,illustration3 ,fig4 #ae4 ,illustration3 ,fig4 #af4 8,it will be seen by ,fig4 #ae1 that when a certain angular pencil ,a ,o ,a proceeds from the object ,o1 and is incident on the plane side of the first lens1 if the combination is removed from the object1 as in ,fig4 #af1 the extreme rays of the pencil impinge on the more marginal parts of the glass1 and as the refractions are greater here1 the aberrations will be greater also4 ,now1 if two compound object-glasses have their aberrations balanced1 one being situated as in ,fig4 #ae1 and the other as in ,fig4 #af1 and the same disturbing power applied to both1 that in which the angles of incidence and the aberrations are small will not be so much disturbed as where the angles are great1 and where consequently the aberrations increase rapidly4 8,when an object-glass has its aberrations balanced for viewing an opaque object1 and it is required to examine that object by transmitted light1 the correction will remain2 but if it is necessary to immerse the object in a fluid1 or to cover it with glass or talc1 an aberration will arise from these circumstances1 which will disturb the previous correction1 and consequently deteriorate the definition2 and this effect will be more obvious with the increase of the distance between the object and the object-glass4 ,illustration3 ,fig4 #ag4 8,the aberration produced with diverging rays by a piece of flat and parallel glass1 such as would be used for covering an object1 is represented at ,fig4 #ag1 where ,g ,g ,g ,g is the refracting medium1 or piece of glass covering the object ,o2 ,o ,p1 the axis of the pencil1 perpendicular to the flat surfaces2 ,o ,t1 a ray near the axis2 and ,o ,t1 the extreme ray of the pencil incident on the under surface of the glass2 then ,t ,r1 ,t ,r1 will be the directions of the rays in the medium1 and ,r ,e1 ,r ,e1 those of the emergent rays4 ,now if the course of these rays is continued1 as by the dotted lines1 they will be found to intersect the axis at different distances1 ,x and ,y1 from the surface of the glass2 and the distance ,x ,y is the aberration produced by the medium which1 as before stated1 interferes with the previously balanced aberrations of the several lenses composing the object-glass4 ,there are many cases of this1 but the one here selected serves best to illustrate the principle4 ,i need not encumber the description with the theoretical determination of this quantity1 as it varies with exceedingly minute circumstances which we cannot accurately control2 such as the distance of the object from the under side of the glass1 and the slightest difference in the thickness of the glass itself2 and if these data could be readily obtained1 the knowledge would be of no utility in making the correction1 that being wholly of a practical nature4 8,if an object-glass is constructed as represented in ,fig4 #af1 where the posterior combination ,p and the middle ,m have together an excess of negative aberration1 and if this be corrected by the anterior combination ,a1 having an excess of positive aberration1 then this latter combination can be made to act more or less powerfully upon ,p and ,m1 by making it approach to or recede from them2 for when the three are in close contact1 the distance of the object from the object-glass is greatest2 and consequently the rays from the object are diverging from a point at a greater distance than when the combinations are separated2 and as a lens bends the rays more1 or acts with greater effect1 the more distant the object is from which the rays diverge1 the effect of the anterior combination ,a upon the other two1 ,p and ,m1 will vary with its distance from thence4 ,when therefore the correction of the whole is effected for an opaque object with a certain distance between the anterior and middle combination1 if they are then put in contact1 the distance between the object and object-glass will be increased2 consequently the anterior combination will act more powerfully1 and the whole will have an excess of positive aberration4 ,now the effect of the aberration produced by a piece of flat and parallel glass being of the negative character1 it is obvious that the above considerations suggest the means of correction by moving the lenses nearer together1 till the positive aberration thereby produced balances the negative aberration caused by the medium4 8,the preceding refers only to the spherical aberration1 but the effect of the chromatic is also seen when an object is covered with a piece of glass2 for1 in the course of my experiments1 ,i observed that it produced a chromatic thickening of the outline of the ,podura and other delicate scales2 and if diverging rays near the axis and at the margin are projected through a piece of flat parallel glass1 with the various indices of refraction for the different colors1 it will be seen that each ray will emerge separated into a beam consisting of the component colors of the ray1 and that each beam is widely different in form4 ,this difference1 being magnified by the power of the microscope1 readily accounts for the chromatic thickening of the outline just mentioned4 ,therefore to obtain the finest definition of extremely delicate and minute objects1 they should be viewed without a covering2 if it be desirable to immerse them in a fluid1 they should be covered with the thinnest possible film of talc1 as1 from the character of the chromatic aberration1 it will be seen that varying the distances of the combinations will not sensibly affect the correction2 though object-lenses may be made to include a given fluid or solid medium in their correction for color4 ,illustration3 ,fig4 #ah4 8,the mechanism for applying these principles to the correction of an object-glass under the various circumstances1 is represented in ,fig4 #ah1 where the anterior lens is set in the end of a tube ,a ,a1 which slides on the cylinder ,b containing the remainder of the combination2 the tube ,a ,a1 holding the lens nearest the object1 may then be moved upon the cylinder ,b1 for the purpose of varying the distance according to the thickness of the glass covering the object1 by turning the screwed ring ,c ,c1 or more simply by sliding the one on the other1 and clamping them together when adjusted4 ,an aperture is made in the tube ,a1 within which is seen a mark engraved on the cylinder1 and on the edge of which are two marks1 a longer and a shorter1 engraved upon the tube4 ,when the mark on the cylinder coincides with the longer mark on the tube1 the adjustment is perfect for an uncovered object2 and when the coincidence is with the short mark1 the proper distance is obtained to balance the aberrations produced by glass one-hundredth of an inch thick1 and such glass can be readily supplied4 8,it is hardly necessary to observe1 that the necessity for this correction is wholly independent of any particular construction of the object-glass2 as in all cases where the object-glass is corrected for an object uncovered1 any covering of glass will create a different value of aberration to the first lens1 which previously balanced the aberration resulting from the rest of the lenses2 and as this disturbance is effected at the first refraction1 it is independent of the other part of the combination4 ,the visibility of the effect depends on the distance of the object from the object-glass1 the angle of the pencil transmitted1 the focal length of the combination1 the thickness of the glass covering the object1 and the general perfection of the corrections for chromatism and the oblique pencils4 8,with this adjusting object-glass1 therefore1 we can have the requisites of the greatest possible distance between the object and object-glass1 an intense and sharply defined image throughout the field from the large pencil transmitted1 and the accurate correction of the aberrations2 also1 by the adjustment1 the means of preserving that correction under all the varied circumstances in which it may be necessary to place an object for the purpose of observation40 ,in the annexed engraving1 ,fig4 #ai1 we have shown the triple achromatic object-glass in connection with the eye-piece consisting of the field-glass ,f ,f1 and the eye-glass ,e ,e1 forming together the modern achromatic microscope4 ,the course of the light is shown by drawing three rays from the centre and three from each end of the object ,o4 ,these rays would1 if left to themselves1 form an image of the object at ,a ,a1 but being bent and converged by the field-glass ,f ,f1 they form the image at ,b ,b1 where a stop is placed to intercept all light except what is required for the formation of the image4 ,from ,b ,b therefore the rays proceed to the eye-glass exactly as has been described in reference to the simple microscope and to the compound of two glasses4 ,illustration3 ,fig4 #ai4 ,if we stopped here we should convey a very imperfect idea of the beautiful series of corrections effected by the eye-piece1 and which were first pointed out in detail in a paper on the subject published by ,mr4 ,varley in the #east volume of the ,transactions of the ,society of ,arts4 ,the eye-piece in question was invented by ,huyghens for telescopes1 with no other view than that of diminishing the spherical aberration by producing the refractions at two glasses instead of one1 and of increasing the field of view4 ,it was reserved for ,boscovich to point out that ,huyghens had by this arrangement accidentally corrected a great part of the chromatic aberration1 and this subject is further investigated with much skill in two papers by ,professor ,airy in the ,cambridge ,philosophical ,transactions1 to which we refer the mathematical reader4 ,these investigations apply chiefly to the telescope1 where the small pencils of light and great distance of the object exclude considerations which become important in the microscope1 and which are well pointed out in ,mr4 ,varley's paper before mentioned4 ,illustration3 ,fig4 #bj4 ,let ,fig4 #bj represent the ,huyghenean eye-piece of a microscope2 ,f ,f and ,e ,e being the field-glass and eye-glass1 and ,l ,m ,n the two extreme rays of each of the three pencils1 emanating from the centre and ends of the object1 of which1 but for the field-glass1 a series of colored images would be formed from ,r ,r to ,b ,b2 those near ,r ,r being red1 those near ,b ,b blue1 and the intermediate ones green1 yellow1 and so on1 corresponding with the colors of the prismatic spectrum4 ,this order of colors1 it will be observed1 is the reverse of that described in treating of the common compound microscope 7,fig4 #ab71 in which the single object-glass projected the red image beyond the blue4 ,the effect just described1 of projecting the blue image beyond the red1 is purposely produced for reasons presently to be given1 and is called over-correcting the object-glass as to color4 ,it is to be observed also that the images ,b ,b and ,r ,r are curved in the wrong direction to be distinctly seen by a convex eye-lens1 and this is a further defect of the compound microscope of two lenses4 ,but the field-glass1 at the same time that it bends the rays and converges them to foci at ,b ,b and ,r ,r1 also reverses the curvature of the images as there shown1 and gives them the form best adapted for distinct vision by the eye-glass ,e ,e4 ,the field-glass has at the same time brought the blue and red images closer together1 so that they are adapted to pass uncolored through the eye-glass4 ,to render this important point more intelligible1 let it be supposed that the object-glass had not been over-corrected1 that it had been perfectly achromatic2 the rays would then have become colored as soon as they had passed the field-glass2 the blue rays1 to take the central pencil1 for example1 would converge at b and the red rays at r1 which is just the reverse of what the eye-lens requires2 for as its blue focus is also shorter than its red1 it would demand rather that the blue image should be at r and the red at b4 ,this effect we have shown to be produced by the over-correction of the object-glass1 which protrudes the blue foci ,b ,b as much beyond the red foci ,r ,r as the sum of the distances between the red and blue foci of the field-lens and eye-lens2 so that the separation ,b ,r is exactly taken up in passing through those two lenses1 and the whole of the colors coincide as to focal distance as soon as the rays have passed the eye-lens4 ,but while they coincide as to distance1 they differ in another respect2 the blue images are rendered smaller than the red by the superior refractive power of the field-glass upon the blue rays4 ,in tracing the pencil ,l1 for instance1 it will be noticed that after passing the field-glass1 two sets of lines are drawn1 one whole1 and one dotted1 the former representing the red1 and the latter the blue rays4 ,this is the accidental effect in the ,huyghenean eye-piece pointed out by ,boscovich4 ,this separation into colors at the field-glass is like the over-correction of the object-glass2 it leads to a subsequent complete correction4 ,for if the differently colored rays were kept together till they reached the eye-glass1 they would then become colored1 and present colored images to the eye2 but fortunately1 and most beautifully1 the separation effected by the field-glass causes the blue rays to fall so much nearer the centre of the eye-glass1 where1 owing to the spherical figure1 the refractive power is less than at the margin1 that the spherical error of the eye-lens constitutes a nearly perfect balance to the chromatic dispersion of the field-lens1 and the red and blue rays ,l and ,l emerge sensibly parallel1 presenting1 in consequence1 the perfect definition of a single point to the eye4 ,the same reasoning is true of the intermediate colors and of the other pencils4 ,from what has been stated it is obvious that we mean by an achromatic object-glass one in which the usual order of dispersion is so far reversed that the light1 after undergoing the singularly beautiful series of changes effected by the eye-piece1 shall come uncolored to the eye4 ,we can give no specific rules for producing these results4 ,close study of the formul for achromatism given by the celebrated mathematicians we have quoted will do much1 but the principles must be brought to the test of repeated experiment4 ,nor will the experiments be worth anything1 unless the curves be most accurately measured and worked1 and the lenses centered and adjusted with a degree of precision which1 to those who are familiar only with telescopes1 will be quite unprecedented4 ,the ,huyghenean eye-piece which we have described is the best for merely optical purposes1 but when it is required to measure the magnified image1 we use the eye-piece invented by ,mr4 ,ramsden1 and called1 from its purpose1 the micrometer eye-piece4 ,when it is stated that we sometimes require to measure portions of animal or vegetable matter a hundred times smaller than any divisions that can be artificially made on any measuring instrument1 the advantage of applying the scale to the magnified image will be obvious1 as compared with the application of engraved or mechanical micrometers to the stage of the instrument4 ,the arrangement is shown in ,fig4 #ba1 where ,e ,e and ,f ,f are the eye and field glass1 the latter having now its plane face towards the object4 ,the rays from the object are here made to converge at ,a ,a1 immediately in front of the field-glass1 and here also is placed a plane glass on which are engraved divisions of a hundredth of an inch or less4 ,the markings of these divisions come into focus therefore at the same time as the image of the object1 and both are distinctly seen together4 ,thus the measure of the magnified image is given by mere inspection1 and the value of such measures in reference to the real object may be obtained thus1 which1 when once obtained1 is constant for the same object-glass4 ,place on the stage of the instrument a divided scale the value of which is known1 and viewing this scale as the microscopic object1 observe how many of the divisions on the scale attached to the eye-piece correspond with one of those in the magnified image4 ,if1 for instance1 ten of those in the eye-piece correspond with one of those in the image1 and if the divisions are known to be equal1 then the image is ten times larger than the object1 and the dimensions of the object are ten times less than indicated by the micrometer4 ,if the divisions on the micrometer and on the magnified scale were not equal1 it becomes a mere rule-of-three sum1 but in general this trouble is taken by the maker of the instrument1 who furnishes a table showing the value of each division of the micrometer for every object-glass with which it may be used4 ,illustration3 ,fig4 #ba4 ,while on the subject of measuring it may be well to explain the mode of ascertaining the magnifying power of the compound microscope1 which is generally taken on the assumption before mentioned1 that the naked eye sees most distinctly at the distance of ten inches4 ,place on the stage of the instrument1 as before1 a known divided scale1 and when it is distinctly seen1 hold a rule at ten inches distance from the disengaged eye1 so that it may be seen by that eye1 overlapping or lying by side of the magnified picture of the other scale4 ,then move the rule till one or more of its known divisions correspond with a number of those in the magnified scale1 and a comparison of the two gives the magnifying power4 ,having now explained the optical principles of the achromatic compound microscope1 it remains only to describe the mechanical arrangements for giving those principles their full effect4 ,the mechanism of a microscope is of much more importance than might be imagined by those who have not studied the subject4 ,in the first place1 steadiness1 or freedom from vibration1 and most particularly freedom from any vibrations which are not equally communicated to the object under examination1 and to the lenses by which it is viewed1 is a point of the utmost consequence4 ,when1 for instance1 the body containing the lenses is screwed by its lower extremity to a horizontal arm1 we have one of the most vibratory forms conceivable2 it is precisely the form of the inverted pendulum1 which is expressly contrived to indicate otherwise insensible vibrations4 ,the tremor necessarily attendant on such an arrangement is magnified by the whole power of the instrument2 and as the object on the stage partakes of this tremor in a comparatively insensible degree1 the image is seen to oscillate so rapidly1 as in some cases to be wholly undistinguishable4 ,such microscopes cannot possibly be used with high powers in ordinary houses abutting on any paved streets through which carriages are passing1 nor indeed are they adapted to be used in houses in which the ordinary internal sources of shaking exist4 ,one of the best modes of mounting a compound microscope is shown in the annexed view 7,fig4 #bb71 which1 though too minute to exhibit all the details1 will serve to explain the chief features of the arrangement4 ,a massy pillar ,a is screwed into a solid tripod ,b1 and is surmounted by a strong joint at ,c1 on which the whole instrument turns1 so as to enable it to take a perfectly horizontal or vertical position1 or any intermediate angle1 such1 for instance1 as that shown in the engraving4 ,this movable portion of the instrument consists of one solid casting ,d ,e ,f ,g2 from ,f to ,g being a thick pierced plate carrying the stage and its appendages4 ,the compound body ,h is attached to the bar ,d ,e1 and moves up and down upon it by a rack and pinion worked by either of the milled heads ,k4 ,the piece ,d ,e ,f ,g is attached to the pillar by the joint ,c1 which being the source of the required movement in the instrument1 is obviously its weakest part1 and about which no doubt considerable vibration takes place4 ,but inasmuch as the piece ,d ,e ,f ,g of necessity transmits such vibrations equally to the body of the microscope and to the objects on the stage1 they hold always the same relative position1 and no visible vibration is caused1 how much soever may really exist4 ,to the under side of the stage is attached a circular stem ,l1 on which slides the mirror ,m1 plane on one side and concave on the other1 to reflect the light through the aperture in the stage4 ,beneath the stage is a circular revolving plate containing three apertures of various sizes1 to limit the angle of the pencil of light which shall be allowed to fall on the object under examination4 ,besides these conveniences the stage has a double movement produced by two racks at right angles to each other1 and worked by milled heads beneath4 ,it has also the usual appendages of forceps to hold minute objects1 and a lens to condense the light upon them1 all of which are well understood1 and if not1 will be rendered more intelligible by a few minutes' examination of a microscope than by the most lengthened description4 ,one other point remains to be noticed4 ,the movement produced by the milled head ,k is not sufficiently delicate to adjust the focus of very powerful lenses1 nor indeed is any rack movement4 ,only the finest screws are adapted to this purpose2 and even these are improved by means for reducing the rapidity of the screw's movement4 ,for this purpose the lower end of the compound body ,h1 which carries the object-glass1 consists of a piece of smaller tube sliding in parallel guides in the main body1 and kept constantly pressed upwards by a spiral spring but it can be drawn downward by a lever crossing the body1 and acted on by an extremely fine screw whose milled head is seen at ,n1 and the fineness of which is tripled by means of the lever through which it acts on the object-glass4 ,the instrument is of course roughly adjusted by the rack movement1 and finished by the screw1 or by such other means as are chosen for the purpose4 ,one very ingenious contrivance1 but applied to the stage1 instead of the body of the microscope1 invented by ,mr4 ,powell1 will be found described in the #ejth volume of the ,transactions of the ,society of ,arts4 ,illustration3 ,fig4 #bb4 ,the greater part of the directions for viewing and illuminating objects given in reference to the simple microscope are applicable to the compound4 ,an argand lamp placed in the focus of a large detached lens so as to throw parallel rays upon the mirror1 is the best artificial light2 and for opaque objects the light so thrown up may be reflected by metallic specula 7called1 from their inventor1 ,lieberkhuns7 attached to the object-glasses4 ,it has been recently proposed by ,sir ,david ,brewster and by ,m4 ,dujardin to render the ,wollaston condenser achromatic1 and they have accordingly been made with three pairs of achromatic lenses instead of the single lens before described1 with very excellent effect4 ,the last-mentioned gentleman has also projected an ingenious apparatus1 called the ,hyptioscope1 attached to the eye-piece for the purpose of erecting the magnified picture4 ,the erector commonly applied to the compound microscope consists of a pair of lenses acting like the erecting eye-piece of the telescope4 ,but this1 though it is convenient for the purpose of dissection1 very much impairs the optical performance of the instrument4 ,illustration3 ,fig4 #bc4 ,for drawing the images presented by the microscope the best apparatus consists of a mirror ,m 7,fig4 #bc71 composed of a thin piece of rather dark-colored glass cemented on to a piece of plate-glass inclined at an angle of #de in front of the eye-glass ,e4 ,the light escaping from the eye-glass is assisted in its reflection upwards to the eye by the dark glass1 which effects the further useful purpose of rendering the paper less brilliant1 and thus enabling the eye better to see the reflected image4 ,the lens ,l below the reflector is to cause the light from the paper and pencil to diverge from the same distance as that received from the eye-glass2 in other words1 to cause it to reach the eye in parallel lines4 ,illustration3 ,fig4 #bd4 ,dr4 ,wollaston's camera lucida1 as shown in ,fig4 #bd1 is sometimes attached to the eye-piece of the microscope for the same purpose4 ,in this instrument the rays suffer two internal reflections within the glass prism1 as will be seen explained in the article 8,camera ,lucida40 ,in this minute figure we have omitted to trace the reflected rays1 merely to avoid confusion4 ,illustration3 ,fig4 #be4 ,illustration3 ,fig4 #bf4 ,illustration3 ,fig4 #bg4 ,annexed are four engravings of microscopic objects1 the true character of which it is1 however1 impossible to give in wood1 and is difficult indeed to accomplish by any description of engraving4 ,illustration3 ,fig4 #bh4 ,fig4 #be shows a scale of the small insect called ,podura ,plumbea1 the common ,skiptail1 magnified about five hundred times4 ,to define the markings on this scale clearly is the highest test of a deep achromatic object-glass2 and this drawing is given rather to explain what the observer should look for1 than as a very correct representation4 ,fig4 #bf is a scale or feather of the ,menelaus ,butterfly2 ,fig4 #bg is the hair of a singular insect1 the ,dermestes2 and ,fig4 #bh is a longitudinal cutting of fir1 showing the circular glands on the vessels which distinguish coniferous woods4 ,these latter objects may be seen by half-inch or quarter-inch achromatic glasses4 ,opaque objects are generally better exhibited by inch and two-inch glasses1 when a general view of them is required1 and by higher powers when we wish to examine their minute structure4 ,in the latter case the light must be obtained by condensing lenses instead of the metallic specula4 ,although the reflecting microscope is now very little used1 it may be expected that we should mention it4 ,in this instrument1 at ,fig4 #bi1 the object ,o is reflected by the inclined face of the mirror ,m1 and the rays are again reflected and converged by the ellipsoidal reflector ,r ,r1 which effects the same purpose as the object-glass of the compound microscope4 ,it forms an image which is not susceptible of the over-correction as to color before described1 and which therefore becomes colored in passing through the eye-piece4 ,this fact1 and the loss of light by reflection1 will probably always render the reflecting microscope inferior to the achromatic refracting4 ,illustration3 ,fig4 #bi4 ,the solar microscope has been so nearly superseded by the oxy-hydrogen1 that a brief description of the latter must suffice1 particularly as their optical principles are similar4 ,the primary object in both is to throw an intense light upon the object1 which is sometimes done by mirrors1 and sometimes by lenses4 ,in ,fig4 #cj1 ,l represents the cylinder of burning lime1 ,r ,r the reflector1 which concentrates the light upon the object ,o ,o2 the rays from which1 passing through the two plano-convex lenses1 are brought to foci upon a screen placed at a great distance1 and upon which is formed the magnified image4 ,illustration3 ,fig4 #cj4 ,fig4 #ca shows a combination of lenses to condense the light upon the object4 ,in either case the optical arrangements by which the image is formed admit of the same perfection as those which have been described for the compound microscopes4 ,a few achromatic glasses for oxy-hydrogen microscopes have been made1 and they will ultimately become valuable instruments for illustrating lectures on natural history and physiology4 ,one made by ,mr4 ,ross was exhibited a few months since at the ,society of ,arts to illustrate a lecture on the physiology of woods4 ,it should be observed1 however1 that the oxy-hydrogen or solar microscope requires either a spherical screen1 or that the objects should be mounted between spherical glasses1 in order to bring the whole into focus at one time4 ,this latter plan was adopted on the occasion just mentioned with perfect success4 ,illustration3 ,fig4 #ca4