,a ,new ,,discovery ,for ,finding the ,,longitude4 ,humbly ,submitted to the ,approbation of the ,right ,honourable the ,lords ,spiritual and ,temporal1 and the ,rest of the ,honourable ,persons1 appointed by the late ,act of ,parliament1 for ,hearing and ,determining ,proposals relating to the said ,,longitude4 ,by ,william ,hobbs1 ,philo ,mathem4 ,illustration ,,london3 ,printed for the ,author1 and are to be ,sold by ,fard4 ,burleigh in ,amen-,corner4 ,price ,six-pence4 ,note1 ,the former ,impression was ,printed ,july #ab4 #agad4 ,a ,new ,discovery for ,finding the ,longitude4 ,for ,finding the ,longitude1 it is to be noted1 ,that if the true ,hour1 and ,minute of the ,day1 at the ,place of our first ,departure1 and where we are ,arrived1 can be both obtained1 the ,difference of ,longitude may be found1 as truly as the ,difference of ,latitude4 ,for which purpose the ,spring-,movement hereunto subjoined1 is most humbly proposed to effect the same1 even to the ,tenth of a ,minute of ,time4 ,so that should the ,error of a ,minute happen to be found in ,practice1 it must proceed from the ,influence or ,vicissitude of the ,air1 and not from any ,defect in the ,rules by which the said ,movement is composed1 as will plainly appear by the ,explication thereof1 in the following ,lines2 and first of ,the ,description of the said ,movement4 ,this ,movement may be either of the ,form and ,bigness of that in a ,common ,clock2 or else of the ,smallness of a ,pocket ,watch1 as may be thought convenient in ,practice4 ,but the larger it is1 the better the ,divisions in the ,horologe will appear4 ,and as for the ,numbers1 they may be at pleasure3 ,only this must be observ'd1 ,that the swiftest ,index must make just ,one ,revolution1 whilst the slow one goes but ,one of the ,hundred ,divisions1 7as is common in ,minute ,watches1 wherein #fj ,minutes goes to an ,hour7 but the rest of the ,numbers may be at pleasure1 as aforesaid4 ,and if the ,slowest moves round in #c1 #d1 or #e ,days2 and the ,movement requires to be wound up once in #bf or #bg ,hours1 it will be sufficient3 ,for the more ,vigor the ,motion is calculated for1 the less the ,air will affect it4 ,how to set it first in ,motion4 ,when it is finished1 let it go for a ,month or two2 after which put the two ,indexes right one with the other1 and both of them pointing just to #ajj4 ,then the ,spring being wound up1 keep it from ,going 7with the ,key7 till the ,shadow of the ,sun is exactly come to a ,meridian ,line1 which must be rightly prepared for that purpose4 ,then let it go till the ,shadow comes just to the same ,line the next ,day1 or rather #dj1 #ej1 or #ajj ,days after1 7the longer the ,better47 ,at which time enter down the ,centesms that the swiftest ,index points to1 as also the ,integers and ,tenths of the slowest1 7but put the last first in your ,numbers7 by this you will be furnished with two general ,numbers1 viz4 the said ,numbers pointed to1 and the ,time 7in ,hours7 spent therein1 to find the ,hour of the ,day to the ,tenth of a ,minute1 at any time2 for that ,place where it was so set going1 tho' you remove it afterwards to any ,distance whatsoever4 ,which two ,numbers ought to be entered in a ,book2 to be used whensoever you would find the ,hour of the ,day4 ,and it is to be noted1 ,that if the ,sun be not then in its ,mean ,motion1 you must ,add to1 or ,substract from what the ,indexes do ,give1 according to the ,inequality thereof3 ,but if you try it for one whole ,year1 there will be no need of either4 ,and that what is said may be the better understood1 ,i shall give an ,example4 ,how to find the ,hour and ,minute of the ,day at ,london1 by the said ,movement4 ,suppose it should be made for the ,slowest to ,revolve in about five ,days1 and after it has gone just two ,days1 the ,slowest ,index should then point between #ci and #dj1 and the ,swiftest to #ba4e4 ,then both these ,numbers 7as set in ,order7 will make #ciba4e4 ,and if the ,sun be in its ,mean ,motion 7if not1 you must ,add or ,substract1 as aforesaid7 then the said ,numbers #ciba4e must always be the ,first2 the said two ,days1 or #dh ,hours1 the ,second2 and the two ,numbers pointed to by the ,indexes1 at the time for which you would find the ,hour and ,minute of the ,day 7as suppose the slow one should point to #hg1 and the swift one to #fe4b1 both making #hgfe4b7 must be the ,third2 by which the ,fourth will be obtained as followeth3 ,which ,fourth ,number being ,divided by #ab1 the ,remainder will be the ,hour and ,minute of the ,day at ,london1 as was required4 ,hours ,hours4 ,as #ciba4e 3 #dh 33 #hgfe4b 3 #ajg4ah ho4 min4 ,remains #aa 3 #aj4h hours4 ,requir'd or #aa ,and so for any quantity of time less than one ,revolution4 ,but if the time required to find the ,hour and ,minute at ,london1 7when at ,sea or ,land17 be some ,weeks or ,months1 after it was first set going2 or 7if cleansed7 after it was last ,cleansed2 then you must add #ajjjj4j to what the two ,indexes do shew1 for each ,revolution1 that it has made1 since it was so set going1 or last cleansed4 ,and if you would at any time know how many such ,revolutions must be added1 to what is shewn by the ,horologe2 you must first note the ,day of the ,month1 that you are then seeking the ,hour for2 as suppose ,novem4 #ab4 #agae4 ,after which note the ,day last entred1 when cleansed2 as suppose ,sept4 #e4 #agae4 ,then compute the number of ,days between ,sept4 #e4 and ,novem4 #ab4 which is #be1 #ca1 and #ab1 ,in all #fh4 ,after which observe the ,time last spent in one ,revolution2 which you see was #e ,days1 #d ,hours1 and 7for which set down for 'twill make no sensible ,difference7 and having thus done1 say1 ,days ,hours ,hours ,revo4 ,days ,as #e #d equal to #abd4a 3 #a 33 #fh 3 #ac4 whole ,revolutions2 ,for which1 as before directed1 you must add #ac times #ajjjj4j to the ,numbers pointed to1 by the two ,indexes3 ,which if we suppose #cgeb4b making in all #accgeb4b will be the ,number required1 for the #ab of ,november1 if the ,indexes should both point as before proposed4 ,and having now found this ,number1 you are prepared to find the ,hour and ,minute at ,london1 in manner following 7viz47 suppose you are in or near #dd ,degrees of ,latitude1 in the ,autumn ,season4 ,then seek the ,latitude #dd ,deg4 and the ,season ,autumn1 in the ,book that is peculiar to your ,movement1 and having found both1 take the ,numbers ,answering thereunto1 which 7in this ,example7 is #bibgd4b and #bdj ,hours2 and then say1 ,hours ,hours ,as #bibgd4b 3 #bdj 33 #accgeb4b 3 #ajif4hd ,which being devided by #ab1 leaves remaining #d4hd ho4 or #d ho4 #ej4d min4 required1 for the ,hour and ,minute at ,london1 by which the ,longitude will be found1 as before directed4 ,and seeing it was near the ,winter ,season3 ,if you should add the ,autumn and ,winter ,numbers1 and ,hours respectively together2 and make them the two first ,numbers in your ,proportion2 it would quate the ,seasons more exactly3 ,i mean1 if the said ,numbers had been really entred from ,practice2 but these are only supposed4 ,and by this method you may quate the ,numbers for finding the true ,hour and ,minute at any ,season2 or for any other ,latitudes whatsoever4 ,how to find the ,hour and ,minute1 at the place where you are1 when abroad1 either at ,sea or ,land4 ,for ,solving this1 there are ,two ,ways1 the ,first and ,infallible is1 when the ,sun is either ,rising or ,setting2 at which times1 if the ,air be clear1 observe what ,numbers are pointed to by the two ,indexes1 7but observe the swiftest first1 because it will soon be removed7 just as the ,center of the ,sun is in the ,horizon2 and enter both the ,numbers down1 as before directed1 with the ,day of the ,month1 and the ,latitude you are then in3 ,which having done1 by the following ,cannon1 say1 ,as ,is to t4 c4 of the ,sun's ,decl4 ,so is t4 ,lat4 ,to s4 c4 of an ,angle2 which1 if converted into ,time 7by #ae7 ,gives the ,hour and ,minute of the ,sun's ,rising from ,midnight2 and if ,substracted from #ab ho4 gives the ,setting4 ,which shews the true ,hour and ,minute at the ,place where you then are1 either at ,sea or ,land4 ,the ,second way for ,solving the said ,question1 is by taking the ,sun's ,altitude1 when about #e or #aj degrees above the ,horizon2 and at the same time let another ,person see what ,number the ,swiftest ,index points to1 and after that the ,slowest3 ,then put them both down as before directed1 with the ,day of the ,month1 and the ,latitude of the place where you are2 then have you the ,sun's ,altitude1 the said ,latitude1 and the ,sun's ,declination1 to find the ,hour and ,minute of the ,day at the place required4 ,now having by the said ,observations and ,cannons found the ,hour and ,minute of the ,day for the ,place where you are1 when abroad2 and by the ,numbers pointed to1 by the two ,indexes1 also found the ,hour and ,minute that it is at ,london1 7if the ,movement was there set going27 ,if you take the ,lesser of these from the ,greater1 and bring the ,remainder into ,minutes1 it will give the difference between the two places in ,time2 by which you may find their difference of ,longitude either ,east or ,west to a ,minute1 by the following proportion1 7viz47 ,suppose the ,difference of ,time was #cg ,minutes1 then say1 ,minutes of ,minutes of ,minutes of ,minutes of ,as ,time 3 ,longitude 33 ,time 3 ,longitude #addj4 #bafjj #cg #eee4e or #bd hours ,deg4 ,min4 or #i 3 #ae4e ,required4 ,which #i deg4 #ae4e4 min4 being added to1 or taken from the ,longitude of the ,place1 where the said ,movement was first set in ,motion1 gives the ,longitude you are come into1 as effectually as the ,latitude is obtained by ,observation1 as was at first proposed4 ,so that it is evident1 that if any defect should be found in practice1 it must proceed from the ,vicissitude of the ,air2 and not from any ,deficiency in this ,discovery1 or from the ,cannons relating thereunto4 ,and that we may ,answer all ,objections1 which may arise1 on ,account of the said ,vicissitude of the ,air1 ,motion of the ,ship1 ,foulness of the ,movement1 c4 as well as render this ,discovery more intelligible1 we will descend to speak thereof more particularly3 ,and1 ,in the first place1 let ,five or ,six 7or what ,number you please7 of these ,movements be made2 and after they have gone for a ,month or two1 7or if designed for the ,sea1 'till within two or three ,weeks of your ,sailing7 then take them asunder1 and set them going by the ,meridian ,line1 as before directed4 ,and having entred down in the ,book1 herein after mentioned1 the ,day of the ,month1 when set going2 how long it is making one ,revolution2 and what ,number is produced1 in just ,ten ,days ,motion1 7all which must be done1 before you ,sail in every ,voyage27 ,let them be carry'd to ,sea1 into any ,latitude1 7suppose #ej ,deg4 or ,newfoundland7 and at their ,return bring them again to the said ,meridian ,line1 and thereby 7with the help of the ,number of ,days from their being first set in ,motion7 find the two first ,proportional ,numbers1 as before directed3 ,which done1 enter them in a ,book1 peculiar to each ,movement1 7the ,form whereof followeth7 together with the ,latitude1 and ,season of the ,year in which the ,voyage was made4 ,then will they all be fitted for a ,voyage to ,newfoundland1 and ,parts adjacent1 for any such ,season4 ,and so for any other1 when ,tried and ,entred1 as now directed4 ,after which1 send them all in a ,ship bound to the ,latitude of about #cg ,deg4 7suppose ,virginia72 and being returned1 let the ,numbers be found and entred1 as aforesaid1 with the ,latitude and ,season2 then will any one1 or all of them1 be fitted for a ,voyage1 either to ,newfoundland or ,virginia1 or any of those ,parts1 for any such like ,season2 and so for any other1 when ,tried and ,entred as aforesaid4 ,this being done1 send them also in a ,ship1 bound to the ,latitude of #ac ,deg4 7suppose ,barbados or ,jamaica27 and being returned1 find the ,numbers1 and enter them with the ,latitude and ,season3 ,so will they all be fitted for these several ,latitudes1 7viz47 #ej ,deg4 #cg ,deg4 and #ac ,deg4 at such a ,season3 ,and by a like ,process to the quinoctial1 and towards the ,north ,pole4 ,upon which several ,tryals1 you will have so many ,movements fitted for all the ,north ,hemisphere1 both for ,hot1 ,cold and ,temperate ,seasons4 ,and1 by only ,counterchanging the ,latitudes1 for the whole ,globe2 or at least for the ,marine ,parts thereof4 ,and to what is proposed to be ,entred1 in respect of ,latitude and ,season1 you may also add the ,time of its being first set in ,motion after ,cleansing2 which ,cleansing must be done only ,annually1 and as near as may be on the same ,day of the ,month2 which will much facilitate the ,inequality arising from its ,foulness3 ,by which all ,objections will be answer'd1 and the ,discovery render'd compleat and perfect4 ,especially if a true ,meridian ,line be made in every considerable ,port in this ,kingdom1 and elsewhere2 for ,examining the ,movement at your ,arrival abroad1 and setting it in ,motion1 before your ,departure4 ,but remember1 that where you set it going1 from thence your ,departure must be reckon'd4 ,and by this ,method all the said ,vicissitudes that may arise in respect of ,latitude or ,seasons1 ,motion of the ,ship 7which will be near the same in one ,voyage1 as in another7 and ,cleanness or ,foulness of the ,work1 will also plainly appear upon ,record1 7by comparing one ,number in the said ,book with another7 and will be ,accounted for1 and quated1 as occasion requires3 ,namely1 by only taking such ,numbers from the said ,book1 to work your ,proportion by1 as are entred for the ,latitude and ,season1 that you are again ,arrived to1 or ,sailing under3 ,as suppose into #ej ,deg4 in the ,summer ,season1 then take the ,number and ,hours answering thereunto2 and so1 if in ,winter1 those for the ,winter4 ,by which proportionable ,numbers1 the said ,contingencies will be truly and effectually ,allowed1 and the ,difference in ,motions justly quated1 as was before asserted4 ,note1 ,that in this ,movement1 the ,time is ,regulated or ,conformed to the ,motion3 ,whereas in former ,movements1 the ,motion is ,regulated or ,conformed to the ,time4 ,and this ought to be well understood1 before you can rightly comprehend what is herein contained4 ,now that this ,movement1 or ,discovery1 does not only differ from1 but also far exceed1 any that has hitherto been proposed2 is evident in this 7viz47 ,that if any former ,movement whatsoever be ,timed here1 as usual1 ,before it is carried to ,sea1 7tho' never so exactly7 yet the change of ,climate1 c4 will so affect it1 as to make it go ,false3 ,and if you fit it there1 then 'twill be also ,false when brought hither3 ,but if by this ,movement1 and the foregoing ,rules1 the said ,numbers be found ,after it is returned from such a ,voyage2 all the said ,defects or ,contingencies will be quated by the said ,numbers only4 ,so that it will be the same in use1 as if no such ,accidents did attend it at all4 ,and this ,assertion must1 and will be granted1 by every one that does fully comprehend the ,nature and ,use thereof4 ,for altho' this ,horologe has no certain ,hours or ,time pre-assigned to it2 yet it hath nevertheless1 greater or lesser ,numbers quated to the ,variableness of ,motion or ,time1 7viz47 ,if fitted to be used here in ,england1 then it hath 7or may have7 one sort of ,numbers 7or ,time7 for finding the ,hour and ,minute1 in the ,summer ,season2 another for ,winter2 and a third for the ,spring and ,fall2 one when it lyeth undisturbed in one and the same place2 another 7if you please7 when carry'd always in a ,rattling ,coach4 ,and on the other hand1 if you carry it to ,sea1 then it has one for the ,torrid1 one for the ,frigid1 and a third for the ,temperate ,zones1 c4 ,and yet still but one and the same ,horologe1 and but one and the same ,indexes4 ,so that all manner of ,natural ,vicissitudes or ,contingencies whatsoever1 may be ,regulated or quated in and by the said ,numbers2 and consequently1 the true ,hour and ,minute of the ,day1 where it is first set going1 may be hereby as effectually found1 as if no such ,impediments did at any time or place attend it1 as aforesaid4 ,and as for what may be suggested in relation to the ,inequality between the ,spring and ,fusie1 if any should be1 it will be compensated1 in that there are five or six ,windings up of them1 to one ,revolution in the ,horologe4 ,so that there is nothing wanting to compleat this ,discovery1 but to put it into ,practice3 ,and seeing the ,charge and ,trouble is very ,inconsiderable2 and the ,legislature by ,act of ,parliament1 hath been graciously pleased to ,incourage hereunto1 it is thought expedient to make this publick ,proposal1 viz4 ,that if any one ,person is willing to ,engage in this so ,noble an ,enterprize1 he will be readily received as a ,partner1 on such ,conditions as may be ,reasonably ,concerted therein4 ,you may hear of the ,author at ,mr4 ,burleigh's in ,amen-,corner1 ,london4 ,,memorandum4 #a4 ,all ,departures must be reckon'd from ,london1 if the ,movement was there ,set going4 #b4 ,that wheresoever they are ,set going1 there must be a large and exact ,meridian ,line prepared by a ,perpendicular1 set up in an ,horizontal ,circle1 as is ,mathematically taught1 c4 #c4 ,that an ,equal time be spent in ,winding it up1 as near as possible2 for which no time need be allowed1 if ,equated for #aj or #ab ,months2 because the time required will be the same for the same time1 and greater for a greater1 c4 #d4 ,that the said ,movement be carefully kept in one and the same ,temperature of ,air1 as near as possible4 #e4 ,that after this ,movement is fully proved1 if it should not 7by reason of any sudden change of ,air7 agree to a ,minute1 yet it ought not in this respect to be altered or much regarded1 because the moistness of one ,month1 may compensate the ,dryness of another3 ,so that by such time as you are arrived to the end of your ,voyage1 the ,movement may even ,rectifie or ,correct it self4 #f4 ,it is to be noted1 ,that if the ,sun comes too soon to the ,meridian1 it will also come too soon to the ,horizon2 and therefore1 ,watch too fast1 or too slow1 must be ,added or ,substracted1 as aforesaid4 #g4 ,that it be always wound up1 as near as may be1 at one certain time of the ,day1 7viz47 if at ,sea1 about ,twylight1 or ,break of ,day1 as may be thought expedient4 ,and if it should happen to be omitted1 so long as to stand still2 you must not set it going again1 but by taking it assunder1 and putting the two ,indexes together1 and bringing the ,movement to the ,meridian ,line1 as at first directed4 ,therefore when at ,sea be careful of such ,omissions4 #h4 ,it is to be noted1 ,that altho' every ,minute of ,time1 does ,answer to about #ae or #af ,miles ,english1 under the ,equinoctial2 yet it is not above #i or #aj ,miles in our ,latitude to one such ,minute4 ,and altho' it be so many under the ,equinoctial1 yet there the ,sun's ,altitude will be taken very exact1 because #ij degrees of ,altitude1 is for #f hours of ,time2 whereas in our ,latitude1 it is but #fb degrees1 for #h hours of ,time2 both which ,advantages will ,facilitate the ,practice4 ,i shall at present conclude with acquanting1 ,that if a common ,minute ,watch 7by ,filing or ,loading the ,ballance1 or otherwise7 be made to go1 or does already go1 any unknown quantity of ,time1 either too ,fast1 or too ,slow2 by this ,device1 we may find the ,hour and ,minute of the ,day by such a ,watch1 more exactly than can be done by the best timed common ,watch whatever4 ,and this even without touching it1 other than by ,winding up the ,spring as usual4 ,there are other ,improvements that may be made of this ,discovery1 but ,i reserve them to some other ,opportunity4 ,the ,,form of the ,book to be kept for each ,movement1 wherein must be entred the ,numbers1 c4 7which are to be found at the ,returning of the ,ship7 for finding the ,hour and ,minute at ,london4 ---------------------------------------- ---------------------------------- ,the ,movement1 ,number #a4 was and ,then made one ,revolution1 in #e first ,set ,going ,sept4 #d4 #agad4 days1 #d hours1 and a quarter4 ---------------------------------------- -------------------------- ,degrees,numbers ,hours ,diff-,seasons ,time when the ,numbers1 of to be spent in erencein which ,movement was shewing how ,lati- found andproducing in the ,ship set in ,motion the ,motion tude4 used in the said ,num- was ,try'd2 at is retarded finding ,numbers4 bers4,sailing4 after first by ,foulness1 the ,making or on a ,tryal ,hour at ,cleaning4 of #aj ,days ,london4 at a time4 ,i4 ,,ii4 ,,iii4 ,,iv4 ,v4 ,,vi4 ,,vii4 ,days4 #ej #bibgf4b #bdj ,autumn,sep4 #af4 #agadbibgf4b #aj #eb #cgifb4d #dcb ,winter,dec4 #d4 #agadbibgb4e #aj #dd #cgidb4 #dcj ,spring,ma4 #bj4 #agaebibfd4 #aj #dh #cgiab4b #dca ,summer,june #a4 #agaebibcg4d #aj ---------------------------------------- ------------------------- ,cleansed ,sept4 #e4 #agae4 ,then made one ,revol4 in #e days1 #d ho4 and 4 ---------------------------------------- ------------------------- #ej #bibgd4b #bdj ,autumn,sept4 #e4 #agaebibgd4b #aj #eb #cgieg4i #dcb ,winter,dec4 #ag4 #agaebibfh4 #aj #dd #cgidb4 #dcj ,spring,ma4 #af4 #agaebibfd4 #aj #dh #cgijg4e #dca ,summer,june #h4 #agafbibcb4g #aj ---------------------------------------- ------------------------- ,note1 ,that the ,numbers to be used after ,cleaning1 7viz4 after ,sept4 #e4 #agae47 are found by ,substracting or ,adding the ,difference between the two ,numbers in the ,seventh ,column1 7viz4 that of ,sept4 #e47 and that of ,sept4 #af4 7which is only #b47 out of the former ,numbers to be used for the same ,latitude2 on which there will remain #bibgd4b for the ,new ,number to be used in ,lat4 #ej4 ,deg4 in ,autumn1 instead of the former1 until the next ,cleaning1 7which must be only ,annually7 and so of the rest1 from one ,cleaning to another4 ,and this method must be used for the respective ,latitudes1 according as ,observations shall be made therein1 and ,numbers found to answer thereunto4 ,note also1 ,that this ,experiment may be sufficiently ,tryed and ,proved1 by only two or three ,voyages1 to the ,south-,west parts of ,ireland1 or to ,newfoundland at farthest4 ,but notwithstanding what has been said1 ,it is chiefly to be noted1 ,that altho' ,i have proposed 7for ,example sake7 that the ,general ,numbers should be found1 by ,sailing to ,newfoundland1 ,virginia1 ,barbados1 c4 and returning again to a ,meridian ,line at ,london3 ,yet if the ,honourable ,persons before-mentioned in this ,title-,page1 to whom the whole is most humbly submitted1 will please to appoint a ,ship for this purpose1 the said ,numbers may be much better found in manner following2 7that is to say7 ,by ordering that the said ,ship shall first make a true ,meridian ,line1 at or near the ,lat4 of #fj ,degrees2 and thereby set the ,movements going1 in manner aforesaid3 ,after which let them ,sail about #dj or #ej ,leagues distant from the ,shore1 and there ,cruise ,northward and ,southward for about a ,month's time2 after which let them return again to the same ,line1 and find the ,numbers1 and also enter them1 as before directed4 ,and having so done1 let them make another ,meridian ,line1 about #ae ,deg4 more ,southward1 and there do in like manner3 ,and so at the like ,distance to the ,equinoctial4 ,after which1 let them begin again1 and repeat the same ,process for three or four times3 ,by which means the ,numbers will be found1 and the different ,motion of the ,movement discover'd1 for all ,latitudes and ,seasons1 as near as needful4 ,and being returned home1 by these ,numbers we may find the true ,difference of ,motion1 in and for the several ,latitudes and ,seasons4 ,which ,difference must be entred in the #dth ,column of the respective ,books1 reserved for that purpose4 ,by the help of which said ,differences1 you may make as many ,movements as may be needful1 at any time2 as also ,books and ,numbers peculiar to each ,movement4 ,the ,rules for which will be imparted to any such ,watchmaker1 as may ,reasonably desire the same4 ,,finis4