TELESCOPE. 



Conjlruaion and UJe of tht TabUs.—VCe have already ex- 

 plained the conftrudion and ufc of Tables I. and II., which 

 are required to be adapted to the particular telefcope with 

 which any given micrometer is ufed ; and we have alfo ex- 

 plained how tlie value of a fingle divifion, or turn of a fcrew, 

 is afcertained by means of the fun's diameter : but this me- 

 thod gives a derivative rather than an original independent 

 value to the micrometrical fcale ; for if the fun's diameter 

 be not truly given in the Nautical Almanac (and the late Dr. 

 Malkelyne had reafon to alter it in the lateil years of his 

 life), the errorof this meafure will be introduced into the Icale 

 derived from it ; Table III. is therefore inlerted, as affording 

 the ready means of obtaining an independent fcale from 

 aftual tcrreftrial meafurement. We have already rtiewn how 

 the table of correftions is conflrufted in this table ; and the 

 reader will have no difficulty in taking out the proper 

 numbers, as correftions to be added to the true angle, in 

 order to convert it into the apparent or meafured angle, if he 

 be careful to take the minutes of the given angle from the 

 left-hand vertical column, and the feconds from the hori- 

 zontal line at the top ; for in every inftance, the meeting of 

 the two columns will contain the additive quantity that is to 

 be applied to the true angle, in order to obtain what the tele- 

 fcope will give when the value of its fcale is once duly 

 affigned. For inftance, fuppofe the true angle 14' 20", 

 where 14' is taken at the fide, and 20" at the top, the junc- 

 tion of the two columns gives + 6".28, which (hews that 

 this quantity muft be added to 14' 20", the true angle, to 

 make 14' 26". 28, the apparent angle, as meafured by a tele- 

 fcope of 63.5 inches focal length. If now this angle, reduced 

 into feconds, be divided by the turns of the fcrew, or divifions 

 on any fcale ufed as a micrometrical fcale, the quotient will be 

 the value in feconds of one turn, or divifion, as the cafe 

 may be, provided the angle in queftion be that which a true 

 yard adlually fubtends at a known diftance. For example, 

 when a yard of 36 exaft inches was erefted at the diftance of 

 190.98 yards, the micrometer of Troughton, attached to 

 Tulley's 63.5 inch telefcope, meafured it by 34.78 revolu- 

 tions of its fcrew ; and by Table V. the true angle, read as in 

 Table III. at the fide and top, correfponding to this dif- 

 tance, is 18' o" ; the additive quantity belonging to this 

 angle, as taken from Table III., is + 9". 89 ; and therefore 

 the apparent angle, if meafured by the faid telefcope, would be 



, ^ i8'9".89 ,, ■ , , r 



18' 9".89 ; therefore = 31.33 is the value ot 



one revolution of the fcrew, which is very nearly the fame 

 as vi:as determined from the fun, and before tabulated. This 

 coincidence of the celeftial and ten-eftrial meafures affords a 

 convincing proof that the fcale has been duly appreciated. 



We have faid, that this table of coiTeclions, and alfo the 

 following one, which we (hall explain prefently, are com- 

 puted exclufively for a telefcope of 63.5 inches focus, being 

 that which is reprefented, with a Troughton's micrometer 

 attached, mjig. 6. of Plate XXIX. ; and that each different 

 telefcope ought to have its own tables of correftions cor- 

 refponding to its focal length, which limitation is required 

 by the theorem on vyhich we have grounded our calculations. 

 But as the diftance, which is the varying term, is the fame 

 for all telefcopes, we find that in praftice the correftions 

 of any other telefcope will be fo nearly proportionate to their 

 refpeftive focal lengths, that they may be taken exaftly as 

 fuch, without any fenfible error ; that is, the error ariiing from 

 the table of correftions will be always as fmall as the error 

 of obfervation in ordinary telefcopes, unlefs the diftance be 

 very fmall, and its correftion confequently great. On this 

 account, Table III., and alfo Table IV., which, it will be 



fcen, is derived from it, like Table V., may be confidered as 

 genera/ tables, admitting of proportional parts of their whole 

 correftions to be taken as fuitable correftions for telefcopes 

 of other dimenfions. This confideration is of great im- 

 portance, with refpeft to the general utihty of our tables 

 of correction ; and therefore the reader (hall not depend 

 folely on the authority of our bare afTertion. We have 

 already computed the corredlion for a telefcope of 63.5 

 inches focal length, to be added when the true angle is 

 34' 59".4, or diftance 100 yards, and found it 37".68 ; let 

 us fee what it will be v^'ith the fame data, when the telefcope 

 has juft one half of the faid focal length : here we have 



■'''■— 00- "f - yard for the focal length ; 



of 



then 



<2 X 



•//> T ' _ .0078? = e, the clonffation of 

 100 - 882 99.118 / 5 ' 6 



the focus, and 



.882 X .00785 X 

 'Ml 



34-99 _ .^, , 

 — 35 '3' 



or 35' 



18" 



for the apparent angle, from which, if we fubtraft 34' 59".4, 

 the true angle, the difference l8".6 wiU be the correfpond- 

 ing correftion, which differs only a quarter of a fecond 



or half the correftion of the telefcope of 



fro 



37".68 



double dimenfions. Beyond 100 yards diftance, the en-or, 

 fmall as it is, will continue to diminifh as the diftance in- 

 creafes, and a fmaller diftance will feldom require to be mea- 

 fured in this way. The accuracy of this conclufion has 

 been ftill farther corroborated by aftual experiment : a gra- 

 duated ftaff was placed ereft at a diftance, by meafurement 

 of a Troughton's chain of five -feet hnks, of 261.9 yards, 

 and the two telefcopes of 63.5 and 45.75 inches focal length, 

 were tried againft each other thus ; a yard by the firft was 

 found, with Troughton's micrometer, to be equal to 25.33 

 turns ; and by the fecond, with the fame inftrument, to 

 be 18.19; the true angle belonging to this diftance by 

 Table V. is I3'7".54; and the correftion for the larger 



telefcope by Table III. + 5' 



.25: therefore, taking: ,' 



or .72 of 5". 25 = 3".8 for the correftion of the fmaller 

 telefcope, we have the following values of the refpeftive 



fcales ; 



•3' 



7"-S4 



+ 5"-25 _ 



3 1 ".2984, &c. and 

 25-33 



= 43". 504, which values accord very 



i3'7"-54+ 3"-8 



18.19 



nearly with thofe that had been previoufly determined by 

 a feries of folar meafures, and the latter of them exaftly, as 

 far as to the third place in the decimal figures. 



Table IV. is the table to be ufed with Table V. for finding, 

 firft the true angle from the apparent one, and then the true 

 diftance at once from this true angle : its correftions are 

 arranged fomewhat differently from thofe in Table III., and 

 have an oppofite fign, but are borrowed from Table III. in 

 fuch way, that by means of a little tranfpofition, the terms 

 of one may be converted into thofe of the other ; as, for 

 example, at the apparent angle 18' 40", in Table IV., the 

 correftion is — 10". 4, and the true angle confequently 

 i8'29".6; and at 18' 30", the neareft numbers for the 

 true angle in Table III., the correftion is + io".44, which 

 makes its correfponding apparent angle 18' 4o".44. In the 

 former of thefe two tables, the correftion is calculated to 

 the hundredth part of a fecond ; it being that from which 

 the fcale has its value appreciated; but in the latter, it was 

 deemed convenient to leave out the hundredth parts, as 



being 



