TELESCOPE. 



being beyond the powers of the telcfcopc, or rather of tlie 

 human eye, when a fingle obfervation is taken. 



Before Table V. was conftruded, it was found by j)laiic 

 trigonometry, that one yard will fubtend an angle of one mi- 

 nute at 3437-7 yards didance ; and, as the dillance d>'creafes 

 in the fame ratio in winch the angle increafcs, the table was 

 made by a continual reduAion of this number into halves, 

 thirds, fourths, &c. as far as to 30', and all the intermediate 

 feconds from i' to 30', were inferted with their correfpond- 

 ing diftanccs. For inftance, at the true angle of 1 8' 30", 

 tlie true dillance is 185.82 yards ; it being always under- 

 ftood, that the meafured angle is fubtcnded by an exad yard 

 placed at right angles to the line of fight, in either a vertical 

 or horizontal pofition, and that the correftion taken from 

 Table IV. has been applied to the meafured or apparent 

 angle. If two yards fliould be ufcd as the oppofed objeCl 

 at a great diftance, then /',///" the angle only muil be taken ; 

 but if half a yard only be ufed at fmall dillances, then double 

 the angle will be proper ; and Ihould the diftance be within 

 110.95 y^i'ds, the fmaJlcft diilance contained in the table ; 

 in which cafe the angle will exceed 30' : the dillance belong- 



With telefcope 30.15 in. 24.59 revol. = 27 2.9 (by 



45-75 in- 37-53 revol. = 27 10.5 



63.5 in. 52.25 revol. — 27 15.43 



1 18.8 in. 98.52 revol. = jy 35.1 



ing to half\.\\e anjrle will always be douMt the didance re- 

 quired, Suppofe tiic angle 33' ; then hilf of this is 16' 30", 

 and the double number 20S.34 ; confcquenlly 104.17 yirdt 

 will be the correfponding dillance ; and thus the table will 

 extend to any Ihort dillance, by taking a given portion of 

 the meafured angle, when reduced to the true one, and by 

 ufmg the fame portion of tlie correfponding dillajice, pro- 

 vided the angle do not exceed 60', which is the limit a( 

 Table IV., and wliich is as much as a telefcope magnifying 

 only 30 times will ufually take into the field of view. 



In order to exemplify the ufe of ihcfe new tables, and at 

 the fame time to prove their accuracy, we obtained from 

 Mr. Troughtou a couple of Haves, having each a (liding 

 yard of brafs, cut into notches for decimal divilions of a 

 yard, which are capable of being feen at a diftance, with 

 an apparatus for placing them perpendicular in any giveu 

 fituation : on the 8th of Oclober 1816, one of thcfe llavea 

 was fixed in a perpendicular pofition at an unknown diftance 

 on level ground, and the following meafures were taken of 

 the angle fubtended by a yard, by Troughton's micrometer 

 fuccemvely adapted to each of the four telcfitopcs, thus : 



Tables I. and II.) - 10.4 (by Table IV.) = 26 52.5 



— 15.6 .- - =26 54.9 



— 21.85 - - =26 53.58 



— 41.0 - - =26 54.1 



4)215.08 



By Table V. the diftance correfponding to this angle is 

 127.81 yards, and by meafurement of a good chain, it was 

 afterwards found to be 5.808 x 22 = 127.776 yards, the 

 difference or error being only .034 of a yard, or fomething 

 lefs than an inch and a half. During the obfervations, the 

 fun was obfcured by clouds, and the objedl viewed had no 

 vibratory motion, which is a circumftance effential to be 

 attended fo. 



With Dollond's divided objedl-glafs applied to the tele- 

 fcope of 45.75, the meafure was 2 in. ii div. 19 ver., or 

 ? 294 of the vernier, which, multiplied by i".24, the folar 



Average = 26 53.77 



value of unity, gave the meafured angle only 26' 44".56 ; 

 but on examining the ratio in which the focus elongates at 

 different diftances, we found that the divergence of the rayf 

 was leffened fo much, in pafTmg through the divided objed- 

 glafs, before they entered the acliromatic objedt-glafs, that 

 the table of corredions would be of no ufe for this arrange- 

 ment of two feparate objeft-glaftes. 



On the 1 6th of the lame month the graduated ftaff was 

 ereAcd at a greater unknown diftance, and the following 

 meafures were taken by Troughton's micrometer, as before, 



With telefcope 



45.75 in. 27.59 revol. =. 

 63.5 in. 38.48 revol. = 



20 0.1 — 8.6 (correftion) = 19 51.5 

 20 4.4 — 12 - - = 19 52.4 



to which angle the correfponding dillance by Table V. is 

 173.0 yards; and the fubfequent meafure by the chain 

 accurately repeated was 172.92 yards, in which determi- 

 nation the error was .08 of a yard, or 2.88 inches only. 



From thefe operations we are perfuaded that a good 

 telefcope, with a Troughton's micrometer, will determine 

 diftances, by fimple infpeftion, when within t'le eighth part 

 of a mile, with more accuracy than is ufually done by a 

 furveyor's chain or meafuring-wheel ; and, confequently, 

 if both a backward and forward view be taken from one 

 ftation, fituated near the middle of a Une joinir-g two gra- 

 duated ftaves, a quarter of a mile may be fo determined at 

 one Jlatlon in the fpace of two or three minutes after the 

 ftation is taken. But it m.ay be faid, why not take a 

 quarter of a mile at one fight, lince the power of a good 

 telefcope will command a fmall objcft at this diftance i 

 To which we anfwer, that the error aiifing from diftance 

 9 



2)103.9 



Average = 19 51.95 



may be confidered rather as a geometrical than an optical 

 error : our experiments have convinced us that a fmall 

 angle may be meafured by Troughton's micrometer, when 

 the thicknefs of the fpider's line is allowed for, {viz. locth 

 of a turn of the fcrew in our micrometer,) fo accurately, 

 that the error of obfervation in favourable weather will 

 feldom exceed one fee or. J ; but the error in diftance, cor- 

 refponding to an error of one fecond in the meafured angle, 

 increafes in the duplicate ratio of the diftance, and confe- 

 quently becomes too confiJerr.ble to be admiflible beyond 

 a hmited diftance ; for inibince, at the diftance of 220 yards, 

 or the eighth of a rnile, an error of 1" in the angle fubtended 

 by a yard produces only an error of 0.23 of a yard in 

 diftance ; but at 440 yards, or a quarter of a mile, the 

 error in diftance corr. fpondiiig to the fane error in the 

 angle is 0.92 ; that is, at twice the diftance the geometri- 

 cal error is four times augmented ; which circunillancc 



limits 



