TELESCOPE 



vifible, by amplifying the vifual angle, yet its application 

 to the mealurement of fmall angles was an objctt tiiat en- 

 gaged the aftronomer's attention at no groat dillance of time 

 from its invention. When the apparent diameters of the pla- 

 netary bodies had once been increafed, fo as to fubtend an 

 appreciable angle at the eye of the obferver, it foon became 

 a matter of intcreft to meafure thofe angles in their enlarged 

 ilale. We have already given the defcription of the differ- 

 ent Micrometers that have been fucceffively a])pliod to a 

 telefcope for the purpofe of meafuring minute angles, and 

 terreftrial diftances correfponding thereto ; but we have re- 

 ferved our account of the means proper to [>•: ufed in thefe 

 operations, as conlUtuting a portion of our prefent article. 

 We propofe to illullrate the ufe of a few of tiie mod accu- 

 rate and ufeful micrometers by fuch examples, as will fuf- 

 fice to render the application of any other micrometer in- 

 telligible. 



When an objeft to be viewed is remote, the rays of light 

 which proceed from it may be confidercd as coming from it 

 in parallel lines, and in this cafe the focus of tlie objeft-glafs, 

 or fpeculum, is the rtiorteft pofliblo ; confequently, the 

 power of the inllrument depending on this focal dillance, is 

 the fmallell poffible with the fame eye-piece ; but the rays 

 which proceed from a near objeft, come to the objeft-glafs 

 or fpeculum diverging, and confequently do not come to a 

 focus fo foon as in the former cafe ; fo that the power is 

 greater than when a diftant objett is viewed. This variation 

 of power depending on the diitance of the objeft viewed, is 

 accompanied by a new adjuftmenl of the eye-piece for dillinft 

 vifion in every telefcope of confiderablc magnitude ; and the 

 longer the focus of the objedt-glafs is, the greater is the va- 

 riation of power with the fame variation of diftance. Hence 

 the angle that is meafured by any of tlie micrometers at- 

 tached to a telefcope, is the true angle only when the objeft 

 fubtending that angle is remote ; and a correftion, depend- 

 ing both on the dillance and fecal length of the telefcope, 

 becomes neceffary for converting the apparent meafured 

 angle into the true one. To a want of attention to this cir- 

 cumftance in tlie praftical application of micrometrical tele- 

 fcopes to the meafurement of terreftrial diftances, is princi- 

 pally to be attributed the failure of their fuccefs ; and 

 celeftial objefts have confequently engroffed their utihty 

 almoft exclufively. We conceive, therefore, that we fhall 

 render our readers an acceptable fervice by Ihewing, not 

 only how fmall celeftial angles may be nieaiured by a tele- 

 fcope fitted up with an accurate micrometer, but alfo how 

 terreftrial angles, fubtended by objefts at various diftances, 

 may be afcertained, and their correfponding diftances be ob- 

 tained with great accuracy ; and that by fimple vifion at 

 one ftation, when the diftance is not very confiderable. The 

 compofer of the prefent article has made experiments with 

 different micrometers adapted to telefcopes of various 

 lengths, and can therefore illuftrate the theory by aftual 

 examples in fuflficient variety. 



Celejlial Meafures When a micrometer of any defcrip- 

 tion, mechanical or optical, is propofed to be ufed with a 

 telefcope, it is neceffary that the value of one of its divifions 

 be afcertained with that identical telefcope when viewing a 

 remote objeft, fuch as a heavenly body ; or otherwife, that a 

 correftion for diftance be applied previoully to the deter- 

 mination of fuch value. We will firft fuppofe the objeft at 

 a fufficient diftance to require no correftion for want of 

 parallelifm of the rays of light, and will ftiew how to ap- 

 preciate the micrometrical fcale for fuch remote diftance 

 without correftion. The diameter of the fun has been fo 

 well afcertained by aftual mealurement of the beft inftru- 

 mcnts, from month to month, and from year to year, that it 

 Vol. XXXV. 



may be taken from the Nautical Almanac, or Connoiff.mce 

 dcs Terns, on any giv.Mi day, as a ftandard, from which the 

 value of a correfponding number of divifions on the fcale of 

 the micrometer may be affigncd with great accuracy, after 

 allowance is made for apparent variation in the fun's dia- 

 meter by altitude ; and when the number of miuutcs and 

 feconds correfponding to a certain number of divifions on 

 the fcale is afcert.iined, the value of one divifion is readily 

 obtained by dividing the whole number of minutes and 

 feconds by the whole nimibcr of divifions that meafure the 

 faid quantity : and then whatever may have been the error 

 of the obfervation, as affi-cling the whole fcale, the quan- 

 tity of it belonging to one divifion will bi- only ,'„ ,V. or-jV 

 ot the whole, accordingly as there ware 30, 4.0, or 50 divi- 

 fions in the fcale that corrcfponded to the corredl diameter 

 of the fun. For inftance, on the 7th of Auguft 18 15, the 

 fun's diameter was meafured at noon by a Troughton's 

 micrometer, .ittached to a five-feet rcfrafting achromatic 

 telefcope made by Tulley, and was found to be equal to 

 60.65 turns of the fcrew, when taken in a vertical dirertion, 

 while the fun paffed horizontally between the two parallel 

 fpider's lines in the focus of the eye-piece. In this fituation 

 the altitude of the fun was fo great, that the diftVrcnce 

 between the refraftions of the upper and lower limbs wa« 

 infenfible, and therefore may be neglcfted in the calculation 

 of the value of the fcale of notches that indicate the revolu- 

 tions of the fcrew. On this day, the frmi-diametcr of the 

 fun, as given in the Nautical Almanac, was 15' 48".3, and 

 the notches correfponding to the fun's diameter were 6o.6j, 



or 60 entire notches, and —^ taken from the divided head 

 100 



of the fcrew : then 



ly 48".3 X 2 

 60.65 



= 3i".27 is the value of 



one notch, or revolution of the fcrew, according to this ob- 

 fervation. Again, on the 15th of Oiflober, of the fame 

 year, the fun's diameter, at nine o'clock P^. M., was found 

 equal to 61.50 revolutions of the fame fcrew, ufed with the 

 fame telefcope, when the fun's fcmi-diameter is g^ven i6' 4". 8, 

 or the diameter 32' 9".6 ; but at the low altitude at which this 

 meafure was taken, the difference of the two refraftions of 

 the upper and lower limbs amounted, by the table of refrac- 

 tions, to 2". 6, to be fubtrafted from the real to produce the 

 apparent diameter, becaufc the vertical diameter was con- 

 trafted by this quantity, the lower limb being more elevated 

 by refraftion than the upper one ; therefore, according to 



32' 7" 



this obfervation, the value comes out ^ = S'''-^^ for 



61.5 ^ 



each revolution ; hence th« average of tjie two mea- 

 fures, taken at different times, and at different altitudes, is 



3 1 ". 2 7 4- 2 1 ". 3 3 



^ '- ^ — -^ = 5i".j, which determination accords with 



2 ■" ■' 



meafuies taken at other periods, and alfo with terreftrial 

 mcafures fubfequcntly taken, as will appear hereafter. 



When this value of the micrometer's revolutions was af- 

 certained, the iolar focus of the objc6l-glafs was exaftly 

 meafured, and found to be 63.5 inches. Three other achro- 

 matic telefcopes were then procured, and had the fame mi- 

 crometer adapted to them refpeftively, by as many rings of 

 brafs, which had each a male and a female fcrew : the former 

 to fcrew into the tube of its telefcope, and the latttr to re- 

 ceive the coarfe thread of the micrometer ; which rings we 

 have called adapters. The focal lengtbs of the rcfpcftive 

 objeft-glaffes were found by accurate meafurement to be 

 30.15, 45.75, and 1 18.3 inches; and the correfponding 

 O o ViducB 



