TELESCOPE. 



being 31' 59". 2 horizontally, and 3 1' 57",9 vertically, at the 

 altitude of 38". 



TerreJIrial Meajures In the examples which we have 



given of ccleftial angular mcafures taken by a microme- 

 trical telefcope, no correait)ii of the meafured angle was 

 iieceflary, becaufe tlie rays of light coming from thefe objefts 

 may be confidcred as parallel on entering the objeft-glafs, 

 and as always converging to the fame focal point, where the 

 image is formed ; hence the magnifying power of the celef- 

 tial telefcope does not vary. But when tcrreftrial objefts 

 are viewed at different diftances, there is a deviation from 

 parallehfm in the courfe of the rays, which increafes in the 

 inverfe ratio of the diftance, and which lengthens the focus 

 of the objeft-glafs, and confequently increafes the power 

 of the inftrument, even with the fame glaffcs. This altera- 

 tion in the effeftive length of a telefcope is praftically dif- 

 covered by the adjuftment of the eye-piece for diflinft vifion, 

 which is neceffarily different at different diftances from the 

 objeft viewed. But we have fhewn, that the fcales of 

 Troughton's and of Dollond's micrometers will vary with 

 the variable powers of even the fame telefcope, and there- 

 fore will require a correftion for each variety of power, or, 

 in other words, for each variety of terreftrial dlltance. 

 The determination of thefe varying correftions, therefore, 

 is. effential to the accuracy of the meafures taken by a mi- 

 crometer in all cafes, where the incident rays of light come 

 diverging from objefts placed at moderate diftances. If we 

 put_/" for the folar or principal focus of the objeft-glafs of 

 any telefeope, and d for the diftance of an objeft from the 

 faid abjeft-glafs when ufed, the addition to the length 

 of the folar focus, which we will call e, according to the 



laws of dioptrics, may be found by this theorem, — . , 



d-f 



Jiat is, the fquare of the folar focus, divided by the dif- 

 tance in the fame meafure, when diminifhed by one focal 

 diftance, will be the elongation, or excefs of the lengthened 

 focus over the folar focus ; then as the powers are to each 

 other refpeftively as the focal lengths, with the fame eye- 

 piece, we fhall have f '■ f -\- c : : true angle : meafured or 

 apparent angle ; and converfely, zs, J -^ c : f ■.: apparent 



angle : true angje. For inftance, let it be required to 

 afcertain what is the neceffary correftion for an angle, itiea- 

 fured by a telefcope of 63.5 inches focus, that is fubtended 

 by one yard at a hundred yards diftanfce from the objecl- 

 glafs. By a fimple cafe in plain trigonometry, the true angle 

 fubtended by a yard, at a hundred yards diftance, is 34' 

 59". 4, or 34'.99 ; and 63.5 inches are 1.764, when reduced 

 into the denomination of yards and decimal parts ; then 



1.764 X 1.764 3.111696 , , . , , 



— — 0.03167 =«, the mcreafed 



100 — 1.764 

 length of the focus 



98.236 

 and 



1.764 4- 0.03167 X 34'.99 _ 

 1.704 



35'.6i8, or 35' 37".o8 will be the meafured angle, therefone 

 35' 37".o8 — 34' 59".4 = 37".68 is the corrtftion to be 

 added to the true angle, in order to obtain the apparent 

 angle, that would have been the true ang!e alfo, if the focus 

 of the objeft-glafs had remained unaltered at the diftance of 

 100 yards. But it is the correftion anfwering to the appa- 

 rent or meafured angle that we want, and the determination 

 of this requires a tranfpofition which is operofe, and there- 

 fore objeftionable in praftice ; on which account we recom- 

 mend each furveyor, military tadlician, and leveller, who is 

 difpofed to avail himfelf of the ufe of a micrometrical tele- 

 fcope, for fhortening his labours, to ufe tables adapted to 

 the focal length of his own telefco;)e, which may give by in- 

 fpeftion the correftion proper in all cafes for reducing the 

 apparent angle into the true one, and •vice iierfd. Tables III. 

 and IV. which are fubjoined, were computed for this pur- 

 pofe, from the theorem juil exemplified, and are adapted for 

 a telefcope of 63.5 inches focal length, to which we have 

 added Table V., as a general table for finding the diftance, 

 in yards and decimal parts, con'efponding to any angle, 

 from i' to 30' 59" inclufively ; even to the accuracy of a 

 fingle fecond, when that angle is fubtended by an exacl yard. 

 The labour of conftrudiing thefe tables has been confiderable, 

 but the facility and accuracy with which they give the de- 

 fired refults, has amply repaid the computer, and, it is pre- 

 fumed, will be a recommendation to the notice of our 

 fcientific readers, to whom their application may in many 

 cafes be found ufeful. 



TABtE 



