494 Scientific Proceedings, Royal Dublin Society. 



Similarly for the right ascension movement, a wheel k is 

 attached to the frame in which the polar axis revolves, into which 

 gears another wheel a fitted to and strung upon the neck of the 

 cross head. in which the declination axis revolves. . Grearing into 

 this wheel « is a pinion b fixed to a rod which passes through the 

 hollow shaft above mentioned, as used for the declination move- 

 ment, and carrying on its lower end a pinion and button-head e 

 which gears into another wheel r also fitted to and strung upon 

 the eye-end of the telescope, and in front of the declination circle 

 d. It is evident that if the wheels Jc and a are equal in size, and 

 that the proportion between b and these wheels is the same as 

 between e and the wheel r, that this circle r will revolve at the 

 same angular velocity as the telescope is revolved upon its polar 

 axis ; but it also happens that this wheel r will be rotated by 

 movements of the telescope in declination as well as by movement 

 in ascension, and, therefore, this wheel r cannot be used as an 

 ascension circle if read by a fixed vernier, but differential readings 

 between the wheel r and the wheel d give actual hour angles. 

 Practically, the method of carrying this out is as follows : — 



The wheel d has upon it a circle of silver, or white metal, 

 divided on the edge to declinations and read by a fixed vernier. 

 Further in, on the same white metal, is a set of divisions corre- 

 sponding to hours and minutes of right ascension, and this is read 

 by a vernier fixed to the circle r, which is cut away in two places 

 to allow the divisions on d to be seen. In this way the right 

 ascensions and declinations of objects can be read at the eye-end of 

 the telescope, and at the same time by attaching milled heads to 

 the outer and inner shafts, as at i and e, these button-heads can 

 also be utilized for producing slow motions in declination and 

 right ascension. 



It will, no doubt, be objected that the unavoidable " loss " in the 

 teeth in various parts of this gearing will cause so much error as 

 to render the readings of these circles useless, and also that even if 

 this could be eliminated, the velocity-ratio of these circles to that 

 of the instrument on its axis will not be constant with any practi- 

 cal form of teeth. 



It will be seen, however, on careful consideration, that whereas 

 the error of, say, the declination circle would be the sum of the 

 errors in the two wheels and pinions, so long as the telescope is 



