Mr. F. Baily on the Circular Micrometer. 179 



to the telescope in the usual manner: 2° in the use of steel 

 instead of brass, whereby a finer edge may be given to the 

 circumferences*: 3° in rejecting the metal arms by which 

 these rings were formerly attached to the sides of the tele- 

 scope, from the unequal expansion of which (or any external 

 violence given thereto) the perfect form of the circle might 

 be injured, without being immediately detected : 4° in thus 

 avoiding the obstructions which those arms might in some 

 cases, by their position, occasion in the observations of the 

 passage of a star before it entered the interior of the ring. 



In Plate III. fig. 4, I have given a drawing of this micro- 

 meter, on a BCald just double its real dimensions: the whole 

 instrument, in fact, not being larger than the broad inner 

 circle there delineated. By means of the outer glass circle, 

 the star can be seen, from the time that it enters the field of 

 view, until it reaches the steel circle; at which lime the ob- 

 server must be prepared to make the observation required. 

 But, previous to the application of this instrument to any 

 useful purposes, it will be necessary to determine with ac- 

 curacy the radius of the inner circle (which 1 shall denote 

 by /) in the following manner. Let the telescope be turned 

 towards any known star, situated as near to the equator as 

 possible; and as nearly in the direction of the meridian as 

 possible, in order to prevent the errors arising from refrac- 

 tion. In the diagram (lig. 4) I have presumed that the tele- 

 scope inverts; and thai the star makes its appearance in the 

 field of the telescope on the right-hand side at Q. If we 

 suppose the path of the star to be along the line QQ', then 

 will this line be one of the parallels of declination, and the 

 line \S, perpendicular thereto, one of the horary circles : 

 N being to the north and S to the south. A very few trials 

 will enable the observer to place the telescope in such a man- 

 ner that the star may pass exact/// through the centre of the 

 field of the circle. Note, by the clock, the time of the ingress 

 of the star, from behind the broad circle at () ; and also the 

 time of its egress at ()'. Let / denote the former, and l' the 

 lath r ; then will ( 



1 5 X — P- X cos 8 = ;• 



be the radius of the inner edge of the broad circle; and will 

 be b constant quantity to be used in all the subsequent com- 

 putations. In this equation I have assumed 8 equal to the de- 

 clination of the star observed; which, in this case, is the same 

 as the declination of the centre of the circle. 



* As iteel may be li;il>le to rust, particularly on sea voyages, probably 

 c-til would In- preferabli "ii uch occaaionR. 



Z 2 When 



