172 



ON THE SQUARE BAR MICROMETER. 



This correction is in practice exceedingly small. Thus, for a square with 

 20 minutes of arc diagonal, and p = 1°, the maximum value amounts to less 

 than 0".2. The correction in declination on account of position zero may there- 



ft 



fore, in general, be neglected. 



12. Determination of position zero. — The angle p, as defined in article 11, is 

 equivalent to the deviation of the diagonal lying on the parallel from the direction 

 of the true diurnal motion ; the angle p r is the deviation from the apparent motion ; 

 and Ap is the difference between the two, due to the refraction; so that 



p ==i p , -\- A p. 



(31) 



The value of Ap has been already given, equation (22) ; that of p' may be 



found by observation of a star over the central portions of the square, by not- 

 ing the transits not only over the sides of the square, but also over the pro- 

 longations of the bars forming the sides at the preceding and following angles. 

 Let 4 and z* 3 be the times of disappearance at the prolongation of the follow- 

 ing and preceding bars, respectively, the notation for the transits over the 



sides being unchanged, or t x and t 2 . Thus the order in which the four tran- 



* 



sits occur is t Q , t x , t 2 , t 3 , over the following prolongation, the following side, the 

 preceding side, and the preceding prolongation, respectively. Then it is obvious, 

 without further explanation, that the value of p' will be given by 



, _ i5cos8 r v-M> _ v+lil . 



P ~~ g sin 1" L 2 2 



(32) 



the upper or under sign to be used, according as the transit is north or south 

 of the centre. 



13. Determination of the diagonal of the square. — The transits of a star whose 



declination is only approximately known, observed as described in the preced 



ing article, will furnish the value of the diagonal. Thus the transits over the 



sides give, equation (27) 



— J- 2(? I (± jut <> cos 2 P 



9~ ± ^ + ft--'i)15cos8— sp 



and the transits over the prolongations, 





from the sum of which we derive 



9 = [(*« - k) + {k - «] -v- cos s ~ gf sin2 T> (33) 



