COMSTOCK STUDIES IN ASTRONOMY 75 



IV. THE SIMULTANEOUS DETERMINATION OF FLEXURE, 



INEQUALITY OF PIVOTS, AND VALUE OF A LEVEL 



DIVISION FOR A "BROKEN" TRANSIT. 



In a "broken" transit, i. e. one in which the rays of 

 light are bent at right angles by a reflecting prism placed 

 in the axis, it is well known that the bending of the axis 

 under the weight which it has to carry produces an effect 

 upon the observed times of transit of a star, which may be 

 represented by the expression f.cos z sec S, where / is a con- 

 stant peculiar to each instrument, and z and 8 denote the 

 zenith distance and declination of the star. Since this ex- 

 pression has the same algebraic form as the corrections 

 for inclination of the axis, and for inequality of pivots, 

 they may all be united into a single term: 



(V 4- *+/) cos z sec d 



where (i+f) is a constant correction which must be ap- 

 plied to the value of &' directly determined with the spirit 

 level. If i +/ is positive for Ocular West it will be nega- 

 tive for Ocular East, and the sign is, therefore, prefixed 

 to it. Since it is not necessary in the use of a broken 

 transit to separate the constant correction i+f into its 

 constituent parts, it will for the present be treated as a 

 single unknown quantity whose value /? is to be determined 

 in connection with T, the angular value of a half division 

 of the level used for measuring &. In a straight transit / 

 is zero, but i has usually an appreciable value and the cor- 

 rection ft must, therefore, be determined, and may be con- 

 veniently determined by the method here developed for a 

 broken transit. 



If from the general equation of the transit instrument 1 

 sin c 4- sin 8 sin n cos d cos n sin (r m] = (1) 



i Chauvenet, Spherical and Practical Astronomy, Vol. II, 123. 



