78 BULLETIN OF THE UNIVERSITY OF WISCONSIN 



similar pair of observations in the reversed position will 

 furnish the equation 



(' + n") r - 2fi = P + Q - (c - c") sec z 



which, with the last of equations (8), suffices for the de- 

 termination of * and ft- A large change in the inclination 

 of the axis, e. g. one which will give values of n' and n" 

 with altered sign, may be employed for the same 

 purpose. If the inclination of the wyes of the instru- 

 ment is not disturbed by the reversal, the level read- 

 ings will furnish directly a determination of the inequality 

 of pivots, and we shall have for the flexure 



/ = ft - i 



Formulae (8) become somewhat simplified when the star 

 observed is very near the meridian, but this advantage will 

 often be outweighed by the convenience of observing 

 Polaris at any part of its diurnal path. 



The application of the formulae is illustrated by the fol- 

 lowing observations of transits of Polaris over the microm- 

 eter thread of a large " broken " transit. Each observed 

 time and corresponding micrometer reading is the mean of 

 from five to seven observations made in quick succession. 

 Owing to disturbance of the mercury surface by wind, the 

 reflection observations were difficult and rather discordant. 

 Since the readings of the micrometer diminish in the di- 

 rection of motion of a star at upper collimation for Ocular 

 West, the collimation corresponding to any reading, 2i, of 

 the screw is given by the expression 



' H 



f - A- *V7 W ( -R 1 ^ + OcwZar W - 

 t - 57.57 (R - 15) _ Qcular E 



The reading of the screw when the thread h is~in the collima- 

 tion axis is assumed to be 15.000 rev. 



