COMSTOCK STUDIES IN ASTRONOMY 65 



will carry the sun across the vertical thread of the instru- 

 ment, and the time at which one edge of the sun is just' 

 tangent to the thread should be noted to the nearest sec- 

 ond upon a watch. Let the instrument be now turned 

 upon the upper motion, keeping the lower motion clamped, 

 in the direction of the sun's movement, and the vernier set 

 at the next integral 10'. The time at which the sun's edge 

 again becomes tangent to the vertical thread should be 

 noted as before. If we represent by n the interval, in 

 seconds, between the two observed times, we shall have : 



dA _40 

 dt ~'~ n 



If desired, the transit may be set so that the second 

 vernier reading is 20', 30', etc. , greater than the first read- 

 ing, and we shall then have: 



dA 80 120 



jj = = etc. and 



dt n z n s 



n = \ n z = n 8 . . . . etc. 



This value of the differential coefficient enables us to 

 express equation (3) in a form adapted to field use, but 

 since for this purpose an error of even several seconds in 

 the value of d is of small consequence, we shall introduce 

 some modifications in the formula which will render it 

 more convenient without seriously impairing its accuracy. 



o 



The declination of the sun can never exceed 23.5, and we 

 therefore write in the place of sec d its mean value, 1.051. 

 We also put in place of the temperature r a mean value, 

 50 F., and assume for the barometric pressure 30 inches 

 of mercury. With these modifications equation (3) be- 

 comes : 



, _ [3.3854] Fain z tan z 

 n 



We may put the numerator of this fraction equal to 

 100 N and tabulate the values of N with the argument the 

 sun's altitude, h = 90 z, as follows: 



