COMSTOCK STUDIES IN ASTRONOMY 



73 



corresponding reading of the middle of the bubble, and 

 these mean readings are given in the following table : 



Since the bubble readings which stand on the same line 

 in the second and fourth columns of the table are approxi- 

 mately equal, it is apparent that the corresponding circle 

 readings lie on opposite sides of A^ and equally distant 

 from it. ^0 may, therefore, be determined by taking the 

 mean of any pair of circle readings which stand in the 

 same line, and the angles A,, — A\ A" — A(„ which we shall 

 designate by r, may be found by taking half the difference 

 of corresponding circle readings. Values of r are given 

 in the fifth column of the table. 



The quantities 2b are the sums of the numbers in the 

 second and fourth columns, and their differences given in 

 the last column show that any irregularities which may 

 exist in the curvature of the level tube are very small, and 

 we may determine a mean value of d to be used over the 

 whole extent of the level tube. Since the values of '' dif- 

 fer so little from 90^ we may assume in equation (3) 



cos^p = 1 sin r.lo - i (A' + ^-i")] =1 



and taking the diiferences between the first and fourth, sec- 

 ond and fifth, third and sixth lines of the table, we shall 

 have A' — A" constantly equal to 30', and equation (3) be- 

 comes 



