OF AETS AND SCIENCES. 397 



Coinparison of 2 Inches of Scale B with the first 2 Inches of R-^'^. 



From observations of July 21, 



J? + 1.9 div. = first 2 inches of R^\. 



From observations of July 22, 



5+1.8 div. = first 2 inches of i?/^ 



The following relations for x and y were found, x being expressed 

 in terms of the first foot of R.^- divided by 4, and y in terms of line 37 

 of the scale B. 



X 



July 15 3 inches +13.2 div. 



Means 3 inches +16.3 div. = 3.000321 inches. +3.3 div. = .000065 incli. 



Expressed in terms of Y, x becomes 3.000327 inches, 



and X + y expressed in the same unit becomes 3.000392 " 



This quantity is now to be corrected by the amount of the error of 

 line 37 of the third half-inch of the scale B. We have, 



2 inches ol B -\- [1.9 + 0.6 — 0.2] div. = j^ i"- 



The correction to line 37 of the third inch of scale B is, therefore, 



2 inches — [l.7 + [1.8 — 1.0 + 0.2]] div. = ^^ 7". 



Expressed in terms of 7, we have, finally, 



x^y=z 3.370339 inches. 



From the observations of 1882, 



a; 4-2/ = 3.370319 inches. 



