448 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



4 Po + e = 

 — i Po + e = 



Ten equations were formed by substituting in equations I the vari- 

 ous values of p and the averages of all corresponding values of x' as 

 follows : 



.4311 based on 



.4155 



i p + e = .6442 



-£p + e = — .6272 



_* Po + e = — .8392 



p + e = 1.2808 



— p + e = -1.2635 



2 p + e = 2.5556 



—2 p + e = -2.5359 



4 p + e = 5.0953 



(A) 



(B) 



(C) 



(D) 



(E) 



(F) 



(G) 



(H) 



(I) 



(J) 



2 values of x' 



3 



6 

 21 



5 



10 

 21 



5 

 11 



4 



x' 

 x' 

 x' 

 x' 



x' 

 x' 



X' 



and these equations were solved in pairs for e and p (D), based on the 

 largest number of the best values of x' being combined with each of the 

 others for this purpose. The following nine values for e and p were 

 thus obtained, weighted in accordance with their relative importance, 

 and combined in a final average. It is the close accordance of these 

 values which seems to attest the reliability of the elements here 

 determined. 



D and A 



DandB 



DandC 



DandE 



DandF 



D and G 



DandH 



Dandl 



D and J 



e = .0078 

 e = .0079 

 e = .0085 

 e = .0088 

 e = .0088 

 e = .0091 

 e = .0094 

 e = .0090 

 e = .0086 



Weighted mean, cot /x = e = .0086 



p = 1.2700 

 Po = 1.2702 

 Po = 1.2714 

 Po = 1.2720 

 Po = 1.2720 

 p = 1.2726 

 Po = 1.2731 

 p = 1.2725 

 p = 1.2717 



= 1.2722 



fi = 89° 30' 28". 



In like manner the value of q was found by subsituting in equa- 

 tion II various values of q and the averages of corresponding values of 

 y', and then weighting and averaging the results. 



