﻿IN THE METHOD OF LEAST SQUARES. 207 



The mean value of if is - , the computed limit being- II < — . 

 Applying these factors to the original equations, -we obtain, — 



By the Method of Least Squares. I. 



= — 371.09 + 



= — 580104.00 + 7203.91 + 10834225.00 — 49.06 — 3229.77 — 198.64 — 143.05 

 = — 113.45— 0.09344— 49.06+ 0.71917 -f 1.13382+ 0.06400+ 0.26341 



= + 268.53— 2.28516— 3229.77+ 1.13382+ 12.00340— 0.37137— 0.11762 

 = + 94.26— 0.34664— 198.64+ 0.06400— 0.37137+ 2.28215— 0.36136 



= _ 31.81— 0.18194— 143.05+ 0.26341— 0.11762— 0.36136+ 5.62456 



Bj/ the Equivalent Factors. II. 



Coef. of Coef. of Coef. of Coef. of Coef. of Coef. of 



dL. dy. dTi. dip. da. di. 



= — 372.23 + 5.89945 + 7208.64 — 0.04729 — 2.22332 — 0.33807 — 0.19932 

 = — 662.04 + 7.85800 + 11830.88 — 0.20089 — 3.15658 — 0.16440 — 0.48494 

 = — 1051.81 — 0.02274 + 126.84 + 7.02511 + 10.51379 + 0.45680 + 3.10941 

 = + 137.76 — 1.90276 — 2453.82 + 1.15752 + 11.43969 — 0.33172 — 0.14026 

 = + 84.26 — 0.42389 — 250.17 + 0.05158 — 0.45069 + 2.27706 — 0.39471 

 = — 42.98 — 0.20005— 247.16 + 0.29S78 — 0.04721 — 0.30249 + 4.50959 



By the Equivalent Factors. III. 



Coef. of Coef. of Coef. of Coef. of Coef. of Coef. of 



t^-t- '')•• d7i. dtp. do.. di. 



= — 371.03 + 5.97864 + 7296.25 — 0.06706 — 2.33932 — 0.37876 — 0.08024 

 = — 560.48 + 7.21446 + 10853.11 — 0.05221 — 3.26575 — 0.20615 — 0.18982 

 = — 1061.36 — 1.13102 — 959.72 + 7.19887 + 11.91488 + 0.34031 + 3.07535 

 = + 251.17 — 2.11274— 2917.00+1.13986+11.78434 — 0.37820 + 0.08665 

 = + 97.46 — 0.29118— 75.36 + 0.07546— 0.22584 + 2.29772 — 0.39567 

 = — 54.37 — 0.12928 — 4.62 + 0.26533 — 0.24548 — 0.37541 + 5.56738 



In order to test the numerical values in these final equations by (33), the decimal 

 points for L, M, N, Sec, and for the coefficients of dy, should be changed three 

 places to the left. This being done, we have for II. 



2: (Pi, Qi, L,,M„ ) = + 57.87362, 



^ (S -) = + 57.87354. 



And for III. 



2" (Pi, Qi, i„ il/„ ) = + 57.56917, 



2'(S^) = + 57.56916. 



