97 



3607 



98 



ind further choosing 1.2700 as the logarithm of the unit of error, 

 jquations of condition (logarithmic coefficients) : 



9.8819 t -H 9.9522,, ;-+- 8.9142/ -f- 



The coefficients are logarithmic and the last column contains the logarithm of the square root of the weights 

 jf the ecjuations of condition. Ap|)lying these weights and introducing new unknowns defined by the relations 



X = [0.4900] dx / = [0.5200] d^ I 



y = [1.1600] d.')/;, u = [0.5200] d/ (A) 



z = [2.8000] (I// TO = [0.4200J d/' I 



there resulted the following weighted homogeneous 



■) 

 2) 

 3) 

 4) 

 5) 

 6) 

 7) 

 8) 



9) 

 .0) 



'•) 

 .2) 



'3) 



8748 ,v 



9912 



8728 



9097 



7961 



4862 



6918 



4979 

 6408 

 6466 

 6100 



5°34 

 4218 



9-99'5 

 9 8477 

 9.8764 



9 7476 

 9.3761 



95578 

 9.5010 

 9.6349 

 9-6113 

 9 5657 

 94423 

 9 2732 



■+■ 9-9929n 

 -h 9 6405,, 



-t- 9-5979n 

 -I- 9.3099,, 

 -+- 8.6056 

 -*- 9. 1 086 



H- 9-55 '6,, 

 -t- 9.6048,, 



-I- 9-33041. 

 -h 9-'944m 

 -+- 8.8494,, 

 -+- 8.9506 



-I- 9.6047 

 -+- 9.8809 

 -i- 9.9706 

 -+- 9.9290 



-+- 9-7577 

 -+- 9. 99 I 2 

 + 8.7783 

 -^ 9-3504 



H- 9.6998 

 -t- 9.7 lOI 

 -+- 9.6679 

 -+- 97325 



5 2 26n n 



632911 



4685,, 



4876,, 



3376,, 



8553.1 



9822n 



91 17 



9996 



8884 



8238 



6687 



3685 



3962n W 



58400 



5746n 

 6295n 



5409n I 



26o7n 



4626,, 



7853 



9507 



9945 



9657 



8720 



8489 



-9773.1 

 • 9926,, 

 •4553n 

 .1560 



2583 

 .4230 

 .8697 

 •4558n 

 -75>8 

 .8279 



8137 

 5643 

 .7027 



The usual least square method gave as normal equations (numerical coeffic 



ients) : 



•) 

 2) 

 3) 

 4) 

 5) 

 6) 



4.2893.V 



40257 



2.7810 



3-8095 



0.1734 



0-2153 



-I- 4.o257.r 

 ■+- 3.8040 

 - 2.7452 

 ■+- 3.4000 

 -I- 0.1372 

 ■+- o. I 669 



2 7452 

 2-5497 

 1. 4801 

 0.0256 

 0.0375 



-+- 3.8095/- 

 -+- 3.4000 ■ 

 — 1. 4801 ■ 



-1-4-7055 ■ 

 -+- 0.3146 

 -+- 0.3909 



0.1734 n 

 0.1372 

 0.0256 

 0.3146 



3 5163 

 3.8867 



-t- 0.2153 ^"^^ 

 -+- 0.1669 

 -*- 0.0375 

 -+- 0.3909 

 -1-3.8867 

 -I- 4.82 ro 



-t- 0.2722 

 -h 0.5226 



- I 6937 



- '-7799 



- 1-6398 



- 2.0085 



The similarity of the coefficients of the first and second ! be indeterminate. Rewriting the normals so that these un- 



md of the fifth and sixth equations indicated that one or knowns appeared last in the solution the following elimination 



nore of the unknowns would be affected with considerable ' equations were found i^logarithmic coefificients) : 

 incertainty, and a preliminary solution showed .v and r to 







3) 

 4) 



0.40649c ■+- 0.17030,,/ 

 0.58504 



8.40909 // 

 9 51786 

 0-54255 



8.57461 

 9.61563 



0.58557 

 9.71950 



o. 44420,1 .V 



o.34«45 

 8.12710 



7-77815 



o.43858n>' 

 0.25682 

 8.00432 

 7-389'7 



-+- 0.22884^ = o 

 -H 0.44l40n = O 

 -K o. 141790 = o 

 -^- 9.i9493n = o 



By successive substitution 7i', u , t and ; were expressed as functions of .v and v through (log. coefficients): 



w = 8.05865,, .V -H 7.66967n.i' -t- 9-47543 

 11= 7-94448 -+-7.35411 -4-8.82905 

 /= 9.75604,, -1-9.671500 -f- 9.83286 

 z = 9.88069 -(- g. 90540 -H 0.02295 



(B) 



ind substituting these into the original homogeneous weighted equations of condition the following series was found for 

 he determination of v and r (logarithmic coefficients) : 1 



