188 





Dr 



Norman Campbell on the 













E 



XAMPLE 2. 













x — 



by-\-cz-\-m. 

 L.S. 



Z.S. 







X. 



y- 



z. 



r~ >* 



r~ A 













vxio 4 . ^xio s . 



uXlO 4 . v 2 Xl0 8 



(1)1 



(2) \ 



8-1950 











- 1 1 



+ 25 



G25 



3-2299 



01 



001 



--18 324 



-14 



196 



(3) ] 



3-2532 



0-2 



0-04 



4-2 4 



-11 



121 



(4) | 



3-2611 



0-3 



009 



+21 441 



- J 



1 



(5) 



32516 



0-4 



0-16 



+ 19 361 



- 6 



36 



(6) 1 



3-2282 



0-5 



025 



+ 31 961 



+ 8 



64 



(7)] 

 (8) | 



3-1807 



0-6 



0-36 



-44 1936 



-59 



3481 



3-1266 



0-7 



0-49 



-33 1089 



-33 



1089 



(9) j" 

 (10) J 



3-0594 



0-8 



064 







+22 



484 



2-9759 



0-9 



0-81 



+ 24 576 



+72 



5184 











2i»+ 97 2v 2 5693 



2u + 127 2v 2 



11261 











•Ev- 96 



2v- 129 





(L.S.) 31*761600 = 10-00m + 4-500# + 2-8500* 



14-089570 = 4-50m + 2-850?/ 4 2*02502- 



8-828813= 2-85m + 2-025y+ 1*5333* 



m = 3-1 951 + 0-001-5, b = 0-4425 + 0-0077, c = -0-7653 ±0-0081. 



(Z.S.) 9-6781 = 3m +0% +0-05.; 



9*7409 = 3m +l'2y + 0*50* 



12-3426 = 4m + 3% + 2*30r 



m = 3-1925 + 0-0034, £ = 0*4678 + 0*0072, c = -0*7960 + 0-0081. 



From eqns. (1-5) t m = 3*21955, b — 0*3652, c = -0'7079. 

 (6-10) m = 3-20265, b = 0*2670, c- -0*3065. 



This discrepancy is, o£ course, due to the fact that it is the 

 sums of the squares of the residuals of loga?, and not of x, 

 that have been made a minimum : this process, though 

 almost always adopted, is not justifiable by the theory on 

 which the method is based. On the other hand, it is 

 legitimate to apply the method of Z.S. to the logarithms ; 

 for, so long as the errors are small, the solution which 

 makes the sum of the errors of x zero will also make 

 the sum of the errors of f(x) zero, whatever may be the 

 function / (so long as it has no singular points in the 

 neighbourhood). Here is another advantage of the method 

 of Z.S. It can be applied directly to an equation ihat 

 is not linear, so long as that equation can be reduced to 



