





A djusi 



ment of Observations 







189 











Example 



3. 



















x = myi 





















logy. 



L.S. 





Z.S. 









U- 



log X. 



yxlO 4 . v- 



XlO 8 . 



VXlOl 



V 



j xio 8 



(1)1 



1-731 



0-1144 



0-23830 



-0-94157 



-f 7 



49 



+ 9 





81 



(2) 



1-853 



01312 



0-26788 



-0-88207 



-38 



1441 



-37 





1369 



(3) 



> 1-984 



01445 



0-29754 



-0-84013 



+ 18 



324 



4-19 





361 



(4) 



2081 



0-1579 



0-31827 



-0-80162 



4- 5 



25 



+ 5 





25 



®L 



2-171 



0-1701 



0-33666 



-076930 



+ 4 



16 



4- 3 





9 



(7) 



2-258 



0-1813 



035372 



-0-74160 



4-15 



225 



+15 





225 



2-326 



0-1925 



036661 



-0-71557 



— 5 



25 



- 6 





36 



(8) 



2-397 



2-460 



0-2026 



0-37967 



-0-69336 



- 1 



1 



— 2 





4 



(9). 



0-2123 



039094 



-0-67305 



- 5 



25 



- 7 





49 













2v+ 49 2v 2 



2134 



2y+ 51 



2v 



'2159 













2v- 49 





2w_ 52 







(L.S.) 



(Z.S.) 



2-9496 = 9-0000 loo- m 



0583Z/ 



-2-2758 =-7-0583 log »i + 5-6008 ft 

 m = 5-98 ±0-050, b = 0-5727+0-0045. 



1-45865 = 5 loo- m -4*23471 b 

 1-49094 = 4 log m- 2-82358 b 



m = 6-004-0-025, b = 0'5743±0-0023. 



From eqns. (1-5) 

 (6-9) 



m = 6-07, 

 m = 5'7o, 



b = 0-580. 

 b = 0-546. 



the linear form by a change o£ variable ; whereas strictly 

 the method o£ L.S. ought not to be so applied. If the 

 method of L.S. is adopted the process of successive approxi- 

 mation, which has to be used when the equation cannot be 

 reduced to the linear form by change of variable, ought 

 always to be applied to a non-linear equation, even when it 

 can be so reduced. 



On the other hand, in Example 2 there is a difference 

 between the values of b and c deduced by the two methods 

 which exceeds the probable error of either method. But an 

 examination of the residuals at once shows the explanation. 

 The equation to which the observations are to be fitted 

 is empirical; the residuals show a systematic variation 

 which indicates that the formula is not strictly true. At 

 the bottom of the table are given the values of b, c, m 

 calculated by L.S. first from the first 5 equations and 



