



Adjustment of Observations. 





187 









Example 1. 















x = by + m. 















L.S. 



A 





Z.S 

 , * 









y- 



r^ 



"""> 



r 











v X 10 5 . 



^ 2 xio 8 . 



UX105. 



y'XlO 8 



(1)1 



3921469 



0-9688402 



+ 318 



1011 



+324 



1050 



(2) 



39-20335 



0-9289304 



- 9 



1 



- 4 







.(3) 



39-19519 



0-8904120 



- 49 



24 



- 42 



18 



(4) 



> 39-17456 



0-7929544 



-281 



790 



-277 



767 



(5) 



39-13929 



0-6127966 



- 26 



7 



- 23 



5 



(6) 



39-10168 



0-4254385 



+ 1 







+ 1 







(7) j 



3903510 



0-0948286 



+ 25 



6 



+ 23 



5 



(8)" 



39-02425 



0-0505201 



-164 



269 



-167 



279 



(9) 



39-01884 



00341473 



-374 



1399 



-377 



1421 



(10) 



39-01997 



0-0218023 



- 12 



1 



- 14 



2 . 



(11) 



* 3902410 



0-0190338 



+457 



2088 



+454 



2oeT 



(12) 



39-01214 



0-0019464 



-393 



1544 



-396 



1568 



(13)j 



39-02074 



00000515 



+ 505 



2550 



+ 503 



2530 









2v + 1306 2 



; 2 9689 



2v + 1305 2i 



2 9706 









2v_ 1308 





2t>_ 1300 





(L.S.) 508-18390 = 13-000000 »i + 4-848702 6 

 189-94441 = 4-848702m + 3-804394 6* 



m = 39-01568 ± 0*00077, b = 0-20213 ± 0-00142. 



(Z.S.) 274-06386= 1m 

 234-12004= 6m 



39-01571 + 0-00089, b 



m 



+ 47212016 

 + 0-1275016 



0-20204 + 0-00184. 



From eqns. (1-7) m = 39*01530 b = 0*20265 

 „ (8-13) m = 38-9751 b = 0-21118 



t This equation is misprinted in Merriman. 



In Examples 1 and 3 there is no material difference 

 between the results obtained by the two methods ; they 

 agree well within the probable error. The probable error 

 in Example 3 is actually less for the result by Z.S. than 

 for that by L.S. Indeed in that example the comparison 

 does not appear as favourable to Z.S as it ought to be. For 

 the residuals are calculated for log x : strictly they should 

 be calculated for x. If they are so calculated, %v 2 is slightly 

 less for the result by Z.S. than for that by L.S. : the Least 

 Square method does not actually produce the least squares. 



