Errors of a Straight Scale. 



343 



Weight. 



n 



Max. 



Min. 



3 



2-15 



2-J5 



4 



2-77 



2*68 



5 



3-35 



3-19 



6 



3-99 



3-69 



lO 



6-49 



5-74 



It will be seen that these weights are nearly the same as 

 those obtained in Gill's own method of reduction. 



Table II. 













Time used 









Gill Method. 



Method 1. 



Max. Weight. 



No. of Obs- 



(arbitrary) 



Min.Wt 



.xlO 2 



n 



Weight. 



Weight. 



Min. Weight. 



Gill 



addit. 



unit). 



Time used. 





Max. 



Min. 



Max. 



Min. 

 3-44 



Gill 



1 



1 



Gill 



1 

 21-5 



Gill 



1 



3 



2-03 



202 



3-45 



1-00 



1-00 



14 



30 



14 



14-3 



16-0 



4 



2-49 



2-44 



4-13 



4-10 



1-02 



1-01 



23 



42 



23 



33-5 



10-5 



12-2 



5 



300 



2-95 



4-93 



4-88 



1-02 



1-01 



34 



54 



34 



47-5 



8-5 



10-2 



6 



3-47 



3-40 



5-65 5-62 



1-02 



1-01 



47 



66 



47 



63-5 



7-1 



8-8 



7 



4-08 



4-00 



6-62i 6-58! 1-02 



1-01 



62 



78 



62 



81-5 



6 4 



8-1 



8 



4-39 



431 



7-091 7-04 "1-02 



1-01 



79 



90 



79 



101-5 



5-6 



6-9 



9 



5-15 



5-05 



8-33 826i 1'02 



1-01 



98 



102 



98 



123-5 



5-1 



6-7 



10 



5-49 



541 



8*93! 8 85; 1 02 



101 



119 



114 



119 



147-5 



4-3 



6-0 



15 



8-06 



7-94 



12-90 12-82; V02 



1-01 



254 



174 



254 



297-5 



3-2 



4-3 



20 



10-53 



10-42 



16-86 16-781 1-01 



1-01 



439 



234 



439 



497-5 



2-4 



3-4 



The last two columns of Table II bring out very clearly the 

 advantage of method 1 over Gill's. It may be objected that 

 these columns depend upon the somewhat arbitrary assumption 

 that the additional observations require only one-fourth the 

 time needed for the first ones. But it should be noted that 

 even without this assumption, these columns would show an 

 increasing advantage for method 1, as soon as n becomes larger 

 than 10 or 12. The same would be true even for the smaller 



values of n if we were to put — equal to 2 or 3 instead of 4. 



But the assumption seems fully justified by the experience 

 gained by Dr. Gill and others in investigating the scales of the 

 Cape helio meter. 



5. The above method 1 leaves very little to be desired on the 

 score of variation in the weight with which the several 

 division errors are determined. Consequently the investiga- 

 tion of a method which will make these weights all equal is of 

 interest chiefly from the theoretical point of view. Still an 

 occasion might possibly arise when it would be worth while to 

 take the extra trouble necessary to bring about this equality of 

 weights. This can be done by the following method, which 

 we will call method 2. Let us resume equation (5) : 



