1880.] 



J. F. Tennant — On Standard Weic/lits. 



57 



Of course this is a very uncertain estimation, but we have a good 

 many such equations, and the mean of the values may I think be taken as 

 tlie fairest estimate. If then n be the number of equations, I take 



% a 



p. e. of any one determination is 1*1955 — — 



The group of equations determining the P weights would give the probable 

 en'or from their i-esiduals ; but, there being only 12 equations to determine 10 

 quantities, I do not think this is so satisfactory as the above method ; and I 

 have used, for evaluating the errors in them, the weights of the results, 

 deduced as usual, combined with the f. e. of an equation derived as above. 

 Assuming that we may neglect the difference between the values of 

 and Eg in these differences, we have 41 values of 2 a ; and it does not seem 

 that there is any marked tendency to decrease with the weights : I therefore 

 take the mean of all and I get 

 !S ci 



= 463-53 R ». e. = 55416 K = 55 651 = e of Section VI 



11 



in which K is taken 0'100464 = 



Hence e^ is 3097-0 

 The probable error of any determination as of that of O.03 for in- 

 stance, depends : — 



1st on the amount arising from its own group. 



2nd jorobable error of the value assumed as known : in this case O. ^ 



3rd on the probable error of the rider which was employed in taking 

 the difference of weights in the pans. 



Lastly Oj itself has its probable error 0'000115 grains from the deter- 

 minations ; but there is also a portion dependent on P.qi, which is involved 

 in determining the difference between it and EI, the mean factor of P.^^ 

 being 0'0877. It is necessary, therefore, to start our evaluations with 

 values of the probable errors of Kj^ Eg and P.gi ; f'Ud, fortunately, these 

 are readily determined. 



Let E be the p. e. of P. ■^ from all sources except R 

 e as before the p. e. of one determination 

 € the^. e. of Rj 



It will be seen from the table of deduction of probable errors that the 

 value of E'-^ is 758'2 and that it involves nothing unknown. 

 Hence (^.e.Rj2 = 



= (1'003813)^ E^ + (0 000842)^ ^ 



= 704 + 0000007 + 3097'0 = 3801-0 



£ = 0-0000G2 = — ^3861 



