5G 



J. F. Tennant — On Standard Weights. 



[No. 1, 



Bj weighing the riders against the nearly equal weight P. i I have 

 = P., + 003813 Pt, Diff. 425 

 = P., + 000375 „ 600 



Subotituting successively for the value of E.^, of P. j, and of 



we get 



grs. 



R^ = 0.1003814 + 000847 R^ s 0-100466 grs. ^. e. = 0-000062 

 R^ = 100000 + 001217 R^ = 0-100122 „ „ = 000062 

 Also— P., = P.Q, + P. 3 + 0-089038 R^ Diff. 825 

 P.„, ^ P.0 3 + P.„, + 0-104750 „ „ 1550 



P.,3 ^ P.„, + 0-105075 „ „ 900 



P.Q, = 0-099438 „ „ 137 



Whence P.^g = f P.^ — 059467 R, = 0-060769 e. = 0-0000i7 

 P.„3 = i P., — 0-029571 „ =0030400 „ 000034 

 P.Q, si P., — 0-134646 Ri = 0019S81 „ 000047 

 P.^^ = 0.099438,, = 009956 „ 0-000056 



Section VIII. — Determination of the prohahle errors of the values of the 



O and P sets. 



In Section VI, I have shown that if the probable error of the constant 

 terms in the equations of a group be known, we can determine the probable 

 errors of the determinations in the group, so far as they depend on it : and 

 we have now to consider what may be taken as the probable error of one 

 determination. 



Each coefficient of R is derived in the preceding work from two 

 determinations which rarely agree. The differences are noted in terms 

 of the 6th decimal place of the coefficient. If we were certain that the 

 true values of the constants lay between the determinations, then, calling 



2 a 



the difference of the two 2a, we should have = the mean oferroi-s 



n 



and p. e. of an equation = e = 0'8454 ; but this value is clearly too 



small ; because, if the occurrence of positive and negative errors be equally 

 probable, then there is an even chance that a fourth of the values of 2a 

 will be the difference and not the sum of the two actual errors. 

 I prefer therefore to use the formula 



mean of errors = — ^ : m being the number of complete 



\/ m (ill — 1) 



comparisons 



S V 



and probable error = 0-8454 — — 



V 711 {ill — 1) 



a]ipl}'ing this to any one determination we shall have its probable error 



=; 0-8454 ^ = 0-8454 = 1-1955 a 

 ^2%L 



