518 Prof. F. Y. fidceworth on the L 



©' 



aw 



Although Hie above discrepancies may in some cases appear 

 large, it must, be remembered thai we nave here the whole pf 

 fche error in each case, and that Buch errors as Don-uniform 

 bore, zero chances (both temporary and permanent), unequal 

 graduation, changes of condition', sticking, &c. are totally 

 absent, while the experimental difficulties of the air-thermo- 

 meter are avoided. 



Thus we conclude, final a platinum-thermometer — especially 

 of Ihe II pattern* — would be a convenient instrument for the 

 determination of very low temperatures where an error of 

 o, 5 is Immaterial ; 'and that Further light on platinum- 

 tlierinomelry only strengthens our belief in its correctness 



over the range of —273° to +700°. 



Sidney College, Cambridge* 

 October lsjw. 



LX1. The Lair of Error and Correlated Averages. 

 Ih/ Professor P. Y. EdGBWOITH, M.A., D.C.L. 



[Continued from p. 488. | 



IV. / lONTINUINGtheinvestigationoftheconditionsunder 



V^ which the law of error is fulfilled, we come now to the 



genera] case in which,every member of a group is any function 



of a number of demerits, each, as before, oscillating, according 



to any independent lajw o\' frequency, through a range which 



is relatively small. Let the function be F(#ij « 2 , &c, ./•„). 

 Put, for .r,, \, + fi ; i'^v ./••_., *a + i& + &c.t, where Xi, x 8 , &c. 

 are the average values of trie Corresponding variables. By 



expansion— putting I r ,\ FY, <fec. For . K, , F, fas. — we have 



asc\ a,r.-, 



forming a Linear function of ?i, £j, &c. ; if the terms containing 

 higher powers of £,, f, may be neglected. This may, in 

 general, be done, provided that F(d?i, ,r i% &lc.) is free from 



* A full description of the construction of 11 will be found in the 

 British Association Report on Electrical Standards, L890, reprinted in 

 the ' Electrical Review, No. 670, p. •'>»>•*'> ; and a short account on p. 16a, 

 Phil. Trans. A. vol. clwxii. 1801. 



t There is some inelegance in using { to denote here a deviation which 



LS of the Older , and in a former passage a deviation which is o[' the 



1 " 



order . (ante, p. 431). l>ut as the subject involves three orders of 



magnitude, it is not vi i r_v easy to distinguish them by differences of type. 



