COMPARISON OF PLATINUM AND (US THERMOMK'I 57 



IP. The coil in question was then changed for some combination of those of lower 

 values giving the same (or very nearly the same) nominal resistance, and the outside 

 resistance remaining untouched, the contact-maker was again adjusted to equilibrium. 

 The distance between the first and second positions of the slider is a measure of the 

 ilitVerence between the two sets of coils, expressed in mean bridge-wire divisions. 

 The process being repeated for all the coils and the different combinations equivalent 

 to each, the results are collected into a set of equations of the following form* : 



A-B-C-D-E-F-G = a, 



&c. 



D E - G = a 



D-E -H-J-K-L =a 



Ac., tec. 



As previously mentioned, the scheme of coil-values adopted was such as to 

 permit of independent values for most of the coils being obtained in a single 

 standardization, the difference between these several values being a measure of the 

 accuracy obtained. 



For the standardization we adopted the same scheme in the four sets of deter- 

 minations of the coil- values taken at different times throughout the research. We 

 ascertained during the experiments, but too late to make any change, that the values 

 chosen for the higher coils were not such as were best adapted for giving a number of 

 inter-dependent relations, and on this account the control only extended upwards to 

 the fourth largest coil. 



We give below the residual errors obtained in one of the standardizations by 

 substitution of the values found by least squares for each coil in the respective 

 equations of condition, suppressing the first three coils for which the control was 

 absent, t 



* The method of forming these equations will be readily seen on reference to the table of coil-values 

 given previously on p. 45. 



t In the opinion of Dr. BENOIT, whose kindness in giving us his advice with regard to the methods 

 of standardization we hero gratefully acknowledge, the l>est way to obtain in one standardization the 

 requisite number of equations from which the relative values of such a system of coils can IKS satis- 

 furtorily determined, is to adopt a system similar to that employed for standard sets of weights. After 

 . .ireful consideration of these we think the following scheme for a set of fifteen coils would be almost an 

 i'lr.-d one. Without counting combinations only involving changes in coils, whose resistance is smali com- 

 ]Mii-d to the total in any comparison, we should have in this system several controls for each coil-value 



20' 20" 10' 10" 2' 2" 1' 



05" -05' -1 -2" -2' "5 1" 



The system of about 44 equations of condition to determine the unknowns, given by the different 

 direct comparisons, can cither bo divided into groups and solved thus, or may be solved as a whole, which, 

 if (\\\ ss' method IKS followed, can 1*> done without undue labour, as the coefficient* of the various terms 

 remain small whole numbers till near the end of the resolution. 

 VOL. i \< IV. A. I 



