foote: an optical ammeter 



81 



temperature and are accordingly matched for the current cor- 

 responding to P. The condition for a match thus defines a 

 standard current which can be adjusted to any desired value by 

 the use of a suitable shunt. The match is effected by use of an 

 adjustable rheostat in series with the two lamps. The precision 

 obtainable is much less than that possible with the first method 

 described and depends upon the slopes of the two curves of 

 figure 2 at the point of intersection. Near the point P these 

 curves can be assumed to be straight lines. Whence we have: 



(6) 

 (7) 



i = a -\- ht for lamp C 

 i' = a' + h't' for lamp F 



From (6) and (7) 



(8) 



8 it — t ) = _ — — - = 8i, smce i =i 



^ b b' bb' 



when the lamps are connected in series. Hence the precision 

 with which the lamps can be matched (i. e., when t — t' = {)) 

 depends upon the relative slopes of the temperature-current 

 curves for the two lamps. As seen from equation (8) it is of 

 advantage to have the slopes of the two curves at P differ con- 

 siderably. There would be no accuracy whatever if the slopes 

 were nearly the same. Using apparatus assembled as shown 

 in figure 1, but without paying special attention to the procuring 

 of lamps having widely different constants, b, the readings given 

 in table 1 were made by four different observers, one of whom 

 was unskilled in photometric matching. The accuracy is only 

 fairly satisfactory, but undoubtedly could be improved by the 

 proper selection of lamps. 



TABLE 1 



