Sine Galvanometer 



393 



difference E through the testing galvanometer, and the difference {RJ e)=D 

 determined. J can then be calculated from the relation J = (zkD+e)/R. 



The first method has the advantage of making it necessary to standardize only the 

 standard resistance coil and the standard cell. It is not flexible, as all Weston cells 

 have nearly the same e. m. f., and thus only one current can be measured with a given 

 standard coil. A standard resistance coil can be constructed with a number of voltage 

 terminals, however, the resistances between their points of attachment being such as 

 to produce balances with a number of fixed currents. 



The second method has the advantage of great flexibility, but requires in addition 

 the complete standardization of the potentiometer, which contains many coils. 



The third method makes it possible to measure a greater range of currents with a 

 given standard resistance coil, and also makes it possible when D is less than E to reduce 

 the error arising from imperfect standardization of the potentiometer. At the same 

 time it introduces a second time whatever error there may be in the determination 

 of e. In the practice of this method it is unnecessary to have available a second standard 

 cell, as by a simple double-pole double-throw switch the cell by which the potentiometer 

 current is standardized may be disconnected from its usual place and inserted in the 

 proper place for the measurement of the unknown e. m. f., as indicated above. 



22. Equation (17) gives by logarithmic differentiation 



ah aG aj , e . e , , . e 



= cot - A \- (cot 



H G ^ J 2 2^ 2 



m . . (-/ y) 



;) A 5 



Xsin 



6 



(18) 



for the error in H due to all the other errors involved. 



9 



In Table III the cotangent and the reciprocal of the sine of are given as functions 



Of) o 



of 2 Since & k, the error in , need not exceed 1" or 2," or 5 or 10 x 10 s radian, and 



the error in the scale readings 



,a(^), 



need not exceed 10" (at the scale distance 



34.4 cm. when 1 small division = 100"), or 5 XlO" 5 radian, it is clear that at large angles, 

 which should be used when great precision is required, the errors comprised in the last 

 two terms of (18) can be neglected entirely, if H is desired only to 1 part in 10*. 



The error AJ/J in determining the current in Table in. 



absolute electromagnetic units with the aid of a stand- 

 ard resistance and a Weston cell need not, according 

 to the experience of the National Physical Laboratory 

 and the National Bureau of Standards, exceed about 2 

 or 3 X10 5 . 1 



The error AG/G in determining the coil constant 

 we have already seen to be probably less than 1 part 

 in 30,000. 



With the instrument as constructed it should 

 therefore be possible to measure the horizontal in- 

 tensity with an error less than 1 part in 10,000. 



23. Early in June, after preliminary tests hi the 

 Experiment Building, the sine galvanometer, to- 

 gether with a Weston cell, a 10-ohm standard resist- 

 ance coil by Wolff, a standard potentiometer, ulso by 



1 See Rosa, Dorsey, and Miller, Bulletin of the Bureau of Standards, vol. 8, 1912, pp. 269, 362. 



