794 Mr. A. Ferguson on the Construction and 



central plane of the rectangle is given by 



ticddx f 1 1 ) 



giving 



r P ( av^ + ^+i? 2 cy/<? + d?+p* 



where 2^o is the breadth of the strip and i Y ( = 2pi) is the total 

 current. 



If we suppose that p 2 is small compared with c 2 + d 2 , and 

 that the tangent may be taken equal to the angle, we have 



^ = Mi f V± - gj__ 1 



which is the expression already obtained for a single turn of 

 wire. 



In the instrument described, p = '5 cm., <f =30 cm., c = 21 

 (say 20) cm., and the error introduced into the value of $ by 

 neglecting p 2 is easily seen to be of the order of 1 part in 

 10,000. The error involved in writing 0=tan 6 in a coil of 

 the above dimensions is also of the same magnitude. 



§8. If the instrument is a " single-layer " galvanometer 

 a similar argument applies, giving 



p t d\/ c 2 + d 2 +p 2 c^c 2 +d 2 +p 2 y 



where N is the total number of turns in the coil, and 2p is 

 the over-all breadth of the winding. 



§ d. In a valuable paper on the Gray Dynamometer *, 

 Mr. E. B. Rosa has discussed several corrections and sources 

 of error in a galvanometer of the single-layer type, and 

 several of the conclusions apply, mutatis mutandis, to a 

 rectangular single- coil galvanometer. In particular, the 

 error introduced by taking the coil as equivalent to a 

 current-sheet is carefully discussed. Without entering into 

 further details, for reference to which Mr. Rosa's paper 

 should be consulted, we have seen that the error involved in 

 considering a current-sheet of breadth 1 cm. as equivalent 

 in magnetic effect to an infinitely thin wire is of the order 

 1 in 10,000 ; and if we consider the current-sheet as formed 



* Technical papers issued by the Bureau of Standards, Washington 

 (No. 28). 



