Constants of a Rectanyular Galoanometer. 797 



Solving for X, and taking the square root, we get 



where the value of the function <£ is quite determinate. 

 With this relation between / and c, the lowest power of x 

 which appears in the expression for <^ P is x\ giving a very 

 uniform field in the neighbourhood of 0. 



§ 12. A very important consideration is the error intro- 

 duced through irregularities in the winding of the coils — an 

 error which, if uncompensated, may often be of sufficient 

 magnitude, however carefully the coils be wound, to 

 render quite unreliable the results obtained by a single- 

 layer galvanometer. 



For this reason, any such galvanometer should be cali- 

 brated according to the method recommended by Mr. E. B. 

 Rosa *. The method consists in dividing up the single layer 

 into sets of 5, 10, 20, or 50 turns, according to the total 

 number of turns in the layer and the fineness of the wire, 

 measuring carefully the dimensions of each set of turns and 

 calculating the magnetic force- at the centre of the coil due 

 to unit current in each set, in turn. The sum of these 

 quantities then gives the galvanometer constant. 



If the single layer be wound on a square frame of side 2c, 

 the expression for the force at the centre due to a turn whose 

 plane is at a perpendicular distance x from the centre is, by 

 equation (ii.), 



Ditferentiating with respect to x, and dividing the result 

 by «^, we obtain 



d$ x(5c 2 + 3x 2 )dx 



. . . (m.) 



& (c 2 + ^ 2 )(2c 2 + ^ 2 )' * * " 



giving the percentage error introduced into the estimation 

 of $ \i the turn considered be displaced by an amount dx 

 from its proper position. The percentage error introduced, 

 as is readily seen from equation (iii.), is zero for a small dis- 

 placement of the central turn, and steadily increases with x. 

 Thus, for a square " coil " of 40 cm. side, if we assume the 

 single layer to be wound over a length of 10 cm. perpen- 

 dicular to the plane of the coil, the percentage error 

 introduced by a displacement of, say, '01 cm. in the last 



* Kosa, /. e. 



