114 Professors Ayrton and Perry on 



preceding it is easy to see that if the maximum allowable 

 value of e is given, the minimum value of the volume that can 

 be employed is given from (22), and for this va ue of the 

 volume, the best value of y, that is the best ratio of the re- 

 sistance of the outside coil to that of the magnetizing coil of 

 the voltmeter, can be calculated from (21). 



VIII. To determine the sectional area to be given to the 

 inner wire of a voltmeter in terms of the maximum 'potential 

 difference so as to make the heating-error a minimum. — By ex- 

 periment ascertain the potential difference that is necessary 

 to produce the maximum deflection with any voltmeter of the 

 shape and size to be employed and wound according to the 



law 



x = x r a , 



where a has the value that makes the heating-error a mini- 

 mum, and which value will depend on the shape and size of 

 the instrument, and may be calculated for any special type 

 of voltmeter in the same way as it has been calculated in 

 what precedes for the Long-Range Magnifying Spring- 

 instrument. Then if it is desired to wind another instru- 

 ment, of the same volume and shape, so that it will have 

 its maximum deflection given by P 2 volts, it follows, since 

 the heating will, as already proved, be the same in the two 

 instruments for their maximum deflections, that their re- 

 sistances must be proportional to the squares of P a and P 2 , 

 and hence, from (5), since the same law of winding is followed, 

 that the cross section of the innermost layer of wire in the 

 two instruments must be inversely proportional to P x and P 2 . 

 To have the same heating-error in the two cases, with out- 

 side resistance-coils of the same shape and size, it follows 

 from (21) that it is necessary to use the same ratio between 

 the resistance of the outside coil and the resistance of the 

 magnetizing coil. To have a less or greater heating-error 

 in the second than in the first case for the maximum deflec- 

 tion, it is only necessary to determine from (22) (the constants 

 of which have been deduced by experiment with the first 

 instrument) the greater or less volume V of the outside re- 

 sistance-coil needed with the second instrument, and calculate 

 the ratio y of the resistance of the outside coil to that o£ the 

 magnetizing coil by (21) . 



IX. As to the second error, arising from the sensibility of 

 the instrument being temporarily varied by external magnetic 

 disturbance referred to in § I. This can be overcome in three 

 distinct ways : by 



