110 



Professors Ayrton and Perry on 



the differential coefficient cuts the axis along which a is 

 measured at a point 0, for which a has the value 0*42 ; or, in 

 other words, a equal to 0*42 makes the differential coefficient 

 equal to nought, and hence is the value of a that makes the 

 heating -error a minimum. As a check on this we have drawn 

 the curve for the values of the heating-error for different 

 values of a (fig. 3), and from this also it is seen that the 



Fig. 3. 



0-19 



£ 0-188 



b£ 



a 



% °" 186 



H 



I 0-184 



o 



1 0-182 

 o 

 "-£ 



e. 0-18 



o 



u 



ft 



| 0-178 

 0-176 



0-3 0-35 0-4 0-45 

 Values of a. 



0-5 0-65 0- 



heating-error has a minimum when a equals 0*42. Hence it 

 follows that the law of increase of the sectional area of the 

 wire with the radius of the convolutions should in our Sole- 

 noid Voltmeter follow the law 



x — x rSr 



0-42 



in order that the error due to heating may be a minimum. 



Fig. 3 not only gives the value of a that makes the heating- 

 error a minimum, but it shows by how much the heating- 

 error is increased if a has a value greater or less than 0*42. 

 For example, if a equals 0, that is to say if the voltmeter be 

 all wound with wire of the same gauge, then, continuing the 

 curve backwards, we find that the heating-error is increased 

 by about one third. 



V. One plan of diminishing the heating-error with volt- 

 meters, and one that we have frequently employed, is to place 

 in the same circuit with the instrument a coil wound with 



