230 HEXEY A. KOWLAKD 



the other, is constant. That is to say, the magnetizing force at any 

 point of one machine is equal to that at a similar point in the other 

 machine. In making a drawing of the machines., it would not matter 

 about the scale of dimensions; the force at a certain point is a certain 

 amount whatever the scale. 



Next consider what must be the current through the wire in the two 

 machines. There are the same numbers of turns of wire around the 

 magnet, and everything is the same except the dimensions. Consider 

 the current passing around the coil of a tangent galvanometer. If the 

 galvanometer grow, in order to produce the same effect at the centre 

 (and not only at the centre but at every point), the current must in- 

 crease in direct proportion to the radius of the coil. When the coil is 

 twice as large the current must be twice as large, in order to produce 

 the same force at every point. Thus, if there is no difference in the 

 material of the two machines, we have their currents in direct propor- 

 tion to their linear dimensions. Make a machine twice as large and 

 the current in the coils must be twice as great to produce the same 

 magneto-motive force. Of course the wire has increased in size; if 

 the machine has increased to twice its original size the cross-section 

 of the wire has increased four times. In other words, from that cause 

 the current per unit of area will vary inversely as the square of I, the 

 linear dimensions; and since we have found the current to vary directly 

 as I, in order to retain the same force in the field, by a combination of 

 the two results, it varies inversely, as I. Therefore, so far as the 

 magnets are concerned, the heating effect, which depends upon the 

 current per unit of cross-section, will decrease with the size, while the 

 surface will increase in proportion to the square of the size. There 

 will, therefore, be less danger of heating in a large magnet than in a 

 small magnet, but this is only with respect to the magnet. 



The resistance of any part of the machine varies, of course, directly 

 as the length of the wire, and inversely as the cross-section. The cross- 

 section varies as Z 2 , so that resistance varies inversely as I. Therefore 

 the larger the machine the less the resistance ; one machine being twice 

 as large as the other, the resistance will be half as great. This applies 

 not only to the work of the magnets, but to the work of the armature. 



I will now consider the electro-motive force. The electro-motive 

 force is proportional to the product of the current and the resistance, 

 or we may write E = RC. We have the current proportional to I, and 

 the resistance inversely proportional to I; therefore the electro-motive 

 force is constant. As we are running the machine, it turns out that 



