722 INDUSTRIAL APPLICATIONS. 



and it has the value 



b(2a + b) + 2b / Ja(a + b) a 



b 



tfHj 



The efficiency is nearer unity the smaller is the ratio of the 

 resistances a and b. Contrary to what takes place with the entire 



current, we should take b>a\ if we assume that the ratio - is 



b 



extremely small, we have, as approximate value, 



T 



and u m = 



Given the value of u m , we deduce from it, for the ratio of the 

 resistances a and ^, 



a 



1273. DIMENSIONS OF MACHINES. Let us consider two machines 

 which are entirely similar, the number of windings being the same on 

 the inductor and on the induced body, and the dimensions of the 

 second being /A times that of the first. 



Let us suppose that the machines are dynamos working with the 

 entire current. A first practical condition of a mechanical kind, 

 is that the absolute velocity of the ring at its circumference, whatever 

 be the diameter shall not exceed a given value. As we endeavour 

 to attain the greatest velocity in each case, the number n' of turns 



of the second machine will then be equal to - . 



J* 



On the other hand, the magnetisation of the armatures is raised 

 to a value near the maximum, or at any rate should be the same in 

 each case. For the same current, the field of the wires in the second 

 machine, other things being equal, is p times feebler; the intensity 

 I' should then be equal to /*!. 



As the action of a magnet is proportional to its volume, and is 

 inversely as the cube of the distance, the fields of two magnets which 

 are similar, and of the same magnetisation, are equal to each other 



