724 INDUSTRIAL APPLICATIONS. 



The volume and the weight of a machine of given form are pro- 



W . 



portional to the cube of its dimensions. As the ratio is nearly 



constant, it follows that the quotient of the energy expended by the 

 volume that is to say, the work for unit volume is greater as the 

 machine is smaller. Yet as the cost of the machine diminishes less 

 rapidly than its total weight, there is no advantage in reducing the 

 dimensions too much. Hence we should choose a form such that 

 the price of the machine varies as the square of the dimensions for 

 slight changes in the dimensions. 



It follows from these remarks that if a particular machine gives 

 excellent results, it does not follow that the same proportions should 

 be maintained for another of larger dimensions. It is better to 

 change the general form, and multiply the parts, by referring them 

 to dimensions of the same order as those of the corresponding 

 organs of the former machine. 



If the inductors are excited by an extraneous current, the energy 

 necessary for magnetisation is proportional to //, that is, to the simple 

 dimensions. The resistance of the coil becomes //. times less, and 

 the electromotive force //. times as great. For the same external re- 

 sistance, the ratio of the currents will be 



I E a 



- + a l + X 



This ratio is equal to p if the resistance x is very great compared 

 with that of the machine. 



1274. GRAPHICAL PROPERTIES OF THE CHARACTERISTICS. 

 Instead of calculating the effects of machines by the algebraic 

 expression of </>(!), M. Marcel Deprez* determines them by graphical 

 constructions on the characteristic curve that is to say, on the ex- 

 perimental curve which represents this function. With Frohlich's 

 formula this curve is a hyperbola, but the results thus calculated 

 do not completely agree with experiment. 



When the inductors have no remanent magnetism, <(!) is null for 

 1 = 0, and tends towards a maximum value when I increases ; the 

 general form of the curve is then hyperbolical. 



Let us assume that the resistance R of the machine is inde- 

 pendent of the velocity that is to say, that we neglect the fictive 



* MARCEL DEPREZ. Comptes rendtis, Vol. xcn., p. 1152. 1881. 



