18S5.] NEW YORK ACADEMY OF SCIENCES. lOo, 



This statement requires to be modified somewhat because of 

 tlie imperfections of machines, and becomes more accurate in 

 proi^ortion to the perfection of the machines used. 



This work lost in resistance of the pipe is plainly a minimum 

 for E=:e, and a maximum for e=o if R remains constant. Let 

 us separate it into its component parts. 



TVe see from the above equation that — ^^-^ = constant 



when E varies as the square of the difference of the heads, or 

 wlien the square root of R varies as the difference of heads. 



If now we assume the resistance of the pumps as trifling in 

 comparison with that of a long pipe or pipes connecting tbem, 

 we see that we must double the difference of heads (E — e) in 

 order to have the same loss of work per second with a pipe four 

 times as long. 



Increasing the resistance four times gives us only ^ the weight 

 of fluid per second assumed to be passing through the pipe, but 

 doubling the difference of heads also doubles the weight of 

 fluid per second, so that under the altered conditions we obtain 

 ^ the weight of fluid per second, and twice the effective head. 

 Therefore the work per second lost in the pipe is 



as before. 



The work done by the pump and motor, each working with 

 twice its former head remains the same as before, and their rela- 

 tive efficiency is the same. 



This is what Marcel Deprcz m-^ant when he said: 



" The tiseful mechanical work and the efficiency remain the 

 same luhatever be the distance of transmission, pi^ovided the eleciro- 

 motive forces, positive and negative, vary 2^f'oportio7iaUy to the 

 square root of the circiiit's resistance." 



I should like to emphatically call your attention to the deadly 

 nature of the very high electro-motive forces demanded by this 

 law, in the case of great distances. 



One cannot but admire the boldness of this knight of science. 

 In the face of mistatement, based on erroneous assumptions, and 

 of ridicule and opposition, in many cases becoming personal, 

 he has adhered to his views and won his battle. 



His detractors, while now forced to admit his results as correct, 

 have shifted their argument from a scientific basis to a pecuniary 

 one. One would think that so shrewd a financier as Baron 

 Rothschild is not likely to be misled, and can safely afford 

 to discount adverse editorial opinions, in the belief that a suc- 

 cessful outcome will be reached before many years. 



