THE LAWS OF ENERGETIC EXPENDITURE 181 



and the maximum work done per second will be : 



QV = K( V) 2 V, 

 K being a constant. 



In the same way (Q -f P) = K(u v) 2 and (Q -f P) v = K 

 (u v) 2 v. 



u 4 



For QV to be a maximum V must equal - hence Q = - Kw 2 . 



o y 



To have (Q -f- P) v maximum it is necessary that 



^3K 

 4 



Replace Q by its value - Ku 2 , then 

 y 



v = 0-474V, about V, 



100 



and from (Q + P) = K (u v) 2 . 



P = 0-597Q or practically P = ? Q. 



o 



124. The work done per second, that is, the product F X v, 

 has a maximum value which various authors have attempted to 

 determine a priori. According to Euler, it can be represented by 

 one of the following formulae : 



or F = F 



F' and v f being respectively the greatest (absolute) effort and 

 speed, which will render all work impossible. 



From the first formula : 



v' 4 4 



v = ; hence F = - F 7 and Fv = ~ F'v' ; this being 

 o y a i 



the maximum power. 



From the second formula : 



v = -JT and Fv = Q F'v'. 



O 



Schultz ( 1 ) obtained by experiments on the haulage of loads : 

 F' = 48 to 49 kilogrammes ; v' = 1-60 metres. 



Hence the first formula gives v = 0-53 metres, and Fv = 11-5 

 kilogrammetres approximately. 



He found by experiment that man develops in continuous 

 work an effort of 13-7 kg. at a speed of 0-76 m., that is a power of 

 10-4 kgm. in accordance with Euler's theory. 



(*) Schultz (Biblioth&que Brittannique, 1783, vol. Ivi.). 



