THE LAWS OF ENERGETIC EXPENDITURE 179 



Geometricians and natural philosophers (Daniel Bernoulli, 

 Euler, Coulomb, etc.), found the maximum of F x v X t, theoreti- 

 cally^ 1 ) The greatest of all, Coulomb, knew how to ally theory 

 to experiment. The principle of his method was as follows : 

 a good labourer, without carrying a weight, could mount to a 

 height H (on mountains) in a working day, the work done being 

 PH. With a load, Q, he could only mount to H ', or a work done 

 of (P + QJ H'. This is a diminution PH --- (P + Q) H', caused 

 by the presence of the load Q. By means of the calculus, 

 Coulomb found the value of the load Q, which gave the mini- 

 mum diminution, that is to say, the maximum daily output. 



The following is an example of this method, according to 

 Coulomb : a man weighing 65 kilogrammes was able to ascend 

 to the summit of the Peak of Teneriffe (2,923 metres) doing 

 189,915 kilogrammetres of work in the day. With a load of 68 

 kilogrammes he was only able to do 105,336 kilogrammetres 



84 579 



of work, a decrease of 84,579 kilogrammetres, or -j per 



Do 



84,579 84579 



kilogramme, or, - x Q' for a load Q'. Let ^ b, and 



bo too 



the work done without a load a. Then a bQ' is the expression 

 of the possible work which can be done. If the height, in these 

 conditions, is reduced to h there wil) be a new expression (65 -f 

 Q') h for the same amount of work : whence the equation : 



a - bQ' == (65 + Q') h, and h =^ = ^,- 

 The useful work being that of the load Q'h, 



For T to be maximum the value of Q' will be : 



Taking numerical values, Q' = 53 kilogrammes and Q'h = 



55 350 

 55,350 kilogrammetres ; which gives h = and a total 



( l ) Following Coulomb, various authors have accused Daniel Bernoulli of 

 ignoring this physiological law, that it is not immaterial to compensate the 

 speed by the effort, in such a way that the power remains constant. The 

 writings of Bernoulli bear witness that this was never his error (Hydro- 

 dynamica, 1738, 13, 21. Prix. Acad. Sciences, 1768, vol. viii., p. 7). He 

 obtained F = 15 K and v =* 0'66 m. as the maximum daily work of the arm. 



