On a Problem in the Calculus of Variations. 1 99 



work, and subsisting upon a diet containing but the merest traces 

 of nitrogen. The following conclusions may therefore be drawn 

 from the foregoing experiments and considerations : — 



1. A muscle is a machine for the conversion of potential 

 energy into mechanical force. 



2. The mechanical force of the muscles is derived chiefly, if 

 not entirely, from the oxidation of matters contained in the 

 blood, and not from the oxidation of the muscles themselves. 



3. In man, the chief materials used for the production of 

 muscular power are non-nitrogenous; but nitrogenous matters 

 can also be employed for the same purpose, and hence the greatly 

 increased evolution of nitrogen under the influence of a flesh diet, 

 even with no increase of muscular exertion. 



4. Like every other part of the body, the muscles are con- 

 stantly being renewed ; but this renewal is scarcely perceptibly 

 more rapid during great muscular activity than during compa- 

 rative quiescence. 



5. After the supply of sufficient albuminoid matters in the 

 food of man to provide for the necessary renewal of the tissues, 

 the best materials for the production both of internal and external 

 work are non-nitrogenous matters, such as oil, fat, sugar, starch, 

 gum, &c. 



6. The non-nitrogenous matters of food which find their way 

 into the blood yield up all their potential energy as actual energy ; 

 the nitrogenous matters, on the other hand, leave the body with 

 a portion (at least one-seventh) of their potential energy unex- 

 pended. 



7. The transformation of potential energy into muscular 

 power is necessarily accompanied by the production of heat 

 within the body, even when the muscular power is exerted exter- 

 nally. This is doubtless the chief, and probably the only, source 

 of animal heat. 



XXV. On a Problem in the Calculus of Variations. 

 By I. Todhtjnter, M.A., F.R.S* 



IN the Philosophical Magazine for July 1866, Professor Chai- 

 ns has communicated some additional observations respect- 

 ing the problem in the Calculus of Variations which had been 

 discussed in various preceding Numbers of the Magazine. The 

 problem may be thus enunciated : To determine the greatest 

 solid of revolution, the surface of which is given, and which cuts 

 the axis at two fixed points. I have stated in the Philosophical 

 Magazine for June what I consider to be the solution of the pro- 



* Communicated by the Author. 



