On the Efficiency of Muscular Work. 



207 



the whole of the heat production on the rest day from the working day's 

 quota is to rate the efficiency too high.* 



Macdonald's recent paper is an attempt to transfer the inquiry to a different 

 plane altogether. If I have followed his extremely ingenious reasoning 

 correctly, his position is as follows. He holds that the efficiency of work 

 performance is a function of body mass, and he found that when the thermal 

 equivalent of the external work performed was divided by the efficiency (as 

 defined above) and the quotient subtracted from the total heat production, 

 the residue was, in his experiments, sensibly constant for a given range of 

 work performance. This residue is defined as the cost of movement, it varies 

 * with the velocity of movement and can again be expressed as a function of 

 mass and rate of movement. 



The details of Macdonald's analysis are perhaps open to criticism. Thus 

 the agreement between his arithmetical calculations and the observed results 

 is not always of such importance as appears on the face of the figures, since 

 he is using formulae with several constants for absolutely few observations. 



Thus, he has a theoretical formula for cost of movement (Q) in terms of 

 velocity of movement, an expression of the form Q = a(bYy^, where a, b and 

 c are constants to be determined from five observations only. But these 

 criticisms are of subsidiary importance and detract in no way from the 

 suggestiveness of the argument. Looking at the theory as a whole, the 

 following con clusi oils appear to follow. The real efficiency of the muscular 

 machine is indeterminate and may even be unity. The apparent efficiency 

 of the same individual performing the same kind of work at different rates 

 will be represented by the reciprocal of the first derivative with respect to 

 W of H = aW + b, i.e., is equal to a is constant and 1/a might be called 

 the indicated efficiency, but b (the cost of movement) will vary with the rate 

 of performance, being a minimum at the most economical rate of movement. 

 Thus the locus of heat produced as a function of work is a family of parallel 

 straight lines intersecting the axis of heat at different points.f 



It seemed desirable to test the deduction on the basis of Benedict and 

 Cathcart's important data. To this end the observations upon their 

 professional subject were sorted out into groups for each of which the rate of 

 pedalling fell within narrow limits. Only two such groups were really 

 suitable for the purpose ; that already given iQ which the rate of pedalling 



* This criticism is implicit in Leffevre's excellent discussion of the efficiency problem 

 ('Chaleur Animale et Bio6nergetique,' pp. 924, etc., Paris, 1911), which I had not seen 

 until most of this paper had been written. 



t It is to be noted that Chauveau's formula also includes a velocity form, see Lef^vre, 

 op. cit., pp. 686 et seq. 



