On the Efficiency of Muscular Work. 



199 



and one only, which makes jb/jy = '^b/^y = 0'73, viz., when r = 40° 29' 

 (45' less than the angle of total reflection for the yellow and 24' less than 

 for the blue). 



At the position so defined there will be a band with borders only faintly 

 coloured. On either side of this band the order in which the colours appear 

 will be reversed. 



On the Efficiency of Muscular Work. 



By M. Greenwood, Captain E.A.M.C. (T.F.), Lister Institute of Preventive 



Medicine. 



(Communicated by Prof. Leonard Hill, F.R.S. Received January 18, 1918.) 



In a paper communicated to the Eoyal Society in 1913,* Prof. J. S. 

 Macdonald published a series of observations upon the heat production of 

 persons performing certain known quantities of work upon a bicycle 

 ergometer. In that paper, and again in a more recent publication,! 

 Prof. Macdonald has outlined certain methods of interpreting his results, 

 which are of much importance ; these I shall discuss in the latter half of 

 this communication, but, before doing so, it will be interesting to examine 

 some purely numerical questions to which Macdonald's paper gave rise. 



In a note on Macdonald's earlier paper, Messrs. Glazebrook and DyeJ 

 have published a formula descriptive of Macdonald's numerical results. 

 This formula is 



H = «+«+^^- « 



where H = heat production in calories, M = body mass in kilogrammes, 

 W = work equivalent in calories, a, h, «, and /3 are constants. 



The values of the constants, which were obtained by a graphical process 

 led in the particular case to the equation 



- H=-138 + 4-5M+j^,jj^^. (2) 



and this equation was found to provide values in very fair agreement with 

 the observed results. 



It will be noticed that, when the body weight is constant, the heat production 



* 'Eoy. Soc. Proc.,' B, vol. 87, p. 96 (1914). 

 t Ibid., vol. 89, p. 394 (1917). 

 X Ibid., vol. 87, p. 311 (1914). 



