50 Mr. R. H. M. Bosanquet on Mountain-Si 



Similarly, consider a man weighing 12 stone. ^ According 

 to a well-known mountaineering datum, lie may lift his weight 

 1000 feet per hour for many hours. Under these circum- 

 stances he is doing about T L of a nominal horse-power. 



Certain experiments on the treadmill gave J horse-power 

 external work, maintained for 3 J hours. 



But any ordinary person can do a whole horse-power, if the 

 time of the effort be short enough. Take a man weighing 

 12 stone = 168 lb. If he raise his weight a little over 3 feet 

 per second, he is doing a horse-power of work. (For 550/168 

 = 3*27, or a little more than 3J.) Now any ordinary person 

 who can run upstairs two steps at a time can do this easily 

 for a few seconds, and an active person for longer, but the 

 duration of the effort will not easily exceed a certain fraction of 

 a minute. 



Further, active people can do 2 horse-power, running 

 upstairs at the rate of 6^ feet of ascent per second, for a very 

 few seconds. 



It appears, therefore, that the power a man is capable of 

 exerting depends on the duration of the effort. 



The following (p. 51) are a few data I have selected as the 

 basis for a numerical law. 



The law adopted is that the time of duration of effort (or 

 the " endurance ") varies inversely as the cube of the power 

 exerted, supposed uniform. Or, conversely, that the power 

 which can be exerted for a given time varies inversely as the 

 cube root of the time (or of the " endurance "). 



Of course the numbers here given can only be rough 

 approximations to an average ; and we need not be surprised 

 if we find wide divergences in isolated cases. 



While the correspondence of the calculated times with the 

 estimates is not in all cases close, the discrepancies are in 

 opposite directions. Further, any considerable change in the 

 assumed law would tend to make the calculated numbers 

 impossible in the one direction or the other. Thus, if we took 

 the fourth power instead of the cube, it would make the tasks 

 at the bottom easier, and that at the top impossible or nearly 

 so, and vice versa if we took the square instead of the cube. 



The treadmill datum has been taken as the starting-point, 

 the calculated endurances of the other cases being derived by 

 multiplying 3^- hours by the cubes of the inverse ratios 

 of H.P. 



It must be noted that we do not know the average weight 

 of Leslie Stephen's party. I have assumed that this was 

 12 stone. If not, a correction will be required. It will be 

 seen that their actual endurance app ears greatly to exceed 



