On the Efficiency of Muscular Work. 209 



Table X.— Observations of Table VIII Grouped for Testing Fit. 



Group. 



Frequency. 



Observed 

 mean. 



Calculated 

 mean. 



Square 

 of difference. 



Square of difference 

 X frequency. 



0-55 



6 



5 -643 



5-747 



-0108 



0-0648 



1 -35 



1 



8-720 



8-631 



0-0079 



-0079 



1-62-1 -63 



2 



10-515 



9-625 



-7921 



1 -5842 



2-05-2-10 



11 



11 -248 



11 -254 



0-00004 



-0004 



2-11 



1 



11 -255 



11 -376 



0-0146 



-0584 



2-12 



4 



11 -240 



11 -412 



-0296 



-1184 













1 -8341 



<rH 2 (1 -v^) = -053366 ; x'^ = 34 -368 ; P = less than 10"^ 



linear law, but some reservations must be made. Thus in each the value of 

 is chiefly due to a single group, while, careful as are the experiments, 

 absolute uniformity of external conditions can never be secured in inquiries 

 of this kind, so that too much stress ought not to be put upon absolutely 

 small deviations. I am not confident therefore that the result of this test 

 is sufficient to condemn the law as being inapplicable. I also think that no 

 significance attaches to the difference between the regression coefficients (the 

 reciprocals of the efficiencies). The dijfference is 0"2708 + 0'0855, which is 

 more than three times the probable difference, but the applicability of the 

 normal law of error to such cases may justly be questioned ; that the 

 divergence may be of no practical importance is suggested by the results 

 obtained with the next higher rates of pedalling, although these are 

 determined from smaller numbers of observations. They are shown in 

 Tables XI and XII, and it will be seen that the regression coefficients do not 

 continue to increase, but are well within the range of likely fluctuation about 

 the value deduced from the observations at lower speeds. 



Table XI. — Heat Production and Work. Observations of Benedict and 



Cathcart on M. A. M. pedalliBg at the rate of 103-107 revolutions per 

 minute (inclusive). 



Work done. 



Observed heat production. 



Mean of 

 observations. 



Heat production given by 

 formula 

 Heat=3-1262 Work + 5 1525. 



calories. 

 0-55 

 1 -35 



1 -64-1 -65 



1 -83 



2 -12-2-17 



calories. 

 6-01 

 9-20, 9-78 

 11 -21, 11 -35 

 11 -53 



r 11 -55, 11 -63, 11 -72, 12 -66, 11 -33 "1 

 1 11 -32, 11 -83, 11 -73, 11 -71, 11 -23/ 



6 01 

 9-49. 

 11 -28 

 11 -53 



11 -67 



6-87 

 9-37 

 10 -30 



10 -87 



11 -87 



