208 



Capt. M. Greenwood. 



was between 68 and 72 and the group 98 to 102. In the remainder either 

 the number of observations was less than 20 or the range of variation of work 

 performed very small. In Table VIII are reproduced the second available 

 set. The linear equations are 



H = 3-;^415W + 3-4131 and H = 3-61225 W + 3-7543 

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



Cathcart on M. A. M. pedalling at the rate of 98-102 revolutions per 

 minute (inclusive). 



Work done. 



Observed heat production. 



Mean of 

 observations. 



Heat production given by 

 formula 



Heat = 3-61225 Work + 3 -7543. 



calories. 



calories. 







0-55 



5 -59, 5 -28, 6 '03, 5 -60, 5 -64 



5-63 



5-74 



0-56 



5-72 



5 -72 



5-78 



1 -35 



8-72 



8-72 



8-63 



1 -62 



10 -15 



10 -15 



9-61 



1 -63 



10 -88 



10 -88 



9-64 



2-05 



11 -24 



11 -24 



11 -16 



2-06 



11 -30 



11 -30 



11 -20 



2-07 



10-82, 11 -21, 11 -43, 10-91 



11-09 



11-23 



2-08 



11-19 



11 19 



11-27 



2-09 



10-98, 11 -65, 11 -74 



11 -46 



11 -30 



2-10 



11 -26 



11 -26 



11-34 



2-11 



11 -13, 11 -15, 11 -39, 11 -35 



11 -26 



11-38 



2-12 



11 -29, 11 -35, 11 -03, 11 -29 



11 -24 



11 -41 



' The first point which arises is whether the observations are, when 

 examined strictly, reasonably probable examples of a linear law (that they 

 are sufficiently so for ordinary purposes of numerical interpolation is no 

 doubt evident). To test the matter, I had recourse to a method proposed by 

 Pearson,* the application of which is seen in Tables IX and X. On the face 

 of the figures, it seems that both cases are very improbable examples of a 



Table IX.— Observations of Table VII Grouped for Testing Fit. 



G-roup. 



Frequency. 



Observed 

 mean. 



Calculated 

 mean. 



Square of 

 difEerence. 



Square of difEerence 

 X frequency. 



1 0-47-0-49 



9 



3-974 



4-018 



0-0019 



-0172 



1-19-1 -33 



4 



6-785 



6-523 



-0689 



-2756 



1-35-1 -56 



4 



7-288 



7-280 



-00006 



0-0002 



1 -57 



8 



7-583 



7-669 



-0074 



-0595 













-3525 



o-H Ml-')'') = 0-01698; x' = 20-760; P = 0-00036. 



* ' Biometrika,' vol. 11, p. 237 (1916). 



