110 



Mr. J. S. Macdonald. Studies in the 



Maximal Aberrations, given as a percentage of the average result of dividing 

 by various simple functions of W. 





W l/3 





W. 





W 5 



3 



„ . r 



Group A ■< 



+ 9 

 -10 



•5 



•2 



+ 7-6 

 - 5-8 



± 3 -3 



±2-5 



+ 5 

 - 4 



i 



•5 



Group B , , -| 



+ 4 

 - 2 



•4 

 •7 



±3-6 



+ 9-8 

 - 5-6 



+ 16 8 

 -10 -o 



+ 20 

 -17 



•7 

 •3 



Group C -| 



+ 5 

 - 4 



•5 

 •9 



+ 11 -4 

 - 3 5 



+ 22 -0 

 - 7-0 



+ 32 -0 

 -12-4 



+ 43 

 -18 



•o 



4 



Group D 



+ 11 



- 9 



■5 



•o 



+ 19-8 

 - 9-0 



+ 30 -6 

 -14-9 



+ 39 -0 

 -19-7 



+ 55 

 -25 



•o 

 •o 



Now, compare with the figures in this table the maximal aberrations from 

 the average experimental result as given in the preceding tables. 



Maximal Aberrations from the Mean Experimental Kesult. 



Group A 12-4 and -13-9 



Group B 9-5 „ -10 



Group C 9-1 „ - 6 



Group D 1-7 „ - 3-2 



It will be seen at once that the experiments of Group D gain nothing 

 by any new process of numerical treatment. The experimental results are 

 almost constant notwithstanding considerable differences in the weights, and 

 therefore in various powers of the weights, of the subjects ; and, indeed, if the 

 observations were sufficient in number, it would be justifiable to write the 

 general summary of the results obtained at this level of mechanical-work 

 performance as 



Heat-production = K d . 



If, on the other hand, we go to the other extreme and examine the results 

 in Group A the original errors are as large as 13 per cent, of the mean 

 experimental result, and it is seen that division of these results by almost 

 any one of these functions of the weight brings them to a more common level, 

 but that this is best done by dividing them by W 4 ' 3 , when the aberrations are 

 only 2-5 per cent, from the average. Here, we might say that, at this much 

 lower level of mechanical-work performance, 



Heat-production = K a W^ s . 



Treating the other groups in the same way we get the following summary 

 of the experimental results : — 



