400 Carhon-dioxide Excretion in Man [April 



Or, out of a total of seventy-seven experiments, there was direct 

 relationship between barometric change and carbon dioxide excre- 

 tion in forty-two experiments, or 54.5 per cent. 



It will be Seen from these results that the apparent degree of 

 correspondence, so far as it is revealed by this method of analysis, 

 is greater in the morning experiments than in those carried out at 

 midday or in the evening. This is probably due to the fact that in 

 the morning not merely the digestive organs, but the whole System, 

 is in a more uniform condition than at any other time during the 

 twenty-four hours. 



Application of the method of least Squares. It now seemed 

 desirable to subject the results obtained in this series of experiments 

 to a more rigorous analysis than that just described, with a view of 

 discovering what is the degree of correlation between the two vari- 

 ables, the barometric height and the rate of excretion of carbon 

 dioxide, during muscular rest. The data obtained in the experi- 

 ments were, therefore, examined by the method of least Squares, 

 which was applied separately to the three sets of data from each 

 subject in order that the effect of different times of day might be 

 determined separately. 



In Table 3 are given the barometric height and the correspond- 

 ing carbon dioxide excretion f the problem is to find the correlation 

 between these two quantities, and also the regression of carbon 

 dioxide on barometric height, i. e., the amount of change in excre- 

 tion of carbon dioxide for a millimeter change in barometric height. 

 The means of columns i and 2 are obtained in the usual manner, by 

 dividing the total in each column by the number of experiments 

 {N). Having obtained these means, two additional columns are 

 formed, giving the deviation of each Observation from the mean of 

 its column. In columns 5 and 6 are entered the Squares of the 

 deviations {X^ and F^). The Standard deviation {a^) is now ob- 

 tained by dividing the sum of the Squares in the fifth column by the 

 number of experiments, N, and extracting the square root of the 

 quotient; the Standard deviation for 3; is, of course, found in the 

 same manner. 



p;ir2 I1642.4 12/ 127078 



"^ = A'^ = >i-2F- = 7.65 and ., = ^^=^-g^ = 3i.i 



* The data are those obtained from experiments on subject A at noon. 



