Contribution to tiie Physiology of Respiration under the Arctic Climate. 91 



in comparison with the variations, that we can reasonably exclude 

 them in this connection. 



It is admitted, that the formulae for large numbers can only 

 be used with caution in cases of small numbers; I have nevertheless 

 carried out the calculations also for the series with quite few num- 

 bers. It seems to me quite possible, that the calculated constants, 

 even if they are not fully valid, mathematical expressions for the 

 variation or uncertainty in the results in question, yet give a pic- 

 ture of — if I may so call it — the density of the series, which is 

 easily grasped and which renders unnecessary a repetition of the 

 series. And an average without such more complete determination 

 appears to me quite without value. For example, 200 is the average 

 of 199, 200 and 201 as well as of 150, 200 and 250, but the number 

 is of very different value in the two cases; any addition therefore 

 which indicates, even if only with an approximation, which of the 

 two series is in question, must be regarded as a necessity. 



It will often be difficult to determine, whether an experiment, 

 which differs very greatly from the others, is due to chance errors 

 or unusual circumstances. Even if the strongly dcAiating variants 

 are relatively seldom, there is still the possibility of finding them in 

 the smallest series; the apparently quite improbable number may 

 also, when the number of chances is increased, prove to fall in 

 quite naturally into the greater whole. 



Leaving aside that such an irregular case ma}' thus be quite a 

 A'alid expression of the function iuA^estigated, it may however be 

 necessary and right to exclude it from the calculation of the con- 

 stants of the series, because it may by chance completely upset the 

 average and alter the standard deviation, so that these factors come 

 to give quite an erroneous impression of the actual appearance of 

 the series. For this reason, after calculating an experimental series 

 in the usual manner, I have determined its probable limits according 

 to a formula given later; I have then recalculated the constants 

 after exclusion of the values which fell outside the calculated limits. 

 In all cases I have noted both the directly found and the corrected 

 values for the average and //. 



The formulae used are given in Davenport's Statistical Methods 

 (New York, 1904). 



In the principal table 75 morning experiments are noted, distri- 

 buted as follow^s: 



Copenhagen, February 1909, 13 experiments 

 N. E. Greenland, April 1907, 14 — 



June — 13 — 



August — 10 



XLIV. 



