54 REPORTS ON THE STATE OP SCIENCE.— 1916. 



explained. We will return to this point in a moment ; but first, as the 

 above means are, except in a few cases, comparatively small, it is 

 desirable to give some information about their probable errors. The 

 residuals in each group were arranged in detail in order of size, and it 

 was soon seen that those exceeding ih 65^ from the mean were pretty 

 clearly mistakes. It would be tedious and expensive to print all the 

 detail : the following summaries will probably suffice. First, the total 

 numbers of residuals for groups of 10^*° (middle group 11^*°) were as 

 in Table XVIII. 



_ 

 232 



167 

 399 



liooking first at the column 'rejected,' we see that the number of 

 positive residuals is much greater than the number of negative. This 

 is only to be expected if these are actual mistakes of one phenomenon 

 for something else which would generally follow the intended reading. 

 In the case of P there is less opportunity for reading anything which 

 precedes than in the case of S, and accoi^dingly the ratio of excess 

 of + to — is greater. But even for P a wind-tremor or other acci- 

 dental tremor may precede P by something like a minute, and be read 

 in error. Now we see that there is no trace of this excess of positive 

 residuals in the residuals between 55^ — 46^; and in the column 45' — 36' 

 the excess is in the negative residuals. It is reasonable to conclude 

 that the residuals up to about 55' are chiefly accidental errors, while 

 above that they begin to make mistakes. To make fairly sure, however, 

 of including all real observations one more column (65' — 56') has been 

 included in taking the arithmetical mean, while the column 75' — 66' 

 has been rejected, and the numbers are included in the rejected totals. 



Coming to the individual gi'oups in A, it seems unnecessary to give 

 even so much detail as for these totals. The gums at the foot show 

 that the numbers of errors 6® to 25®, on each side are rather less than 

 the middle group - .5* to + 5' : and the numbers in the next four 

 columns 26' — 65' are less than half these. To follow the behaviour of 

 the groups in A it will perhaps suffice to give the corresponding figures 

 as in Table XIX. 



