312 Prof. A. W. Riicker on the Density and 



Thus, if between 53 and 58 we suppose the terms 

 { 12,-50-53)} xlO- 6 



to be added to the equation, the calculated values from 53 to 

 58 become 



10059, 10270, 10488, and 10602, 

 which make the values of /3 — a 



5, -5, +22, and 0. 



These are about of the same magnitude as the corresponding 

 values of 7— a, and, except at the abnormal* point, are less 

 than 0*000008. 



Why the large difference matters so little and the small 

 differences are so important I do not know, but it appears to 

 me that Mr. Pickering has been performing with a ruler an 

 operation analogous to that I have here performed by modi- 

 fying a formula. 



It is, however, possible to perform the same operation over 

 other ranges. Thus, taking the percentages in round num- 

 bers, and subtracting from the part of the curve between 65 

 and 54 terms given by 



{1 + 2-6(60-^ xlO" 6 , 

 we get the numbers in the following Table : — - 



p- 



Correction 

 term. 



ds 

 dp 



/3-«. 



63 



-24 



11119 



-8 



61 



- 4 



10944 



+8 



59 



- 4 



10723 



-8 



58 



-11 



10604 



+2 



57 



-24 



10472 



+6 



The tenths of a per cent, omitted might affect the last 

 figures to the extent of one unit ; but the Table proves that it 

 is possible by such devices to bring even the point at 56*89 

 per cent, into line with those near to it to within limits which 

 are admittedly less than the error of experiment. A group 

 of points from 64 to 74 per cent, shows errors no larger than 

 Mr. Pickering's from 59 to 71 per cent. Such a method of 

 treating the results, whether the instrument be a ruler or a 

 formula, appears to me unjustifiable. 



There is no doubt that the larger differences between obser- 



* It must be remembered that Mr. Pickering does not apply this term 

 to these points, though he appears to regard them as exceptional. 



