Composition of Dilute Sulp7iuric Acid. 311 



Omitting these points, however, the next most striking fact 

 is that the values of 7 — a are large for the two largest per- 

 centages, viz. 80*54 per cent, and 80°04 per cent. This is not 



ds 

 a mistake. The value of -7- x 10 6 at 80 per cent, is given in 



Mr. Pickering's Table III. as 11230, and the numerical value 

 of ds/dp diminishes as p increases. The observed value at 

 80*04 per cent., 11251, must therefore necessarily be a great 

 deal too large. 



If, then, we omit the abnormal points (marked with aste- 

 risks) and confine ourselves to those for which I have been 

 able to calculate 7 — «, we find that, out of 14 points, errors of 

 appreciable magnitude (to this order of approximation) occur 

 eight times when my curve is used and seven times when 

 Mr. Pickering's five curves are employed; the sum of the 

 errors in the first case is 9 and in the second 11. 



For my own part I think this result is sufficient to show 

 that, in attempting to discriminate between representations of 

 the experiments under consideration, Mr. Pickering is dealing 

 with quantities less than the error of experiment. 



The same conclusion is supported by a study of Table IV., 

 if Ave admit that figures in the last place are trustworthy. 



It is evident that my own results in the column {3— a could 

 be a little improved. Positive errors are the more numerous, 

 and to make positive and negative errors balance we should have 

 to subtract 2 from all the figures in that column. Hence it 

 would have been better to choose for the constant a the value 

 0-010955 instead of 0*010957. I have not thought it worth 

 while to rewrite the Tables to introduce this small correction. 



The only point that I can see in Mr. Pickering's favour is 

 that, if we omit the points at 80*54 per cent, and 80*04 per cent., 

 and if we omit the points which I have called abnormal at 

 which the errors are large, the errors obtained from his curves 

 are kept more nearly within the limit 0*000008 than in the 

 case of those obtained by myself. 



I do not press the point that the maximum error in this 

 case is admittedly larger than 0*000008, but I must insist that 

 it is extremely unlikely that errors so large as those at the 

 abnormal points exist, and that there are none larger than the 

 estimated amount elsewhere. 



Why, for instance, are we to admit an error of 22, or three 

 times the lower limit to the maximum error, at 56'89 per 

 cent., and insist that an error of 16, which is only twice the 

 same limit, is impossible at 63*08 per cent. ? If we do make 

 this extremely improbable assumption, it is of course possible 

 to reduce the errors thus arbitrarily picked out by making the 

 curve discontinuous. 



