Miscellanea 
415 
With regard to samples of two it will be seen that odds of 9 : 1 are reached at a little more 
than three times the s.d., of 99 : 1 at a little more than thirty times, of 999 : 1 at a little more 
than 300 times, while 9999 : 1 is reached at in or about 3000 times the s.d. ! 
Perhaps I may be permitted to restate my opinion as to the best way of judging the accuracy 
of physical or chemical determinations. 
After considerable experience I have not encountered any determmation which is not 
influenced by the date on which it is made, from this it follows that a number of determinations 
of the same thing made on the same day are likely to lie more closely together than if the repetitions 
had been made on different days. 
It aLso follows that it the probable error is calculated from a number of observations made 
close together in point of time much of the secular error will be left out and for general use the 
probable error will be too small. 
Where then the materials are sufficiently stable it is well to run a number of determinations 
on the same material through any series of routine determinations which have to be made, 
spreading them over the whole period. 
Thus if an analyst is determining the percentage of nitrogen in different samples of seed 
corn and wishes to know the probable error of the determination, i.e. how accurately his 
figures give the percentage of nitrogen in a bulk of corn. 
Let us suppose that he makes ten determinations a day for sixty days and that it is of some 
real importance to him to get a clear idea of his error ; he will do well to get sixty dijferenf samples 
from the same bulk of corn and analyse one of these on each of the sixty days ; unless I am much 
mistaken he will have a more modest idea of his infallibihty than he had before he compared 
the sixty results together. He will also, in so far as his repeated sample is representative, get 
a close approximation to the probable error of a single determination. 
In some cases it is not possible to obtain a sufficient bulk of material and then it may be better 
to determine each result in duplicate, the repetitions being separated as widely as possible in 
point of time. Then the square root of the mean of the squares of the differences between 
corresponding pairs gives twice the standard deviation of the average of a pair, and if enough 
pairs can be taken and the determinations made on different samples this is a better method 
than the other, as the error of the sampling is better sampled. 
In the preparation of the tables a slight mistake was discovered in the second row of the odd 
numbers in the original table by Mr W. L. Bowie to whom I am indel)ted for the calculation of 
the new figures. 
