38 
Proceedings of the Royal Society 
Omitting the exceptionally high discrepancy of IV. the differ- 
ence as a mean of three results is 0 '00002 8, and even including 
it, it does not touch the fourth place. 
To form an idea of the reliance to be placed on the hydrometer 
readings, all those cases (164 in number) in which the weights 
1 and 1 + 7 were used in consecutive determinations of one water, 
were investigated and classified. Temperature does not appear to 
affect the differences. 
Let r he the reading with weight 1, and r' with weights 1 and 7 
in the same water, then, as these weights can only be used for water 
of nearly the same density, in a perfect hydrometer perfectly read 
r-r' should be a constant, and in an actual instrument read with 
ordinary care the mean of a sufficient number of observations 
should approximate very closely to the constant. In 164 cases 
r — r' had the following values : — 
Values, 38 37'5 37 36*5 36 35'5 
Times, 2 16 48 49 40 9 
The mean of all the values is 36'5. Hence out of 164 cases — 
49, 
or 29*9 per cent,, 
differed from the 
mean by 
0 
88 , 
or 53'6 „ 
f) 
0'5 
25, 
or 15 '3 
5 ? 
}) 
1-0 
2, 
or 1*2 „ 
?> 
}? 
1-5 
Here the maximum variation from the mean is L5, while nearly 
84 per cent, of the observations showed a deviation no greater 
than 0'5. 
0*5 of a division of the hydrometer corresponds to a difference in 
density of 0'00003 in the case of a sample of sea water of ordinary 
density, while 1 *5 division is equivalent to a difference of 
0 '00009, the temperature being the same. 
The four triple determinations of distilled water give the total 
error as 0 '000066 as a mean of the whole, and in all cases the 
variations were in the same direction. 
As stated in describing the method, each determination of 
density was made in duplicate, and the results independently 
worked out. The two densities obtained in this way invariably 
differed, that obtained when the greater part of the stem was im- 
