of Edinburgh, Session 1884 - 85 . 
39 
mersed being always the greater. The differences between the two 
readings in 204 cases have been classified and examined. 
The following table (I.) exhibits the results, which are not 
apparently affected by temperature, deviations of each magnitude 
appearing in densities determined at all temperatures from 4° to 20°. 
The differences are given in units of the 5th place. 
Table I. — Discrepancies in Double Determinations. 
Discrepancy, S -S'. 
^3 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
>12 
Number of cases in 
204, . 
1-3 
16 
4 
19 
32 
7 
25 
19 
4 
16 
19 
29 
Percentage, . 
6-3 
7-8 
1-9 
9-0 
15-6 
34 
12-2 
9-0 
1-9 
7-8 
9-0 
14-2 
Percentage of cases 
where one read- 
ing was greater 
than 80, 
23 
37-5 
75 
42 
25 
43 
76 
58 
50 
68-7 
73-7 
73 
The mean of all these discordances is 8-4, but omitting the 14*2 per 
cent, over 1 2, as being probably due to careless readings, the mean 
becomes 6 ’9. In order to take the least favourable view of the case, 
the higher number will be considered, and as the mean of the two 
observations was always taken for the correct density, this discordance 
is reduced to 4'2 as deviation from the mean. 
It is not allowable to change this 4 ‘2 as error, since it is always 
positive, and since the amount of it is roughly proportional to the 
difference between the length of stem immersed by the addition of 
the second weight, and more nearly proportional to the number of 
the reading. The last horizontal line of the preceding table shows 
that (omitting S - 8' = 4, and = 10 on account of the small number of 
cases) the percentage of readings over 80 increases, roughly speaking, 
as the discrepancy increases. 
The reason of the difference may be that the stem of the hydro- 
meter is slightly conical, instead of being truly cylindrical, as 
assumed. It might also be that the weight of the brass pieces was 
not correctly known, but a careful reweighing showed that this 
was not so. Capillarity should act equally in each case, and 
need not be considered. The only remaining explanation which 
suggests itself is the difference in weight produced by the film of 
water adhering to the part of the stem above the surface. To test 
