TIIE VOYAGE OF H.M.S. CHALLENGER. 
86 
±2 nun., 2 of tlu i hydrometer, and occasionally even by more. On classifying tlie 
errors of series I., as deduced from the original line — 
w= (w t0 ) a + (60 — h) x 0*00805, 
according to their magnitudes I counted — 
-t- Error under. 
0- 5 
10 
1- 5 
20 
2- 5 
3- 2 
Number of Cases. 
11 
27 
38 
53 
59 
65 
The entry 32 ( = nearest integer to 32-5) in Column II. if interpolated would correspond 
to some value between TO and 1*5 for the error, hence the probable error may be set 
d<>\vn as ± T3 degrees of the hydrometer scale ; the probability of the error being less 
than ±20 is seen directly from the table to be about ^| = 0'81. I think it is a fair 
assumption that the “A” put down by Mr. Buchanan in his volume table for a given 
■r at t as a result of his standard experiments, is uncertain by at least ±0‘5 mm. Adding 
dbl‘5 as the probable uncertainty of the reading for a given sample of sea-water in the 
- . ment practical applications of the instrument, we arrive at ±2’0 x 0’008-r- 160 as 
an estimate of the probable relative error in the individual specific gravity reported, 
which comes to ±0*1 fora specific gravity referred to water =1000. The corresponding 
uncertainty in \ (number of grams of chlorine per kilogram of sea-water) is ±0'072. 
This then is about the degree of precision which we may presume Mr. Buchanan to 
li iv< r ach'd in lib numerous specific gravity determinations. But my determinations of 
tie chlorine in waters examined by him, enable us, to some extent, to actually measure 
the precision of his work. 
Column IX. of Table L gives the differences \ between the chlorines x 1 calculated 
from Mr. Bui hai pecific gravities ,s. and the values x which I found in my analyses. 
I have arranged their values x' — X according to their magnitude, which, in the first 
in.Ht.in' ■ , led to the detection of the following exceptionally high numbers, which may be 
Le as bring probably owing to blunders in the specific gravity determination, or to 
mistake-, in regard to the identity of t lie waters which I analysed — 
X -X, . . -0-376 -0-474 -0522 -0307 +0-245 +0512 
So. of the water, . 1520 1533 388 1265 485 1 
In looking down the ninth column of our Table L, we are struck by the predominance 
values, win- g’-.-t- that ili'-ii' must be a relatively constant element in the 
■l.iT : n l"tv.' a x and xi as expressed in the equation x' — x = constant ± observa- 
tional error. 
