REPORT ON THE COMPOSITION OF OCEAN-WATER. 
31 
But 5 times the sum of the two values of r 0 comes to 0*0325 ; even this difference 
might be accidental. 
The Quantities of Potash. 
(Taken in terms of 100 parts of total Salts.) 
For all the 77 cases analysed, 
x 0 
1-333 
r r 0 
not calculated. 
For the 34 deep-sea waters, 
1-336 
0-019 
0-0034 
For the 43 shallow waters, 
1-330 
0-023 
0-0035 
Here the sum of the two values of r 0 by itself comes to rather more than the 
difference between the value of x 0 for deep-sea and for shallow waters. 
The Quantities of Lime. 
(Taken in terms of 100 parts of total Salts.) 
x o 
r 
r o 
For all the 77 cases analysed, 
1-692 
0-029 
0-0033 
For the 34 deep-sea Avaters, 
1-710 
0-028 
0-0048 
For' the 43 shallow waters, 
1-679 
0-027 
0-0042 
Value of x 0 for deep-sea minus that for shallow 
waters . . . x 0-031 
According to my calculation the mean of the mean errors in the analyses which served 
to fix the 77 values is ±0'0147 (referred to x — 1*7). The two means for the shallow and 
deep-sea waters respectively should not be wrong by more than this, the probability is 
that it is less ; and supposing even the errors in the two values of x 0 to be=±0'015, 
we must assume them to have different signs to account for the fact that the value of x 0 
for the deep-sea waters is greater by 0'031 than that for the shallow. 
A consideration of the two values of r 0 leads to a similar result. The probability is 
9993 to 7 that the actual errors of the two means are less than 0'024 and 0'021 respectively. 
It is true the two values taken together come to 0'045, or more than the difference, 0'031, to 
be explained. But there is no occasion for putting such a strain on our assumptions 
According to the law of frequency of error the probability is 957 to 43 that the errors 
in the two mean values x 0 are less than three times the respective values of r 0 . And adopting 
3(r 0 + r 0 ) = 0'027 as being the maximum possible difference between the two values of x 0 , it 
still takes 0 - 004 unit to come to the actual difference. It really appears as if the cleep-sea 
waters did contain more lime than the shallow, on account of their coming from greater 
depths. And this result need not surprise us, because the lime in the upper strata of 
the sea is constantly being used up by living organisms, to be replaced by lime dissolved 
