THE VOYAGE OF H.M.S. CHALLENGER. 
N mr t.f tlu- tables showed any marked contrast between deep-sea waters on the one 
h i! d uid surface-waters or medium-depth waters on the other ; but this did not exclude 
5 nihility ..f the data containing some hidden evidence of a relation between richness 
■i , or other component and depth, which I thought might perhaps be brought to view 
d> U"ing each table in the light of the law of frequency of errors. Only, as the 
. .i d '■ r of surface-waters analysed was too small to accommodate themselves to this law, 
1 ■: • d them in common with those from “ medium-depths ” as “ shallow waters, ^ and 
i r mimed each table into three diagrams, one for the whole set of 77 waters 
Iv -• 1. another for the 34 deep sea-waters, a third for the “ shallow ” waters. In each of 
- tie values in the first column of the table were laid down as abscissae, and the 
: 'Hiding numbers in the other columns as ordinates, in a system of rectangular 
: it-s, t h« • idea being that each series of points would suggest the probability-curve 
: i-’tcristic <»f the respective set of cases. I had no special anticipations regarding 
dt"_rive of definiteness in the expected suggestions, but I hoped that at least 
maxima of t he curves would be indicated clearly, and certainly more truth- 
tlian by mere mechanical calculating. Even in this, however, I was disappointed: 
;r\ - had to be drawn in too arbitrary a fashion to be relied upon as offering objective 
h*m •<•. I accordingly omit the more or less indefinite indications which they furnished, 
] mss on to give the results which I obtained subsequently by the ordinary arith- 
metical method. 
In the fallowing paragraphs x 0 always stands for the arithmetical mean of the set of 
:.:". -ri< d values, .r, considered; n, for the number of the latter ; r, for the probable 
error 
of the single x as calculated by the formula r = 0 • 6 7 4 5 is/— ^ - p -- , while r 0 signifies 
the 
probable error of the mean x Q , 
as calculated by the formula r 0 = 
The Quantities of Chlorine. 
\ th« 77 values given in our table, the one for number 871 differs so much 
r. • ly from the mean than any of the rest, that, after some hesitation, I decided 
uj»on excluding it. 
/ /• th> remaining 76 values we have x„ = 55 - 420 ; r= ±0 - 06 ; r 0 = iO'OOGO. 
1 : >v dual c hlorine determinations as such, 1 feel sure, are not infected by a 
! i rror than about ± 0*03 ; but the quantities of chlorine in the 77 reports, 
M * ! 5 ■ d by all tin- r< -t of tin- analytical determinations conjointly, could not be 
’■n* rt ,in by less than ± 0‘0G ; and if it were not for a number of excep- 
f"r :r, .r registered, I should say the results on the whole are in 
lf ’ tli- a sumption that, as a matter of natural law, the percentage of 
