04 
THE VOYAGE OF H.M.S. CHALLENGER. 
The large values under II — D suggest that Hubbard's thermometer registered too 
low. What he called 25° 0 really was 25 '43 — virtually, at least. Leaving the 
Hubbard column on one side, the other discrepancies might be called moderate (the 
more bo as they really represent the conjoint effect of two discrepancies — A(S) and A(0 
— as one discrepancy charged against the thermometer), if it were not for the uncom- 
fortably large values entered in the line for t = 0°. It will not do to charge the tempera- 
ture error against the (virtual) observation at 1 5°*56. It would then, as a temperature 
error, appear small, but the pleasant smallness of all the other A(y)’s besides those at 0 ° 
would vanish. 
Assuming the truth to lie mid-way between Thorpe and Rucker on the one side, and 
myself on the other, the y for the reduction of a specific gravity from 15 0, 56 to 0°, or 
rice verso, according to either authority would be uncertain by ± 0 ,o 03 (pure water of 4° = 
1000). Table IV. is constructed on the model of a far more extensive table, which I 
calculated long ago for the reduction of specific gravities from 15°’56 to t° and vice versa. 
That table, which gave the values y under the successive headings of x=lL 18 . . . 21, 
was used at the Challenger Office for the final reduction of Buchanan’s specific gravities ; 
but I have cancelled it as part of this memoir, because I found that Thorpe and Rucker’s 
plan is more convenient for purposes of computation. Their reduction table is founded 
up' in a proposition which they extracted from their general interpolation formula, but 
which stands out more visibly in my own equation for S =f(x> 0* Assuming S, and © t to 
be the specific gravities of two different sea-waters at t°, and S 0 and 0 O to be the cor- 
responding values for 0\ then 
where f(t) is a function <'f temperaturr, which, according to my formula is simply 
/y t \ Hi ft bt -p ct 2 
J V } ~D 0 a 
(compare page 58). Hence, by analog}' for any other temperature r (instead of t) 
Hence, 
os wc will call it. 
According to my equation obviously 
<M0 = 
D, 
H t 
' u 1 T 15*56, and we have a convenient formula for the reduction of specific 
6, provided we have a table giving the specific gravities of a 
standard water for the requisite scries of temperatures. 
