THE VOYAGE OF H.M.S. CHALLENGER. 
84 
l.M'r nt t* mi •« ‘natures. The readings then were all reduced to a medium temperature 
of 16 7. and classified according to the over- weights iv corresponding to them. 
As the several temperatures differed from 16°7 by at most 1° C., the coefficient of 
xpansion of water was taken as having the constant value e = 0'000 169; the coefficient of 
expansion of glass was taken to be &=0'000 025. 
Supposing the hydrometer to read h mm. in water of 16 7 + A t, and the temperature 
to fall to 16 7, then, on account of the contraction of the water, the hydrometer rises 
l»v h j, and, on account of the contraction of the glass, sinks by h 2 mm., the conjoint effect 
being a rise of 
. ,_(A0W (e-k) 
a 0-0081 
mm., 
md as the scale is numbered from above downwards, a positive fall of temperature 
A t corresponds to a positive A h in the reading, and a negative to a negative. Substi- 
tuting numerical values, we have 
A/i = A^ x 2*86 mm. 
The G5 pairs of values for h and w were subjected to graphic rectilinear interpolation, and 
the constants w a 0 and a of the equation iv = w GO + a(60 — Ji) taken from the line drawn. 
2 ml Srrien. In a second series a certain sea-water of exactly known specific gravity 
wa.' u-' d, the table belonging to the instrument, and a variable amount of gram-weights 
>< rving to establish the w'a. The number of readings this time was 62, and the tempera- 
tures lav within a degree of 17, which latter was adopted as the standard temperature. 
The co-efficdenf of expansion of the sea-water operated upon was taken from my own tables 
• is deduced from the formula, page 58. The graphic interpolation led to a formula — 
w 1 = (w c o), + «, x (60 — h ) . 
As the specific gravity of the sea-water at 1 7 was about 1-028, the value ought to have 
1-028 x a. Unfortunately I had great latitude in drawing my two lines, and so 
it • am* that this relation did not hold at all exactly. I therefore took the mean of a and 
of j 0 !, s as applying t<> pure, and the multiple of this mean by T 028 as applying to the 
■ r, slightly altering the constant terms on both sides, so as to keep the lines 
fairly within their respective dots on the diagram. I thus obtained for the total weight 
of t.. !) instrument standing at A mm. ill .'■•a-watt r wliat forms the numerator, 
a d tor th«- « on-' -p aiding weight for pure water what forms the denominator in the 
following formula : — 
165-077 +(60- A) x Q ‘00868 . 
i« ;^i7 - 160-579 + (60 - A) x 0 00845 * 
As 
166-077 
160-579 
x Q'00845, 
0 008G8 = Sx 0-00845 
