176 
LORD RAYLEIGH AND MRS. SIDGWICK 
only amounts to about a thousandth part, even a ten per cent, error in our estimate 
would scarcely be material. 
Let r = resistance of a column of mercury 1 metre long and 1 square millimetre 
in section, at 0°, expressed in B.A. units. 
R =r resistance of the tube full of mercury at 0° in B.A. units. 
L = length of the tube at t'° in centimetres as measured with brass rod. 
I = length of a thread of mercury of nearly the length of the tube at f as 
measured with brass rod. 
W = weight of the same thread in grammes. 
t jl = coefficient correcting for conicality of tube. 
8L = correction to L on account of the connecting rods not being close up to 
the ends of the tube ='82 X diameter of tube. 
p — specific gravity of mercury at 0° — 13'595. 
y = cubic expansion of mercury per degree = ’0001795. 
g = „ glass „ = ’000025. 
b = linear expansion of brass „ = ’000018. 
t 0 = temperature of brass measuring rod to which the lengths are corrected 
= 17°’2. 
Then the volume of the thread at 0° = W /p 
>> „ t° = -(1+yt) 
Mean section of the tube at f = 
Mean section at 0° 
W(1 + yt ) 
pl{l + b ( t — Q } 
W(1 + jt ) 
pl{l + b ( i —^ 0 )} {l + $ gt } 
Length of the tube at 0° = (L + gL){1 +M-h)} 
-n in -4. (L + 8L){1 + b ( t ' — 1 0 )} pl{l + b ( t . — ^q)}{1 + |^} 
1 + W ‘ W(1 + yt ) 
r= 
lffiEW(l+ 7 0(l+^O/ n 2L 
pp /L(l + |y0 
1 — 
{1 — b(t + t'—2t 0 )} 
The value of p is that used by the Committee of the British Association in reducing 
Dr. Matthiessen’s experiments (see reprint of ‘ Reports on Electrical Standards,’ 
p. 114), and stated to be the mean of the values given by Kopp, Regnault, and 
Balfour Stewart. The values of g, y, and b are taken from Everett’s ‘Units and 
Physical Constants ’ — y being Regnault’s value for the expansion of mercury. The 
measurements of the other quantities, which depend on the particular tube used, are 
given in the following table, together with the resulting value of r. The description 
of the means employed to obtain these data follows. 
