305 
and third members to those portions in which the temperature is 
uniform. 
If we further write 
m—m, ‚ m, 
a Pp, = 4,7, — een 
1 Ds 
7 
ae ee 
v 
in which v, represents the volume at the lower temperature, v, that 
at ordinary temperature, and 7 the total mass, and then integrate 
(9) we obtain, with the omission of an integration constant 
ry) 
‘ 
ati 
m—m,) + ——m 
Ve ( ) Koen nRa, 
if = == ae es : 
og 5 IK (11) *) 
(m—m,) — 
~ 
is 
The case discussed in $ 3 and graphed in fig. 1 gives an example 
of the curves given by this equation. 
§ 3. Application to a special case. Deductions. 
From measurements made during the experiment of 18 July 1911 
temperatures were to be taken as 
—258° C. for 10 em. in the liquid bath 
— 228° Be teem: 
ed Ma ce gt sine 
— 25° 5( 14 em. 
Room temp. at + 22°  ,, 22 em. projecting outside the cryostat. 
For the calculation of (2) the temperature of each portion is 
regarded as the temperature at its centre. 
Wer imneremre eee. 4 — 10 2,11, 7,215, TT, = 299; 
and from «= 10 to c= 49 equation (2) holds with the values 
g=166 L,—=0389 m,; = —0,00278 n, = 0,00000682 ; 
1) In the simpie case in which p,+p, may be regarded as constant, and 
T,=T,, m=v, d+v,d in which d is the common density in both vessels, 
substitution of (10) in (11) gives 
U,V, Cs 
og es 
C,(v, + %) PTP: 
The subscript 4 is here replaced by 2. 
This is the formula given by RAyLetGH Scientif. papers Vol. IV 1892—1901 - 
p. 53. This formula does not hold for instance for the evacuation of a vessel by 
a pump through a capillary, to which (11) is applicable as long as the pressure 
is not so small that the mean free path becomes comparable with the diameter 
of the capillary. 
