Mr. G. G. Stokes in reply to Professor Challis. 55 
change in density, and find it to be 1°35 per cent., which agrees 
well with the sp. gr. found. 
The sp. gr. of the soft sulphur they found = 1:959. It 
rose as the sulphur became hard to 1-98, and when it assumed 
the yellow colour the density was 2'041. 
They found the specific heat of the brown sulphur to be to 
that of the yellow as 1:021: 1. 
The solidifying point of sulphur was found to be 111°5 C.; 
and during the solidification the temperature rose to 113°. 
Weehler has in many cases of dimorphism shown that the 
temperature required for fusion varies in the different condi- 
tions of the bodies.* 
Marchand and Bunsen found the point of fusion of brown 
sulphur to be 112°C., and of the yellowmodification 113° C., 
(Journal fiir Praktische Chemie, xxiv. S. 129-156; und xxv. 
S. 395-398.) 
X. “ OntheAnalytical Condition of Rectilinear Fluid Motion,” 
in Reply to Professor Challis. By G. G. Strokes, B.A., 
Fellow of Pembroke College, Cambridget. 
PROFESSOR Challis has brought forward a new proof of 
his theorem, that when ud xv + vdy + wd s is an exact 
differential the surfaces of displacement are surfaces of equal 
velocity, in which he has not defined the quantity 7 which 
he employs, but only dr. In order that the equation s 
= /V dr should hold good for all points of the arbitrary 
curve PQ, we must evidently have 7 = /cos @ ds, where s 
is the arc of the curve, and 4 the angle between a tangent to 
the curve at any point and the direction of motion at that point. 
Consequently, we must make a distinction between 7 along 
the curve P Q, and r along the trajectory PR. Let the for- 
mer be denoted by 7’, and the latter by 7; then 
, ds ; ds 
velocity at R = a velocity at Q= a” 
The proof therefore falls to the ground ; for, to assume that 
r = 7! would be to assume the theorem to be proved. 
I cannot see where Professor Challis conceives it to be 
proved that da, dy, dz are independent of the time, in the 
equation uda+vdy+wdz=0, which is the differential 
equation to a surface of displacement, supposing the first side 
an exact differential. The instance which he brings forward 
only proves that they may be independent of the time, which 
is not denied; but a single instance where they are not, such 
* See the present number, p. 76, + Communicated by the Author. 
