430 
The phase of the fluid is such that # is positive for all 
phases differing slightly from its own phase, and its equilibrium 
is therefore stable, but for certain widely different phases, 
namely, ice, cryohydrate and anhydrous salt, K is negative. 
If none of these substances are in contact with the fluid, the 
fluid cannot alter in phase without a transport of matter 
through a finite distance, and is therefore stable; but if any one 
of them is in contact with the fluid, part of the fluid is enabled 
to pass into a phase in which K is negative. The conditions of 
consistent phases are that the values of 0, p, m,...~,, and K are 
equal for all phases which can coexist in equilibrium, the sur- 
face of contact being plane. 
This was illustrated by Mr Main’s experiments on co-exist- 
ent phases of mixtures of chloroform, alcohol and water. 
Monpay, May 22, 1876. 
THE PRESIDENT (PROFESSOR CLERK MAXWELL) in the Chair. 
The following communication was made to the Society : 
On Curvilinear and Normal Co-ordinates. By the 
Rev. J. W. Warren, M.A. (Communicated by 
Prof, Cay.ezy.) 
Tue Memoir refers partly to the general theory of curvilinear 
co-ordinates, partly to the special case of normal co-ordinates. 
Taking (wu, v, w) each of them a given function of the rect- 
angular co-ordinates (#, y, z), so that a point is determined 
either by its rectangular co-ordinates (#, y, z) or by its curvi- 
linear co-ordinates (uw, v, w), and writing 
dx? + dy’ + dz = (a, b, ¢, f, g, h) (du, dv, dw)*, 
