66 
high repute for the medicinal qualities of its water, more 
especially in the cure of various cutaneous disorders, but at 
the present time it is seldom visited except from curiosity, 
though a few of the country people around seem to have a 
lingering belief in its virtues. 
For some of the figures in the above analyses we owe our 
thanks to Mr. Chaster, late a student of the Owens College. 
Since the above was written, our attention has been 
directed to an analysis of the water of this spring, published 
in the year 1868 in the Journal of the Chemical Society 
(2nd Series VI 20), by T. E. Thorpe, (now F.E.S.), in which 
the Author gives more minute details of the constituents of 
the water, than we have done in this paper, but which in 
the main shows that the quality of the water remains very 
constant. The exception to this is in the amount of Potash, 
which in our case (calculated from the amounts of acid and 
base) is very mnch larger than in Thorpe’s analysis. We 
hope at a later date to perform other and more minute 
analyses of this spring, in order to see as far as possible 
whether this uniformity is still maintained. 
“ On Ternary Differential Equations,” by Sir James 
Cockle, F.RS., Corresponding Member of the Society. 
1. Suppose that the criterion of integrability is not satis- 
fied for 
■dz = M.dx + ^dy (1) 
and is satisfied for 
dz—pdx-\-qdy (2) 
which is the same thing as supposing that when 
<xM 
dy dz 
dN" TT 1 dp dp 
- = U and ^ + q 
dx 
dz 
dq dq 
dy ^ dz dx ^ dz 
= u. 
then U is finite and u is identically null. 
2. Using D to denote total and d partial differentiation, 
we may write the last two equations in the respective 
forms 
