358 Mr J. Brill, On Solutions of Differential Equations. [May 20, 
We may now assume 
Ou ag 
ay (yf at — yf?) —c'}8((ary' — 64) (y? — a’) 
Ou a? 
and — = = —, 
da [a Qa? — a) — oF (ae? 0) — a) 
and then we may complete the solution in the usual manner. 
9. In the last two cases, in accordance with a remark made 
in Article 3, it is evident that we cannot tell a priori whether we 
have hit upon the solution we are in search of, or whether we 
have hit upon one referring to a more complicated form of boundary 
containing portions of the given curves as parts. This matter can 
only be tested by working out the solution to the end, although 
it is not a priort improbable that the simplest solution obtainable 
may be the one required. Our difficulties are also increased by 
the fact that, as our original transformation is an imaginary one, 
there is not a real point for point correspondence between the two 
diagrams. However, in the case worked out in Article 5, to every 
circle whose radius lies in magnitude between a and b there cor- 
responds a rectangular hyperbola lying between the curves vy = a” 
and #y=b’; and consequently the region between the two rect- 
angular hyperbolas may be said to correspond in a certain sense 
to the region between the two circles. A similar remark will 
apply to the case worked out in Article 6; and it is not improbable 
that a similar statement will apply to every case. 
May 20, 1889. 
Mer J. W. CLARK, PRESIDENT, IN THE CHAIR. 
A. C. Dixon, B.A., Trinity College, 
was elected a Fellow of the Society. 
The PRESIDENT announced that Prof. Sir G. G. Stokes, Bart., 
Sir William Thomson, and Lord Rayleigh, the adjudicators of the 
Hopkins Prize for the period 1877—1879, have awarded the prize 
to Professor G. H. Darwin, F.R.S., for his researches on the 
Physics of the Karth. 
The following Communications were made: 
(1) On the change of shape in turgescent pith. By Miss A. 
Bateson, Newnham College, and F. Darwin, M.A., Christ’s College. 
The experiments were as follows. Small blocks, cut from the 
turgescent pith of various plants, were placed in water, and the 
