441 
Monpay, May 23rp, 1853. 
THOMAS ROMNEY ROBINSON, D.D., Presipent, 
in the Chair. 
se S.-Y 
Pe ee 
Sir Wituiam Betuam read a letter from W. D. Haggard, 
Esq., accompanying two thin discs of silver, used for over- 
laying modern forgeries of Spanish dollars, in illustration of 
the forgeries of the old Scottish coins exhibited to the Aca- 
demy by Dr. A. Smith (see Proceedings, vol. v. p. 324). 
: Rev. Professor Jellett read a paper on the properties of 
__-inextensible surfaces. 
, Adopting Gauss’s definition of an inextensible surface, 
namely, “A surface in which the length of any curve arbi- 
trarily traced upon it is invariable,” the author has proceeded 
to consider the conditions which the displacements of the se- 
veral points of any such surface must fulfil. Denoting by 
x, y, z, the co-ordinates of any point on the surface, and by 
éz, dy, dz, the displacements of this point parallel respectively 
to the three axes of co-ordinates, he finds that these quan- 
tities are connected by a system of three partial differential 
equations of the first order, and ofa very simple form. He 
finds also, that any one of these displacements may be deter- 
mined by a single partial differential equation of the second 
order. Some interesting results follow at once from these 
general equations. Thus, for example, it is easily shown that 
if the displacements be all parallel to the same plane, the sur- 
face will move as a rigid body. 
Having established these fundamental equations, the au- 
thor has proceeded to deduce general expressions for the 
variations which the differential coefficients 
dz Oe i A wel 
ax’ dy’ ax’ dxdy’ dy” 
2u2 
