441 



Monday, May 23rd, 1853. 



THOMAS ROMNEY ROBINSON, D. D., President, 

 in the Chair. 



Sir William Betham 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 

 Sx, Sy, 8z, 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 of a 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 dz d-z d 2 z d 2 z 



dx* dy dx 2 ' dxdy* dy 2 * 



2 u 2 



