296 



The second case related to the torsion of cylindric rods, and a 

 method was given by which m may be found. The quantity 



E = — ']i2!L- was found by elongating, or by bending the rod 

 m + 6 n 



used to determine m, and fju is found by the equation, 



_ Em 

 ^ ~ 9m-6~E" 



The effect of pressure on the surfaces of a hollow sphere or cylin- 

 der was calculated, and the result applied to the determination of the 

 cubical compressibility of liquids and solids. 



An expression was found for the curvature of an elastic plate ex- 

 posed to pressure on one side ; and" the state of cylinders acted on by 

 centrifugal force and by heat was determined. 



The principle of the superposition of compressions and pressures 

 was applied to the case of a bent beam, and a formula was given to 

 determine E from the deflection of a beam supported at both ends 

 and loaded at the middle. 



The paper concluded with a conjecture, that as the quantity w, 

 (which expresses the relation of the inequality of pressure in a solid 

 to the doubly-refracting force produced) is probably a function of m ; 

 the determination of these quantities for different substances might 

 lead to a more complete theory of double refraction, and extend our 

 knowledge of the laws of optics. 



2. Two Letters from W. E. Logan, Esq., to Earl Cathcart. 



These letters were dated in August 1846 and September ISiV- 

 Earl Cathcart intended himself to have read them to the Society, 

 but, having been pi-evented by his oflficial duties from coming to 

 Edinburgh, had sent them, to be communicated in his name. 



In the first letter, the author, who had been sent to examine the 

 geology of Canada, describes a visit which he made, on his way to 

 Fort- William, Lake Superior, to the silver and copper mines on the 

 south side of the lake, in the territory of the United States. 



He considers the formation in which the mines occur as being 

 older than the new red. They consist of parallel ranges of trap 

 and conglomerate, apparently interstratified. They are well displayed 

 at and near Copper Harbour. They are sometimes so thick as to 



