Royal Society. 303 



Each primitive function must satisfy the condition 

 / d 1 d- d- \, n 

 \dx a -^dy^dz q J 

 and may belong to one or other of eight classes, according as it is 

 even or odd with respect to x, y and z. 



The processes of derivation applicable to the primitive functions 

 contain three arbitrary constants for each primitive function. Hence 

 when there is a series of primitive functions of different orders, there 

 are twenty-four arbitrary constants for each order of terms. 



In the developments of the residual external pressures, there are 

 also twenty-four constant coefficients for each order of terms, of 

 which the arbitrary constants are linear functions. 



The notation of M. Lame's work on the Mathematical Theory of 

 the Elasticity of Solid Bodies, so far as it relates to isotropic sub- 

 stances, is compared with that of this paper. 



Reference being made to the known method of representing the 

 elastic pressures at a given particle of a solid, in magnitude and di- 

 rection, by the radii of an ellipsoid, and the positions of the surfaces 

 to which those pressures are applied by those of the tangent planes 

 to an ellipsoid or hyperboloid, the difference (not generally attended 

 to) between the cone of tangential pressures, and the cone of sliding, 

 is pointed out. This difference is important in the theory of the 

 strength of materials. 



January 18, 1S55. — Sir Benjamin Brodie, Bart., in the Chair. 



A paper was in part read, entitled " Ocular Spectres and Struc- 

 tures as Mutual Exponents." By James Jago, A.B. Cantab., 

 M.B. Oxon. 



The paper opens by stating that for want of a methodical elimi- 

 nation of ocular spectres from one another — a want which its aim is 

 to meet— physiological optics remain to this day without any real 

 foundation ; and even when we have followed the rays of light 

 through all the refracting media of the eye, we cannot safely assert 

 what sensations belong to them until we have detected everything 

 connected with the percipient membrane which may obstruct the 

 action of light on it, or which may originate sensations as of light 

 through other sorts of impulses. Our eyes in many important re- 

 spects provide us with an opportunity for microscopical research 

 that no optical instrument employed on the dead eye can rival. We 

 may thus gather a variety of information, physical and physiological, 

 solve points of ocular structure that escape other means of investi- 

 gation, and bring a profusion of ingenious speculations to a termina- 

 tion, by showing that the phenomena (and this is especially true of 

 the retinal phenomena) which have occasioned them are simply 

 exponential of anatomical facts ; and important physiological laws 

 may be arrived at by like means. 



The first step in the author's task is to determine the conditions 

 which render objects existing upon or within the eye visible by their 

 shadows, and to obtain optical principles by which we may examine 



J'/til. Mag. S. 4. Vol. 9. No. 59. April L8B5. X 



