32 



whose axes to the axis of x will depend upon the inclination 

 of the primitive axis to the same fixed axis. The envelop 

 of this ellipse is given, and also the locus of the extremities 

 of its axes. By means of the relation between the coordi- 

 nates, inverse questions may be solved, viz., given the pro- 

 jected curve to find the primitive. In three dimensions, if 

 an arbitrary curve be traced on the primitive solid and 

 curves drawn on the projected solids passing through the 

 corresponding points, a simple relation may be found among 

 the infinitesimal arcs of these curves. A similar proposition 

 holds in two dimensions, the relation in this case being be- 

 tween the infinitesimal arcs of the perimeters of the primi- 

 tive and its two derivatives. Finally, it is remarked that 

 each projected area may again be regarded as a primitive 

 subject to projection, and if we suppose the operation to be 

 repeated n times, we shall obtain 2** areas, variable if we 

 suppose the primitive to have any motion of rotation, yet 

 subject to the condition that their sum is constant and equal 

 to the primitive area. 



Ordinary Meeting, January 27th, 1885. 



Professor W. C. Williamson, LL.D., F.R.S., President, 

 in the Chair. 



"The Morphology of the Sexual Organs of Hydra/' by 

 Prof. A. MiLNEs Marshall, M.D., D.Sc. 



Hydra stands alone, or almost so, among Hydrozoa, inas- 

 much as its reproductive organs, whether ovaries or testes, 



