1895.] in Geometrical Optics. 313 



other line. The problem is to find pairs of points on the two lines 

 which are in homography with these pairs. The graphical solution 

 is to regard the three lines AiA.,, BiB.,, C\C.,, the two given lines 

 A^B^Ci and A^BJJ.,, and the unknown line through D^, arranged in 

 any order, as the sides of a hexagram, when the lines connecting 

 opposite corners will meet in a point. We might then find the 

 elongation corresponding to the conjugate points D^ and D.2,, by 

 determining the conjugate E.2 of a point E^ very near to D^, and 

 taking the limit of the ratio D^E^ to D^E^ . And then the transverse 

 magnification will be derived from the theorem, which might be 

 conveniently named after Maxwell, that the elongation of any 

 finite segment on the axis is equal to the ratio of the extreme 

 indices multiplied by the product of the transverse magnifications 

 corresponding to its two ends. 



But there is a much simpler course open. Let the given 

 foci be laid off so that a pair of them coincide at the point 

 of intersection of the lines : then the lines connecting all 

 other pairs will pass through a fixed point, which is at once 

 determined. The principal foci will be obtained by drawing 

 parallels to each of these lines through the fixed point ; and the 

 product of the principal focal lengths will be equal to the product 

 of the distances of any pair of conjugate foci from the respective 

 principal foci. As the ratio of the focal lengths is that of the 

 extreme indices, their values, involving the positions of the 

 Gaussian principal points, are known except as to sign. Whether 

 the positive or negative sign is to be taken, requires the further 

 knowledge of whether the image of some one object is erect or 

 inverted ; there being always two optical systems, with equal and 

 opposite focal lengths, that give the same relation of conjugate foci 

 along the axes. The cardinal points being thus determined, 

 everything else follows as usual.] 



(2) Note on the Steady Motion of a Viscous Incompressible 

 Fluid. By J. Brill, M.A., St John's College. 



1. My object in the present communication is to obtain the 

 analogues for the viscous fluid of certain well-known theorems 

 relating to the perfect fluid. I suppose the fluid to be homo- 

 geneous and incompressible, and the motion to be steady; and 

 proceed first to consider the case of two-dimensional motion. If 

 we write 



p 



