208 Mr Greenhill, On the Rotation of a [March 20, 



magnifying powers and not very large object-glasses, the diameter 

 of the aperture next the eye is sometimes reduced to ^th or -^th 

 of au inch, the concentration of rays at this point must be enor- 

 mous. 



It is mainly on these last considerations, that I would suggest, 

 secondly, that while the geometrical theory holds good for the 

 magnification, the great accumulation of rays received through the 

 object-glass, but then concentrated in the comparatively speaking, 

 very narrow eye-piece, or in the pupil of the eye, may create there 

 what may be looked on as a new centre of light, and so produce 

 increased illumination in the eye itself. When the Sun is observed, 

 the intense heat at that point and its power to crack the glasses is 

 well known : and though there is formally no screen there to 

 arrest and exhibit the light, it seems possible that the unexplained 

 result, which certainly seems to be established, may be due in part 

 to this cause. 



(2) On the Rotation of a Liquid Ellipsoid about an Axis, not a 

 Principal Axis, but lying in a Principal Plane. By A. G. Green- 

 hill, M.A. 



In a preceding paper in Vol. IV. Part I. of the Proceedings of 

 the Cambridge Philosophical Society, page 10, it was asserted that 

 it did not appear possible for a liquid ellipsoid to rotate about an 

 axis other than a principal axis and to have a free surface ; but 

 Mr W. M. Hicks has drawn my attention to § 6 of Riemann's 

 article "On the motion of a liquid homogeneous ellipsoid" in the 

 Gottingen Transactions for 1861, where it is asserted that a possible 

 form of equilibrium is obtained for an axis lying in a principal 

 plane of the ellipsoid. 



Recalling the notation of the preceding paper in Vol. IV. 

 Part. I. of the Proc. Camb. Phil. Society, the liquid rilling the 

 ellipsoid 



x 2 if z" , 

 — I- — -I — = 1 



is first supposed to be rotating, as if rigid or frozen, without rela- 

 tive displacement of its parts, about a fixed axis with constant 



