THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[SIXTH SERIES.] 



JANUARY 1916. 



I. Skating on Thin Ice. By Sir Gr. G-reenhill *. 



THIS title is used metaphorically to describe a method of 

 argument which glides so rapidly over the facts as to 

 be able to dispense with their support, but will not bear 

 to be arrested to examine a detail or difficulty. 



It is derived from the action of a skater, when he is able 

 to go so fast over ice as to ride on the top of a wave, and to 

 change his place so rapidly as not to allow time to break 

 through, although the ice is not thick enough to support his 

 dead weight at rest. 



Analogous action is to be seen in the motion of a bicycle, 

 or of an express train over an elastic bridge. 



So, too, a chain in rapid motion, a jet of water, or a 

 gyroscopic flywheel may be hammered with a stick, harder 

 and harder, without flinching to an appreciable extent. 



1. The mathematical theory is an extension of Sir William 

 Thomson's investigation in the Philosophical Magazine, 

 November 1871 (reprinted in 'Mathematical and Physical 

 Papers/ vol. iv.), of the propagation of waves and ripples 

 in water, and the tremble of a dewdrop ; resumed in 

 Lamb's ' Hydrodynamics,' and by J. R. Wilton, Phil. Mag. 

 May 1915. 



Sir W. Thomson shows that the ripples are not propagated 

 below a certain minimum velocity. 



* Communicated by the Author. 

 Phil. Mag. S. 6. Vol. 31. No. 181. Jan. 1916. B 



