6 Sir G. Greenhill on 



A skater, then, who can progress up to this minimum 

 value or! U and beyond, is able to place himself at will at 

 any point of the ice-wave he forms, say a little beyond the 

 crest, so as to have the advantage of the downhill ; and if 

 the ice should crack he will be able to escape. 



Then V has the special value given in (2), 



/V»\* W 2 k \ V 2 /l,xi /k\i ^ 



\Te)=T&=& s=7 = U^ = 'te)- • (3) 



With the value of k above in § 3, this works out for ice : 



\=2< 



(H 



V 



u 



6. But when the depth h is small compared with X, say 

 h/\<jr, the variation in think becomes sensible. 



For a value of h still smaller, replacing thmh by mh, 



One inch thick. 



Two inches thi 



1 

 12 



£, foot. 



26 



44, feet. 



11-5 



15, f/s 



13*2 



17-25, f/s 



(9) 



(12), m/h 



V 2 = 





4 & 



1 + w 2 ^/i 



(i) 



and U is large when X is a fraction of e ; but as \ becomes 

 a large multiple of e, U 2 tends to a limit 



*-H£y*]«* j • • • • (2 > 



su that a long flat wave in ice of thickness e on water of 

 uniform depth h will have velocity 



7. The value of E and k was determined experimentally 

 by B. Bevan (Phil. Trans. 1826, H. of E. p. 189) with a 

 cantilever of ice, cut out as a tongue except for one end ; of 



