Skating on Thin Ice. 3 



Neither E nor W is given numerically in the list of 

 Everett's ' Units and Physical Constants,' or in the ' Smith- 

 sonian Tables of Physical Constants ' either, although it 

 is curious as mathematical history that Ice was the 

 first substance of: which the Modulus of Elasticity was 

 defined and measured by Bevan and Young (Phil. Trans. 

 1826; Todhunter-Pearson, 'History of Elasticity,' p. 189). 



3. Thomas Young measures the elasticity of a substance 



F 



by — , a length, k suppose, called the elastic length, such that 



r 



for a small fraction fk of this length, of uniform cross section, 

 hanging vertically, or standing up supported, the material 

 would be stretched or compressed, at the top or bottom end, 

 hj an extension or compression /. 



k 

 Thus a length ^a nan gi n g vertically would be stretched 



•one per cent at the top. 



Or otherwise, n times the length producing extension 



- will give k, the elastic length. 



So, too, the tenacity or breaking tension may be defined 

 by the breaking length, as of an icicle ; and the stress in 

 the material must be designed in a structure so as to be kept 

 well below the limit of tenacity, for the material to recover 

 itself, and obey the laws of Mathematical Elasticity. 



In the 'History of Elasticity' (H. of E.) p. 189, k is 

 taken in feet as 2,100,000 — say twenty-five million inches, 

 or two million feet, one-tenth of the value given in Thomson 

 .and Tait's 'Natural Philosophy' § 686. 



This makes W= \/(gk) = b000 f/s, nearly eight times 

 sound-velocity in air ; and so explains the story quoted in 

 Ganot's ' Physics ' from Parry's * Arctic Voyages,' where 

 at some distance the sound of the gun fired on the ice was 

 heard before the word of command to fire ; the report of 

 the <iun being transmitted through the ice and so overtaking 

 the sound through the air and arriving ahead. 



So also in an experiment on long-range fire, the report 

 is heard on the telephone long before the sound is trans- 

 mitted by air. And the crack of a rifle is carried along by a 

 high-velocity bullet, moving faster than ordinary sound, and 

 will be heard up the range a little to one side when the 

 resolved part of the bullet velocity in the direction of the ear 

 is equal to the ordinary sound velocity ; the sound through 

 the air from the muzzle is heard appreciably later. 



B2 



