MEMOIR OF THE LATE PROP. E. HODGKINSON^ F.R.S. 173 



5. The elasticity is tlie same, whatever be the relative 

 weights of the impinging bodies. 



6. On impacts between bodies differing very much in 

 hardness, the elasticity with which they separate is nearly 

 that of the softer body. 



7. In impacts between bodies whose hardness differs in 

 any degree, the resulting elasticity is made up of the elas- 

 ticities of both, each contributing a part of its own elasticity 

 in proportion to its relative softness or compressibility. 



The following rule, given by Mr. Hodgkinson, agrees 

 remarkably well with the results of experiments : — 



Let € =the elasticity of A] as determined by A strik- 

 e' = do. B J ing against A, &c. 



' as determined by 

 ?w = modulus of elasticity of A extending the 



m'= do. B material in the 



^ ordinary way. 



Then the elasticity of A against B= -, . 



'' m' + m 



This paper concludes with a table of elasticities of sixty 

 various substances used in the construction of build- 

 ings, &c. 



The Fifth Report of the British Association contains a 

 paper on the " Impact of Beams.^^ 



The author has deduced from the experiments the fol- 

 lowing laws : — 



1 . If different bodies of equal weight, but differing con- 

 siderably in hardness and elastic force, be made to strike 

 horizontally with the same velocity against the middle of a 

 heavy beam supported at its ends, all the bodies will recoil 

 with velocities equal to one another. 



2. If, as before, a beam be struck horizontally by bodies 

 of the same weight, but different in hardness and elastic 



