538 FOURTH REPORT — 1834. 



each body contributes a portion of its own proper elasticity in 

 proportion to its relative compressibility. Hence in collisions 

 between bodies whose hardness differs in any other degree, it 

 seems natural to conclude that the same law is preserved. 



To exhibit this in a form capable of submitting it to the test 

 of experiment : Let a and h represent the relative hardness of 

 two bodies, a! and V their respective elasticities, to find the 

 elasticity resulting from their coUision. 



Since in bodies considered as springs the compression of 

 each is inversely as the hardness, or resistance to compression, 



calling — = the compression of the first body, we have 



b 

 Whence — "^ T" ~ ^^^ compression from the two. 



= the compression of the second. 



1_ 



b 



a 

 J_ 



.*. -; r- = — r~r = thfi compression from the first 



I J^ a + b * 



a b 



body in terms of the whole compression. 



J_ 



b a . • P , 



"1 r = — ; — 1 = the compression rroni the se- 



II a + b '■ 



a b 



cond, in terms of the whole. 



But by the 7th Conclusion, 



^ "' — the elasticity contributed, by the first 



body ; 



+ b 



a + b 



X b' = the elasticity from the second. 



Whence their sum j — = the required elasticity from 



both. 



The modulus of elasticity seems to afford the best means of 

 judging of the relative powers of bodies to resist incipient com^- 

 pression. I have therefore selected that datum from Tredgold's 

 Essay on Cast Iron, in the few cases that answered my purpose, 



