536 FOURTH REPORT — 1834. 



other bodies increasing in hardness : thus, malleable clay, stone, 

 hard-baked clay, glass, give elasticities of about '17, "79, '89, 

 •94. (Expts. 18, 27, 29, 24.) 



Conclusion 2. There are no perfectly hard inelastic bodies, 

 as assumed by the earlier, and some modern, writers on me- 

 chanics. 



If Conclusion 1. be true, this will follow as a consequence, 

 the proofs of both being of the same nature. 



Conclusion 3. The elasticity, as measured by the velocity 

 of recoil divided by the velocity of impact, is a ratio which 

 (though decreasing as the velocity increases,) is nearly constant, 

 when the same rigid bodies are struck together with consider- 

 ably different velocities. 



The proofs of this are very numerous ; they may be taken 

 (with some anomalies,) from almost every experiment. In ex- 

 periments 1 and 2, cast-iron balls striking together with ve- 

 locities as 4, 6, 8, 10, 12, gave, in the one case, elasticities 

 •69, -66, '66, '61, '59; and in the other case '70, '69, '66, '64, 

 •62. In expei'iments 10 and 11, balls of soft brass struck to- 

 gether with velocities varying from 4 to 20, gave for their elas- 

 ticities '38, •37, '36, '30, '33; and even lead, which permanently 

 changes its figure at evei'y impact, preserves considerable ap- 

 proximation to equality in its elasticities, as may be seen from 

 Experiments 13 and 14. The same may be said of other bo- 

 dies besides metals, as will be evident by inspection of the 

 tables of results ; the irregularity and decrease of elasticity 

 being greater in those bodies that least recover their forms 

 after impact. It is probable, too, that the decrease of elasticity, 

 in some bodies, from the larger impacts, is somewhat less than 

 as indicated in the table, on account of the great difficulty then 

 of obtaining perfectly central impacts. 



Conclusion 4. The elasticity, as defined in Conclusion 3, is 

 the same whether the impinging bodies be great or small. 



This fact is proved by Experiments 1, 2, and 20, in which 

 the elasticities of cast iron are "64, '66, and '73 ; differing in 

 the first and second experiments only ^j, though the weights of 

 the equal balls in experiment 1 are more than five times the 

 weight of those in experiment 2. In the 1st and 20th experi- 

 ment, the difference of elasticity is but ^th, though the balls 

 vai'y in weight as 74 to 1 . 



Conclusions. The elasticity is the same, whatever be the 

 relative weights of the impinging bodies. 



This will be shown by comparing the results of expei'iments 

 5 and 58, in which the same stone ball was struck against two 

 balls of cast iron, one 33 times as heavy as the other ; the elaa- 



