216 MEMOIR OF EATON HODGKINSON. 



7. In impacts between bodies whose hardness differs in any degree, the result- 

 ing elasticity is made up of the elasticities of both, each contributing a part of 

 its own elasticity in proportion to its relative softness or compressibility. 



1'he following rule, given by Mr. Hodgkinson, agrees remarkably well with 

 the results of experiments : 



Let £ =the elasticity of A) ,, -j-.*,.,. . .- 



^/_ u -^ B ( ^^ determined by A strikmg agamst A, &c. 



w =modulus of elasticity of A ) as determined by extending the material 

 'in':= . " B ) in the ordinary way. 



Then the elasticity of A against B=^ — ptf — 

 •^ * m' + m 



This paper concludes with a table of elasticities of 60 various substances used 

 in the construction of. buildings, &c. 



The Fifth Report of the British Association contains a paper on the " Impact 

 of Beams." * 



The author has deduced from the experiments the following laws : 



1. If different bodies of equal weight, but diflfering considerably 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 force, the deflection of the beam will be the 

 same, whichever body be used. 



3. The quantity of recoil in a body, after striking against a beam as above, is 

 nearly equal to what would arise from the full varying pressure of a perfectly 

 elastic beam as it recovered its form after deflection. 



4. The effects of bodies of different natures striking against a hard, flexible 

 beam seem to be independent of the elasticities of the bodies, and may be cal- 

 culated, with trifling error, on a supposition that they are inelastic. 



5. The power of a uniform beam to resist a blow given horizontally is the 

 same in whatever part it is struck. 



6. The power of a heavy uniform beam to resist a horizontal impact is to the 

 power of a very light one as half the weight of the beam, added to the weight 

 of the striking body, is to the weight of the striking body alone. 



7. The power of a uniform beam to resist fracture from a light body falling 

 upon it (the strength and flexibility of the beam being the same) is greater 

 as its weight increases, and greatest when' the weight of half the beam, added 

 to that of the striking body, is nearly equal to one-third of the weight which 

 wckild break the beam by pressure. 



There can be but one opinion as to the importance of these deductions, direct 

 from the voice of nature, made, as they were, at a time when such an appeal was 

 by no means common. 



There are several interesting problems on impact, of a high mathematical 

 character, solved in this paper. In these inquiries Mr. Hodgkinson is very 

 particular in acknowledging his many obligations to his friend Mr. Fairbairn, 

 engineer, of Manchester, to whose labors and liberality practical science is deeply 

 indebted. 



We now pass on to notice his contributions to the transactions of the Eoyal 

 Society. 



In the Philosophical Transactions for 1840 there is an extensive inquiry by Mr. 

 Hodgkinson, " On the Strength of Pillars of Cast Iron and other Materials." 



The object of this inquiry is to suppl}?^ a desideratum in practical mechanics, 

 which had been pointed out by Dr. Eobison and Professor Barlow. In order 

 to accomplish this it was necessary to institute a series of expensive experiments 

 more varied and extensive than any which had hitherto been made public. The 



