On the Resilience of Malcrials ; with Experiments. 2/7 



Icrably correct data to go upon ; and that the theory is imper- 

 fect, in as far as it does not include the whole of the principal 

 circumstancee affecting the case in question. 



In the first place, I propose to lay before you the invest'- 

 gation according to which the heights of the falls were com- 

 puted. 2dlv, Some additional experiments : and then conclude 

 with some ohservations on the probable cause of the difference 

 between the theoretical and experimental results. 



I. Put i = the strength, or weight that would break a bar sup- 

 ported at both ends; G = the deflexion at the time of fracture; 

 *=any variable degree of deflexion; W = the weight; A = the 

 height of the fall ; zi' = the weight of the bar ; and V Agh — i\iQ 

 velocity with which W strikes the bar. 



So? 



Then a : .r : : S : — =the motive force atany deflexion x; cou- 



S X 



sequentlv —rrrr = the accelerative force there. 



* •'a ( W + w} 



By mechanics— fi'=2£f/'i= "",' ' , : of which the fluen:? 

 are — v^= — ^r — : ; but when z — o,v^ = ^^h. : therefore Ash — 

 v'^ — "fy ^ , . Also, when x=c^ i;=o; consequently 4gA= 



CfS/i ,__ Sa ^ 



It is shown by writers on the resistance of solids, that at the 

 time of fracture S is inversely as / ; / being the length, and tha^ 

 a is directly as P. Hence, all other things being equal, we have 

 h is as I. 



The resilience of bodies has been considered by Emerson, in 

 his Fluxions, sect. 3, prop. 21, p. 404 ; and by Dr. Thomas 

 Young in his Nat. Phil. vol. ii. art. 337 ; and their conclusions 

 are the same as those above stated. 



Experimetits on the Resilience of Timber. 



II. As Memelor Riga timber, when it is straight-erained, and 

 the portions of the annual rings vertical, almost always breaks 

 short or without splinters, it afforded an opportunity of trying 

 each piece thrice ; and the same was done with some of the others, 

 when the splinters did not extend too far along he piece. 



To avoid referring to the results given in your last Number f, 



Sx ... 



• The motive force ought to be (W + w), but for the sake of simplicity 



a 

 the quantity (\V + w) is nesrlecteJ, as when it is only very small in respect to S, it 

 does not matpriallv alfect the res-ult. Were it included, the correct solution would 



^Sn-i(\V + w) Sd . . , 



b« *= —- '- = . a : that is, ess than the quantity al)o\e, 



Ahich is itself le.<s than it ought to be. 



t mi. Mag. vol. Ji. p. 216. 



S3 



