ELASTICITY. 



edfrom their natural position ; whence all 

 bodies will in such cases exert a spring or 

 force to restore themselves, in the same 

 manner that the bent wire did. Others 

 attribute the elasticity of all hard bodies 

 to the force of the air included within 

 them : and so they make the elastic force 

 of the air the principle of elasticity in all 

 other bodies. Se.e PNEUMATICS. 



All substances that we know of are in 

 some degree or other elastic, but none of 

 them perfectly so ; such are most metals, 

 semi-metals, stones, and animal and vege- 

 table substances, however they may differ 

 in degree. 



We may consider all elastic bodies to 

 be made up of such strings or fibres as 

 A B (Plate IV. Miscel. fig. 9.) or rather 

 of elastic strata parallel to eaeh other, re- 

 presented by A B in the ball D C. If this 

 ball be struck at D by a hard or elastic 

 body, all the strata will be bent in towards 



C, as expressed by the dotted lines, 

 whilst the ball is flattened or dented at 



D. But the strata quickly restoring them- 

 selves, the surface of the ball re-assumes 

 its first, figure, and that more or less ex- 

 actly, according as the elasticity is more 

 or less perfect. 



The great law of perfectly elastic bo- 

 dies is, that their relative velocity will re- 

 main the same before and after collision ; 

 that is, perfectly elastic bodies will re- 

 cede from one another after the stroke, 

 with the same velocity that they came to- 

 gether. Many curious phenomena may 

 be explained from this property in bo- 

 dies. 



If the ivory ball A, (fig. 10.) weighing 

 two ounces, strike with the velocity 16 

 against B at rest, weighing also two oun- 

 ces, the body B will move forward after 

 the stroke with the velocity 16, A remain- 

 ing at rest in its place. The reason of 

 this is, that the body A loses one half of 

 its motion by striking the equal body B, 

 aid. the other half by the elasticity of B 

 recovering its former figure. From this 

 experiment, several curious phenomena 

 arise : thus, if a row of shovel-board 

 pieces (that is, metalline cylinders of 

 about half an inch in height, and two 

 inches diameter) be laid upon a smooth 

 table, and you take a single piece, and 

 drive it against the row, the last piece of 

 the row will fly off; for if A (fig. 11.} 

 strike the row of pieces, B, C, D, E, F, G, 

 H, I, in the direction A a, then will the 

 last piece I fly off to i with the same ve- 

 locity that A struck B : and whatever be 

 the velocity of A, no other piece but the 

 last piece I will fly off. But if you take 



two pieces, as A and B, (fig. 12.) and 

 strike them together against the row C,D 

 B, F, G, H, I, the two last pieces, H and 

 I, will fly off from the other end of the 

 row, with the same velocity that A and 

 B made the stroke. 



If three or more pieces are made use 

 of to make the stroke, the very same num- 

 ber will fly off from the other end of the 

 row ; and it is to be observed, that the 

 same will happen with equal elastic balls, 

 suspended in a row by strings of the same 

 length. 



Again, if the elastic body A, (fig. 13.) 

 weighing four ounces, strike the quies- 

 cent body B, weighing only two ounces, 

 with a velocity equal to 12 ; then will 

 the velocity ot A, after the stroke, be 4, 

 and that of B 16. Just the reverse of 

 this happens when a lesser body strikes 

 against the greater : in which case, the 

 striking, or lesser body, will be reflected 

 with one-fourth of its first motion, and the 

 greater be carried forward with a motion 

 which is as 16. 



The magnitude and motions of spheri- 

 cal bodies perfectly elastic, and moving 

 in the same right line, and meeting each 

 other, being given, their motion after 

 reflection may be determined thus : let 

 the bodies be called A and B, and the re- 

 spective velocities a and b ; then, if the 

 bodies tend the same way, and A, moving 

 swifter than B, follows.it, the velocity of 

 the body A, after the reflection, will be 



A -j- D 



, and that of thebody B= 



; but if the bodies meet> 

 A f- B 

 then changing the sine of b, the velocity 



ofA W iIlbe" A -" flB ~ 2 -; and that 



A-f-B 



- :and if either 



of B= 



A -f- B 



of these happen to come out negative, 

 the motion after the stroke tends the 

 contrary way to that of A before it ; which 

 is also to be understood of the motion of 

 the body A in the first case. 



ELATE, in botany, a genus of the 

 Appendix Palmx. Natural order of Palms. 

 Essential character: male, calyx three- 

 toothed; corolla three-petailed; anthers 

 six, sessile. Female, calyx one-leafed ; 

 corolla three-petailed ; pistil one ; stig- 

 mas three ; drupe one-seeded. There is 

 but one species, viz. E. sylvestris, prickly 

 leaved elate. This palm grows to the 

 height of fourteen feet, covered with an 





