VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 303 



for the mark z ; then set off the distance sv or st from y each way, and from z 

 each way ; and from these points, drawing lines to the respective centres 1 and k, 

 they will give the place and position of the marks a, b, and c, d ; and thus is the 

 machine prepared for use. 



For trials on elastic bodies. — For this use, take out the pins and ratchets from 

 each respectively, and the springs being then at liberty, with a short bit of stick, 

 suppose the same size as the rods, turn aside the rod gh with the right hand, 

 carrying the body d upwards till the stick is on the mark w, as suppose at ; 

 there hold it, and with the left set the body c perfectly at rest ; in which case the 

 rod ef will be over the mark t ; then suddenly withdraw the stick, in the direc- 

 tion that the rod gh is to follow it, and the spring of the body d, impinging on 

 that of the body c, they will be both bent, and also restored ; and the body c 

 will fly off, and mount till its rod ef covers the mark x ; the rod of the striking 

 body D remaining at rest on its proper mark of rest v, till the body c returns, 

 when the body d will fly off in the same manner ; the two bodies thus rebound- 

 ing a number of times, losing a part of their vibration each time ; but so nearly 

 is the theory of elastic bodies thus fulfilled, that the single advantage of ori- 

 ginally pushing the rod gh beyond the mark w, by the thickness of the stick, 

 or its own thickness, is sufficient to carry the rod of the quiescent body c com- 

 pletely to its mark x. 



There are several other experiments that may be made with this apparatus, in 

 confirmation of the doctrine of the collision of elastic bodies ; which being uni- 

 versally agreed on, and well known, it is needless further to dwell on here ; but 

 respecting the application to non-elastic soft bodies, it is far more difficult to 

 come at a fitness of materials for this kind of experiments, than it is for those 

 supposed perfectly elastic. The conclusions however may be attained with equal 

 certainty. 



For trials on non-elastic soft bodies. — For this purpose, the ratchet must be 

 applied and put in order as before described, and the springs being both set to 

 their point of rest, let the body d be put to its mark w in the same manner as 

 before described, and the body c to rest. The body d being let go, and striking 

 the body c at rest, in consequence of the stroke, the springs being hooked up 

 by the ratchets, they both move from their resting marks t, v, respectively to- 

 ward M : now if they both moved together, and the rod ef covered the mark c, 

 and the rod gh covered the mark d at their utmost limit, then they would truly 

 obey the laws of non-elastic soft bodies ; because their medium ascent would be 

 to the mark z, which is just half* the angle of ascent to the mark x ; but as in 

 this piece of machinery, though the main or principle springs are hooked up, yet 



* It should be said nearly half the angle. 



