89 



was a heavy iron ball, hanging down, when at rest, from a point of 

 suspension vertically above the centre of the beam. The ball was 

 raised through different arcs, and after descending by its own gra- 

 vity, struck the beam. The deflection corresponding to different arcs 

 of descent were carefully noted by a graduated scale. 



The object of the present paper is to show that the results might 

 have been predicted by known theoretical principles with consider- 

 able precision and confidence. The problem is divided into two 

 parts: — 1st, to estimate the amount of velocity lost by the ball at 

 the first instant of collision ; 2nd, to ascertain the effect of the elastic 

 forces of the beam in destroying the vis viva which the whole system 

 has immediately after collision. In the first part of the investigation, 

 a general formula, derived from the combination of D'Alembert's 

 principle and that of virtual velocities, is given for the motion of 

 any material system subject to impact. The requisite geometrical 

 condition required for the application of this general formula to the 

 present case is obtained by the assumption, that immediately after 

 impact the form of the beam is a gradual and tolerably uniform curve, 

 such as, for example, tbe elastic curve of equilibrium. In this way 

 it is determined that about one-half the inertia of the beam is ef- 

 fectively applied at the instant of collision to retard the ball. 



The vis viva of the whole system thus computed is destroyed by 

 the elastic forces of the beam developed by deflection. These, in 

 the second part of the problem, are assumed to vary as the amount 

 of central deflection. By the principle of vis viva a formula is easily 

 obtained, connecting the amount of total deflection with the vis viva 

 of the system immediately after collision. 



Tables are given in which the theoretical and experimental results 

 are compared. The correspondence is of the closest and most satis- 

 factory nature. Indeed the theoretical result generally differs less 

 from the mean of several experiments than those experiments differ 

 among themselves. Both in the theoretical and experimental in- 

 quiries, every possible variation of the elements of the investigation 

 — the relative masses of the beam and ball — the velocity of the latter 

 — the rigidity and dimensions of the former — have been included. 



February 11, 1850. 



A paper was read by the Master of Trinity, " Criticism of Aris- 

 totle's account of Induction." 



The passage criticised was Analyt. Prior. 11. 25, and is by Aris- 

 totle illustrated by this example. Elephant, horse, mule, &c.,are long- 

 lived ; but elephant, horse, mule, &c. have no gall-bladder. If we 

 suppose that the latter proposition may be converted and put in this 

 form, " all animals which have no gall-bladder are as elephant, horse, 

 mule, &c," we may draw the conclusion that all animals which have 

 no gall-bladder are long-lived. This convertibility and generalization 

 of the second proposition are the necessary conditions for translating 



