(1)
Mathematics in Naples, Naples, Italy
Deceased
Hitherto we supposed a perfect hardness and rigidity as well in the body delivering the blow as in the struck body. Now let us suppose them to be yielding and elastic as are all the solid bodies which exist in the nature of things. These either are made of small particles absolutely separated or their parts are connected together by some adherence or by some ties which sometimes display more tenacity, sometimes less. As a result, whenever they are pressed by some hard body, all their parts are not moved together in the same movement and at the same velocity. The first particles which receive the blow can be agitated while others are at rest or modify their previous position by a different and slower movement. This results in the softness of the body or its elasticity. Let us start from what is better known.
Proposition XXIV
A percussion carried out on a heap of separated bodies transmits to this heap an impetus which weakens continuously with time.
Let a solid body BCD supposedly be made of particles B, C, D completely separate from each other, which have no resistance and are indifferent to movement (Table 3.1, Fig. 21). Let the solid body BD be struck by a hard body A with an impetus E resulting either from an internal or from and external principle. Then the body A does not carry out one percussion alone but several ones. The first is inflicted to the bodies B exposed in front and which are supposed to be absolutely hard. The percussion impresses in them a velocity FG which, according to the above propositions, will be propagated in one instant. After the first blow the conglomerate formed by the bodies A and B attains the following particles C and thus must be moved a little to arrive to the contact C. Therefore, the movement from the position B to C must occur during some intermediate time. Afterwards, a second percussion occurs at C which again, for the same reason, will be instantaneous. The whole velocity FG which had been diffused into the conglomerate of the bodies A and B must then rarefy further in the three bodies A, B and C. Consequently, the velocity is decreased by, for example, the slowing down FH. Therefore, the remaining velocity HG by which the body C is moved together with the conjoined bodies A and B, is also generated instantaneously. Certainly, it must take the bodies some time to be led to the contact of the more remote particles D. Then, the last impulse must be carried out by the impetus GH of the three bodies A, B, C so that there is a second slowing down HI and the last degree of effective velocity IG remains impressed in the particles D as in all the solid body BD.