360 £).'5 Replj/ to C.'s Observations [MaYj[ 



This intensity of impulse is equally felt by the hammer, not 

 from any vzs viva of reaction in the nail, but from what may be 

 termed a passive opposition to its motion. The same also must 

 evidently hold good in the intensity of the stroke between two 

 bodies moving towards opposite parts ; each of the bodies like 

 the hammer and nail receives an impulse equal to the whole 

 intensity of the contact. However, since C. finds a difficulty in 

 this case, to oblige him I will try if I can put it more. 

 simply than Mr. Herapath could well be expected to do, 

 when writing to the Royal Society. And to prevent C. from 

 confusing himself by attending to more than one idea at a time, 

 I will endeavour to demonstrate the separate steps in separate 

 propositions; taking care, for like reasons, to make the proofs, 

 as far as I can, analogous to those notions in the old theory to 

 which I dare believe him he has paid much attention, though 

 unfortunately with, as I have shown, but little advantage. 



Prop. A. 



If two perfectly hard and equal balls at rest be similarly struck 

 by two other perfectly hard balls moving with equal momenta, 

 the intensities of the strokes are equal. 



For because the two bodies struck are perfectly hard, equal, 

 similar, and quiescent, and the strokes similarly given, no differ- 

 ence on either of these accounts can be made in the intensities 

 of these strokes. Whatever difference exists must, therefore, 

 depend on the momenta and the manner in which the impulses 

 are communicated. But all the bodies being absolutely hard, the 

 strokes are mere impulses, which are begun and finished with 

 the very commencement of the contact; and are, therefore, 

 equally smart with respect to duration under every velocity. 

 Hence the velocities of the moving bodies have no efiect on the 

 intensities of the strokes, all other things being alike. The 

 »iomenta, therefore, alone influence the intensities of the strokes; 

 but in the present case the momenta are equal ; the intensities 

 consequently are equal. 



The substance of this theorem appears in Mr. H.'s Cor. to 

 Prop. 1, Annals for April, and is distinctly mentioned and made 

 the foundation of Mr. Herapath's demonstration of his Prop. 3, 

 though C. in his parody of this demonstration has, notwithstand- 

 ing its evidently indispensable importance, descended for the 

 purpose of suiting his own views, to an artful omission of it. 



Prop. B. 



If two perfectly hard, equal, and quiescent balls be similarly 

 struck by any two other perfectly hard balls, the intensities of 

 the impulses will have a ratio equal to that of the generating 

 momenta. 



By the preceding Prop, if the momenta were equal, the inteu- 



