364 D/5 Reply to C's Observations [May, 



Cor. 2.^ Hence also the velocities of the bodies m motion 

 before and after the stroke are reciprocally proportional to the 

 bodies. 



Cor. 3. — And because the momentum communicated is equal 

 to the momentum of the movint^ body before the stroke without 

 respect to the relative magnituues of the bodies, it follows that a 

 double, treble, &c. quantity of motion will generate a double, 

 treble, Sec. quantity of motion, not in the same quantity of matter 

 only, but in any quantity. 



This, though at variance with the results of the old theory, as I 

 have shown above, precisely (Coincides, in the case of the same 

 quantity of matter struck, with the views in some of the above 

 quotations from Dr. Hutton and Emerson. But the following 

 declaration in Hutton's Dictionary, vol. ii. p. 170, puts it beyond 

 a doubt that results from Mr. H.'s theory accord with the usual 

 opinion of mathematicians on thi§ subject. " Now it is a law," 

 says Dr. Hutton, " universally allowed in the communication of 

 motion, that when different bodies are struck with equal forces, 

 the velocities communicated are reciprocally as the weights of 

 the bodies that are struck." Therefore, if it be true, as the same 

 writer says in one of the preceding quotations, *' that the velo- 

 cities being equal, a double mass will strike w^ith a double force. 

 Sec." we want no further evidence that Mr. Herapath's theory 

 furnishes consequences " which have been admitted as incon- 

 trovertible by the ablest mathematicians in all ages." 



The demonstration of this Prop, and its Corollaries, it will be 

 seen, is rigorously mathematical from data which have been 

 admitted by decided advocates for the old theory, — the very 

 authors C. has opposed to Mr. Herapath. Nothing more, there- 

 fore, need be advanced in support of the proposition ; but I 

 might observe that I could here subjoin a rigorous proof similar 

 to the one C. has, by leaving out certain principal parts, paro- 

 dying others, and unhandsomely offering them to the world, 

 as C. has done with Mr. Herapath. Taking, however, no 

 further notice of this part of the affair, I cannot but compare the 

 reasoning C. tells the world is Mr. Herapath's to a picture whose 

 intention the artist thought it needful to explain by writing 

 under it, ** 17/26' is a Coiv ; " lest it might be mistaken for any 

 thing else. 



From the views here developed, and the constitution of aeri- 

 form bodies, as laid down by Mr. Herapath, if a body composed 

 of absolutely hard particles nuitually impinging on one another 

 in the way Mr. H. has assumed in his theory of heat, be projected 

 in such a body as our air, it will proceed with a velocity gradually 

 diminishing on account of the resistance it continually expe- 

 riences from the opposition of the air. For a single particle may, 

 from Mr. H.'s principles of collision, be stopped, or even driven 

 backwards, by the lirst particle it met with at rest, or moving iu 



