'392 M. Camot's Theuri/ of Defence 



of small balls, discharged at an elevation of 75° or 80°, such 

 accelerated velocities, as would, if true, be quite sufficient to do 

 good service in the way M. Carnot suggests ; but the fact is, 

 that there can be no acceleration beyond a limit which, with 

 small balls, is very much less than is generally imagined. 



" From the vertex of the curve, where all the vertical motion 

 is lost, the ball begins to descend by an urging force which is 

 nearly constant, viz., its own weight. This force would pro- 

 duce equal increments of velocity, in equal times in vacuo ; 

 but in air, the descent of the ball being resisted more and more 

 as the velocity accelerates, the urging force will, at a certain 

 velocity, be opposed by an equal resistance of air; after which, 

 there can be no further acceleration of motion, and the ball will 

 continue to descend with a velocity nearly terminal." 



In considering this problem as applied to vertical fire, 

 Sir Howard Douglas remarks that, M. Carnot has entirely over- 

 looked terminal velocity ; " and I shall show," says he, " from 

 his own words, that this is the case. It is not necessary to 

 exhibit here the investigations by which I have established the 

 impotency of M. Carnot's vertical fire ; I shall only state the 

 results, not to embarrass the conclusions with abstruse matter. 

 The solutions are computed from the theorems given in 

 Dr. Hutton's tracts ; and although the results may differ a little 

 from the truth, yet it is quite clear, that in the descent of the 

 balls there can be no acceleration of motion beyond a certain 

 limit; — that with small balls this velocity is very much less 

 than persons who have not investigated this curious problem 

 would imagine ; and that M. Carnot has evidently overlooked 

 this circumstance. 



" The velocity which a musket ball has acquired when the 

 resistance becomes equal to the weight, or urging force of 

 descent, is only about 180 feet in a second. The potential 

 altitude, or the height from which the ball must descend in 

 vacuo, to acquire a velocity equal nearly to the terminal velo- 

 city, is 523 feet. Hence, in the first place, it would be a waste 

 of means to use the full charge ; for a musket-ball fired up- 

 wards with the ordinarv quantitv ot powder, would be pro- 



