^f Projectiles thrown from Cannon. 229 



two vertical planes, the extent and distance of which may 

 be considerable, and which therefore may give very accu- 

 rate measures. 



3d, By the advantage it affords, not to be found in any 

 other kind of apparatus yet known, of measuring the velo- 

 city of bullets of different sizes thrown in directions in- 

 clined to the horizon. 



It remains for us to give an account of some experiments 

 made to ascertain that the ball underwent no sensible devia- 

 tion in traversing the disks. It is manifest from the first 

 principles of dynamics, that the moment when the ball is 

 m the plane of one disk in motion, it receives perpendicu- 

 larly to its direction an impulse which, according to certain 

 mathematical hypotheses, would give it parallel to the plane 

 of the disk a velocity almost equal to that of the point 

 where it meets (the mass of the ball being verv small in 

 regard to those of the different moving parts of the ma- 

 chine) ; and then the velocitv of the ball, calculated accord- 

 ing to the formula before given, would be infinite. The 

 inflective phaenomena differ considerably from those deduced 

 from similar hypotheses, considering the compressibility of 

 the disks, their little hardness, and the prodigious rapidity 

 with which they are penetrated* (the duration of the pas- 

 sage of the semi-diameter through the disk not being the 

 40,000dth part of a second) ; but it is no less important to 

 determine exactlv the influence which they have on the re-! 

 suits. One of the commissioners is employed in analysing 

 a dynamic problem, from which this determination may be 

 concluded a priori; but as such a conclusion would not rest 

 on physical data sufficiently certain, he preferred verifying 

 by experiment whether the deviation was appreciable or not. 

 For this purpose he placed three fixed screens at equal di- 

 btances from each other ; the second and third being placed 

 respectively before the first and the second moveable disks. 



• It K here proper to give the reasoning on which these assertions are 

 founded. Every body in nature being more or less compressible, the state 

 of final motion, resultniji from the action of two bodies on each other, is not 

 acquired even at the moment of contact, but after a fixed term, which is 

 very short; and bodies during their contact pass through all the interme- 

 diate states of motion between initial and final. From these incontestable 

 facts, if one of the bodies escapes the action of the other before the moment 

 when by the natural conse(iuence of the shock they would have ceised to 

 press each oti»er mutualiy.thc state of motion at which that body will really 

 arrive in that case will differ so much less from its initial state, ;ind so much 

 more from that in which it would have been had the shock been cuiisum- 

 inated, as the contact has been of less duration, and this duration may be so 

 •■hort that the- initial state is not sensibly modified. This is the case of the 

 experiments mentioned in the text. 



P3 Tt 



