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Full text of "An Account of an Experiment Contrived by G. J. s'Gravesande, Prof. Math. at Leyden, F. R. S. Relating to the Force of Moving Bodies, Shewn to the Royal Society, by J. T. Desaguliers, LL. D. and F. R. S."

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( i<B ) 

XIII. An Account of an Experiment contrived hy 
G.J. s'Gravefande, r Prof. Math, at Leyden, 
F. % S: relatingto the Force of moving Bo- 
&k$,fhewn to the Royal Society , by J # X 
Defaguliers, LL T>. and F. % S. 

HAving laft Year (hewn ieveral Perfons in HoU 
land the Experiment contrived by Mr. Geo, 
Grab am j to explain theDoQxine relating to the Mo* 
mentum of Bodies (viz. That the Momentum ox 
Quantity of Motion in Bodies is always as the Mafs 
multiplied into the Velocity) which Experiment is 
made with a flat, pendulous Body, that receives the 
Addition of a Weight equal to -itfetf at the lower 
Part of its Vibration, and by the Reception of that 
equal Quantity of Matter always lofes half its Ve- 
locity. Dr. Mufchenbroek, ProfeiTor of Mathe* 
maticks and Aftronomy at Utrecht, communica- 
ted to me the following Experiment, made in Op- 
pofition to that which I fhewed,* by Mr. ProfeiTor 
iGravefande. In this laft a Spring equally bent 
every time, pulhes forward, unequal Quantities of 
Matter fucceflively, and in every Experiment the Pro* 
du& of the Mafs of the Body by the Square of the 
Velocity is the fame ; and therefore, as the Quantity 
of Motion muft always be the fame from the fame 
Caufe (viz. the fame Tenfion of the Spring) it fol* 
lows, by every Experiment, that it is as the Mafs mui« 
liplied intothe Square of the Velocity* 

( l 44 ) 

Exp. i.] The pendulous Cylinder is fliot by the 
Springfrom o Deg. to 7 Deg. meafured upon a Tan- 
gent Line. 

Exp. 2.] The Cylinder with a leaden Weight in 
it that makes its Weight double, is (hot forward to 
4 Deg. and 9 Tenths. 

Exp. 3.] The Cylinder with a Weight in it that 
made its Weight triple, was (hot forward to 4 Degrees 
and a little farther. 

Exp. 4J The Cylinder with a triple Weight of 
Lead fo as to quadruple the whole Weight, was (hot 
forward to 3 Deg. and an half. 

Thefe 4 Experiments at firflt feem agreeable to the 
new Hypothecs ; for according to the old, the Cylin- 
der in the xd Experiment ought to have gone but to 
3 \ Deg. in the 3d Experiment but to 3 7 Deg. and in 
the laft but to 2 Deg. . 

But if we take in the Confederation of Time, all will 
be reduced to the old Principle. As for Example, let 
us compare the firft and laft Experiments. . 

In the firft, the Spring during a certain time a£b 
upon the Cylinder which is driven forward with the 
Velocity 8. When the quadrupled Weight is driven 
forward with the Velocity 4 inftead of 2,, it is be- 
caufe the fame Spring ads twice as long upon the Cy- 
linder before it ceafes to impel it - 5 and certainly the 
fame Caufe a&ing twice as long muft produce a doubk