TRACT 34.

IN GUNNERY.

325

5'6T3,1 g c v'o; which is an easy theorem to be used

on all occasions ; and being within the 5000th part of thetrue quantity, it will always give the velocity true withinless than half a foot, even in the cases of the greatest velo-cities. Where it must be observed, that c, g, i, r, may betaken in any measures, either feet or inches, Sec, providedthey be but all of the same kind ; but o must be in feet,because the theorem is adapted to feet.

23. As the balls remain in the pendulum during the timeof making one whole set of experiments, both its weight,and the position of the centres of gravity and oscillation,will be changed by the addition of each ball which is lodgedin the wood ; and therefore p, g, o must be corrected afterevery shot, in the theorem for determining the velocity v.Now the succeeding value of p is always p + b; or p isto be corrected by the continual addition of b: and thesucceeding value of g is g + -— -b, or g -f- l —^b } nearly ;

^b to the next preccd-

P + b

or g is corrected by adding alwaysing value of g : and lastly, o is to be corrected by taking

for its new values successively or by adding always

\l>i, or l ~~-b nearly, to the preceding value of o: so that

pg + bi ' pthe three corrections are made by adding always,b to the value of p,x b to the value of g,

- —- x b to the value of o.

.f

That is, when b is very small in respect ofp.

24. But as the distance of the centre of oscillation o, whosesquare root is concerned in the theorem for the velocity u,is found from the number of vibrations n performed by thependulum; it will be better to substitute, in that theorem,the value of o in terms of n. Now by Art. 20, the value of

ois- feet, and consequently */p =-; which

value of i/o being substituted for it, in the theorem v —5*6127 gc x \/o, it becomes v = 614*58 gc x or

^ o %r T / ° oirn 7