TRACT 34.

IN GUNNERY.

351

and sometimes in defect; and therefore the above numbers,which are the means among the whole, as long as the ironwork remains the same, will probably be very near thetruth. And b) r using always these, with proportional altera-tions in g and n, for any alteration in the weight p, thecomputations of the velocity of the ball will be made by a rulethat is uniform, and not subject at least to accidental singleerrors. When the weight of the pendulum varies by thewood alone of the block, or the straps about it, the altera-tion is to be made at the centre of the block, which isexactly 88 - 3 inches below the axis; that is, in that case

the value of i is 88 - 3 in the formula*— ^5, or the correction

for^r; and in the correction of n. But'

when the alteration of the weight p arises from the balls andplugs lodged in the same block, then the value of i in thosecorrections is the medium among the distances of the pointstruck. And when the iron work is altered, the middle ofthe place altered gives the value of fin the same theorems.

In these corrections too, p denotes 660, g 77‘3, ra 402,and b the difference between 660 and any other givenweight of the pendulum ; which value of b will be negativewhen this weight is below 660, otherwise positive; so thatp + b is always equal to this weight of pendulum.

And if these values of p, g, n be substituted for them inthose corrections, they’will become

•l _77.3 2__77<3

-b, or- b, the correction for g , and

660 + b

40'2 bi{i — 87 *1)

the correction for n.

, 8887336+ bi(i + S7'l)

And further, when i n 88-3, the same become

116 n 7260 .

or 11 — -the correction for g, and

660 + bb

P

or -4545

160

the correction for

n,

2086 +■ 3-66 “ f —80

as adapted to an alteration at the centre of the pendulum.And, in that case,

g = 88-3 -

M = 39-923 +

7260

P

160

;T^80

is the new value of g, andis the new value of k.