TRACT 34.
IN GUNNERY, 1789.
125
Middle
Veloc
iesist
First
2d
Velocities
lost
mces
Dili's.
Diffs
feet
feet
oz
2. 645
9
174
12
J. 654
9i
186
i
3 664
10
199
i
67 .V
104
218
933
2 4
604
955
22
632
i
co 978
22 i
661
i
3 1001
23
691
i
1024
23i
722
i
1048
2 4
754
1132
26
883
56
1 159
27
939
2
S U86
28
997
2
o 1215
29
1057
3
1244
30
1120
3
1275
31
1186
1347
34
1374
1382
35-1
1455
8 t
8
-1418
36-3
1544
97
8
= 1455
37-6
164!
10
1494
39
1748
i i n
10
1535
40-5
1865
1491
39
1744
1530
40-6
1864
10
-1571
42-3
1994
1
12
3 1614
44'1
2136
12
1659
46
2290
154
13
1706
48
2457
1 0 l
167. Taking then the me-diums between every two ofthese vel ocities,for each chargeof powder, place them in thefirst column of the annexedtable; after which, in the 2dcolumn, set the correspond-ing velocities lost in passingthrough 50 .feet of air. Themto these data applying thetheorem where v denotesthe middle velocities in thefirst column ; v' the velocitieslost, as in the 2d column ;s = 50 feet, the commonspace; and b = 3lb = 48oz>the weight of the ball; with
which data, the theorem v ^b
becomes — = - w, whichtheorem will bring out thecorresponding resistances inthe 3d column ; the first andsecond differences of whichare set in the 4th and 5th co-lumns, showing that the resist-ances are not far from beingregular. '
But now, to adapt the resistances to the series of veloci-ties differing by the constant difference of 50, and to renderthem regular, it will be convenient to construct the curve ofresistance, making the velocities the ordinates, and the re-sistances the corresponding abscisses; which gives the curveah plate 2 ; from which we perceive that the numbers inthe table above the velocity 900, are much too small, butthat the rest of them run pretty regular; and when reducedto every 50 feet difference of velocity, came out nearly as inthe following table.