TRACT 34.

IN GUNNERY, 1789.

125

167. Taking then the me-diums between every two ofthese velocities,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. T lien 5to these data applying thetheorem where v denotesthe middle velocities in thefirst column ; v the velocitieslost, as in the 2d column ;s = SO feet, the commonspace; and b = 3lb = 48oz,the weight of the ball; with

which data, the theorem v ^~ b

i 48w/ 3 f i.i

becomes — = - w, which

theorem will bring out thecorresponding resistances inthe 'id 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.

Bnt 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 absdisses; 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.

Middle

Velocities

i^eloc

lost

tesist

mces

Firs'

Dirts.

2d

JifFs

feet

5. 645£ 654§ 664675

feet

9

9i

10

IQ*

oz

174

186

199

213

12

13

14 |

1

J

933955co 978° 100110241048

2 422

09 t

-'-'a

2323i

24

604

632

661

691

722

754

28

29 ■

30

31

32

i

i

i

i

11321159-1186g 121512441275

26

27

28

29

30

31

88393999 7105711201186

56

58

60

63

66

2

2

3

3

13471382-1418ol45514941535

3435" 1

36- 3

37- 63940-5

1374

1455

1544

IG41

1748

1865

81

89

97

107

117

8

8

10

10

14911530$21571£ 161416591706

39

40-6

42-3

441

46

48

1744

1804

1994

2136

2290

2457

120

130

142

154

167

10

12

12

13