270

THEORY and practice

tract 57.

118. And first then, having given the initial velocity,and the size and nature of the shot, we may thence findnearly the elevation of the piece to produce the greatestamplitude, and the extent of that range.

Now these will be found nearly by means of the followingtable, altered from professor Ilobison’s, iti the Encj'clopaidiaJkitanuica, and founded onan approximation of Sir I.

Newton’s. The numbers inthe first column, multipliedby the terminal velocity ofthe ball, give the initial ve-locity; and the numbers inthe last column, being mul-tiplied by the height, givethe greatest ranges ; themiddle column showing theelevations to produce thoseranges.

119. To use this tablethen, divide the given initialvelocity by the terminal ve-locity peculiar to the ball,found in the table in prob.

10, and look for the quotientin the first column here an-nexed. Against this, in theltd column will be found the elevation to give the greatestrange; and the number in the 3d column multiplied by a,the altitude due to t ie terminal velocity, also found in thetable in problem to. will give the lange, nearly.

Table of Elevations giving thegreatest Range.

Initial vel.<liv. by v.

Elevation.

Range iliv.by a.

0-6910

44° O'

0-41 10

0-9445

43 15

0-6148

1" 1980

42 30

0-8176

1-4515

41 45

T0210

1-7050

41 0

1-2244

1-9585

40 15

1-4278

2-2120

39 30

1-6312

2-4655

33 45

1-8346

2-7190

38 0

2-0379

2-9725

37 15

2-2413

3-2260

36 30

2-4447

3-4795

35 45

2-6481

3-7330

35 0

2-8515

3"9865

34 1.5

3-0549

4-2100

33 30

3-2533

4-4935

32 45

3-4616

4-7470

32 0

3-6650

5-0000

31 15

3-8684 |

120. Ex. 1. I.et it be required to find the greatest rangepf a 24lb ball, when discharged with 1640 feet velocity, andthe corresponding angle to produce that range. By the ta-ble in prob. 10, the terminal velocity of the 24lb ball is 419,and its producing altitude 2729 : hence = 3-92, nearly

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