TRACT 37 .

OF GUNNERY.

221

27 . Now, to find how neartothe truth this theorem comes,in every instance in the table,by substituting for v, in thisformula, all the several velo-cities, 100 , 200 , 300 , &c, to2000, these give the corre-spondent values of r, or the re-sistances, as in the 2d columnof the annexed table, their ve-locities being in the first co-lumn ; and the real experi-mented resistances are set op-posite to them in the 3d or lastcolumn of the same. By thecomparison of the numbers inthese two columns together, itis seen that there are no whereany great difference betweenthem, being sometimes a littlein excess, and again a little in defect, by very small differ-ences; so that, on the whole, they will nearly balance oneanother, in any particular instance of the range or flight ofa ball, in all degrees of its velocity, from the first or smallest,to the last or greatest. Except in the first two or threenumbers, at the beginning of the table, for the velocities 100,200 , 300 , for which cases another theorem may be employed.Now, in these three velocities, as well as in all that aresmaller, down to nothing, the theorem ' 0000176 V 1 = r theresistance, will very well serve, as it brings out for the firstthree, resistances - 176 , and ' 704 , and 1 ' 584 , differing in thosecases by a very small fraction only.

The same otherwise .

28. If however the foregoing rule, (-00002665V-’ ’004025)v = r, for the ball of 2 inches diameter, be not in all casesquite near enough, as it varies from the truth so much as ^

a 2

Veloc*.or u.

Comput.

resists.

Exper.

resists.

100

—’133

•174

200

+ ’266

•709

300

1-200

1-612

400

2-666

2-906

500

4 - 66 Q

4-650

600

7-200

6‘900

700

10-206

9-750

800

13-866

13-250

900

18-000

17-519

1000

22-666

22-625

1100

27-866

28-556

1200

33 266

35*275

1300

39-866

42-706

1400

46-666

50-719

1500

5+000

59-194

1600

61-866

67*931

1700

70-466

76-775

1800

79-200

85-537

1900

88-666

94-106

2000

98-666

1102-362