232

THEORY AND PRACTICE

TRACT 57.

that these two numbers arc really too small, and that theyshould probably be. about 95 and 104.

33. Carol. 1. The foregoing rule •00003026 , o 1 — ’OGlu= r, in the 6tl) column, denotes the resistance for the ballin the table whose diameter is 2, the square of which is 4;hence to adapt it to a ball of any other diameter d, we haveonly to alter the former in proportion to the squares of thediameters, by which it becomes ^ (•O0CO3O26v I —’00 lv)d 1 —(•()00007565v l — '0017 ov)d 1 , which is the resistance for theball whose diameter is d, with the velocity v.

34. Corol. 2. And, in a similar manner, to adapt thetheorem 'OOOOnfry 1 =: r, for the smaller velocities, to anyother size of ball, we must multiply it by q<7% the ratio ofthe surfaces, by which it becomes , 0000044f/V' = r.

We shall soon take occasion to make some applications inthe use of the foregoing formulas, after considering the ef~fects of such velocities in the case of nonresistance.

PROBLEM III.

35. To determine the Height to which a Ball will rise, whendischargedfrom a Cannon Perpendicularly Upwards with aGiven Telocity, in Nonresisting Space, or supposing no Re-sistance in the Air,

By art. 73 pa. 151 vol. 2 of the Academy Course, it ap-pears that any body projected upwards, with a given velocity,will ascend to the height due to the velocity, or the heightfrom which it must naturally fall to acquire that velocity;and the spaces fallen being as the square of the velocities;also 16 feet being the space due to the velocity 32 ; there-fore the space due to any proposed velocity v, will be foundthus, as 32 1 : 16 : : v l : 5 the' space, or as 64 : 1 : : v* : ^ v 1= s the space, or the height to which^the velocity v willcause the body to rise, independent of the air’s resistance.

Exam. Pof example, if the first or projectile velocity, be2000 feet per second, being nearly the greatest, experimented