208

EXPERIMENTS WITH, &C.

TRACT 36.

Where the numbers in the 2nd column, when multiplied by84, and divided by 1000, will give the resistance in decimalsof an ounce, to a plane of 32 square inches area, moved withthe velocity of 12 feet in a second of time, meeting the airin the several angles shown in the first column of the table:and the general formula for every case of that plane, as be-fore, is 84s" c , wdiere s denotes the sine, and c the cosine ofthe angle of inclination, also n = T842, or T84 only. Forother surfaces and velocities, the formula will vary nearlyas the surfaces, or but little higher, about -f, and nearly asthe 2‘04 power of the velocity. Or, for any other greaterplane a, and velocity v, the formula will be nearly ’OSav 1 ' 0 *s l ' 84c feet.—For water, or any other fluid, different from air,this theorem will be varied in proportion to the density ofthe fluid.

59. Though the figure of the plane makes no sensibledifference in the resistance; yet the action on a plane willnot apply to such curve surfaces as those of a cone or asphere, as clearly appears by the table of experiments inpage 189 ; where the convexity of the hemisphere, on a sur-face equal to double its base, has less than half the resistance ;and the cone, with a surface of nearly 14 square inches, atan angle of 25°42', with the path, suffers a resistance far lessin proportion to the plane at an equal angle; for, the ratioof the surfaces is that of 74 to 32, much more than double,while that of the resistances, 376 to 255, is less than 3 to 2.