192

EXPERIMENTS WITH

TRACT 36.

that 10 v : ll*::r:r'. Dividing the first two terms by 10,and the latter two byr, the proportion becomes 1 : l - 1*: : 1 :T

consequently IT* = the logarithm of this is x x log, 1*1

= log. r' — log. r; and hence x — —^—rw— = 2'049,by using the aforesaid numbers for r and r'. In like man-ner, taking, irt the denominator of the general expression forx, the successive numbers 1’2, 1’3, 1'4, &c, to 2'0 ; and inthe numerator the successive values of r, viz, 370, 435, &.c,that of r being constantly — 2 55 ; all the numbers in the3rd column will be easily found.

(3.) The round ends, and sharp ends, of solids, suffer lessresistance than the flat or plane ends, of the same diameter :thus, the cylinder, and the fiat ends of the hemisphere andcone, have more resistance than the round or sharp ends ofthe same. But the sharper end has not always the smallerresistance: thus, the round side of the hemisphere has lessresistance than the pointed end of the cone.

( 4 .) When the hinder parts of bodies are of different forms,the resistances are different, though the fore parts should beexactly alike and equal; owing probably to the differentpressures of the air, on the. after parts. Thus, the resist-ance to the fore part of the cylinder, is less than that on theequal flat surface of the cone, or of the hemisphere; becausethe hind part of the cylinder is more pressed or pushed for-ward, by the following air, than those of the other twofigures: also, for the same reason, the base of the hemisphereshows a less resistance than that of the cone, and the roundside of the hemisphere less than the whole sphere.

(5.) The resistance on the base of the hemisphere, is tothat on the convex side, or on the wdiole sphere, nearly as2|. to 1, instead of 2 to 1, as assigned by theoiy. And theexperimented resistance, in each of these cases, is nearly ^part more than that which is determined by the theory.

(6.) The resistance on the base of the cone, is to that onthe vertex, nearly as 2 - 3 to 1. And almost in the same ratiois radius to the sine of the angle of inclination of the side of