OP PROJECTILES. 189

then in the direct shock, the force with which a 32 lb. shotwith an initial velocity of 1350 feet, impinges on an objectplaced very close to it, is to its force at 4056 feet, as 1350 t759 : and the force with which a i 61 b. shot, with an initialvelocity of 1416 feet, strikes an object at the distance of 932feet, is to its force at 3229 feet, as 1226 : 817. On com-paring in the same manner shot of different diameters, it ap-pears, that the force with which a 321b. shot, with an initialvelocity of 1350 feet, strikes an object at the distance of 330feet, is to the force of a 41b. shot, with an initial velocityof 1467 feet, at the distance of 3520,3s 32 x 1300 : 4X 528 ;that the force of a i 61 b. shot, with an initial velocity of 1416feet, at the distance of 3886 feet, is to the force of an 81 b.shot, with an initial velocity of 1449 feet, at the distance of350 feet, as 16 x 716 :: 8 x 1361. If under similar circum-stances, the shocks be oblique, so that with a i 61 b. (hot theangle of incidence be 20°, and with an 81 b. shot 75 0 , thetwo shocks will be to each other: : 16 X 716 X 34202 : 8 x1361x 96592.

179. In the preceding paragraph it was supposed, that the

compound velocity B K of the shot, when it impinges on anobject, was equal to the remaining velocity H K, which isin the ratio of the, retarded motion of impulsion : this isthe cafe not only in this particular instance, but in all othersthat do not admit of geometrical precision. Nevertheless,on ascertaining the greatest difference that can be betweenthese two velocities, in the common service of guns, we shallfind it to be too inconsiderable to occasion any material error;for, if the value of the compound velocity BK be deter-mined (168), the gun having been sired at the highestelevation the carriage will admit of, B K is less than H K inthe proportion of about in the 100 ; that is B K : H K

: : 397 : 400 ; and if the gun be depressed as much as pos-sible, B K will exceed H K in the proportion of about in

the xoo; that is B K : H K : : 801 : 800.

180. Among the several works against which cannon arefired ; there are some which do not yield to the most violentshocks ; and others of very slight resistance. Of the firstkind are those cut out of the solid rock, the hardness ofwhich joined to the cohesion is such, that the most violentshocks cause no disunion in the parts. If the weight of theshot —m, the velocity with which it impinges — V and n —the object impinged on; the whole effect of the shot on

this