Motion of Projectiles. 199 



31 1. But if at the point C, where the body meets the surface Fig.152. 

 there be a mound or eminence CE, the motion according to MC 

 being decomposed into two others, one according to QC perpen- 

 dicular to the surface CE, and the other PC in the direction of 



this surface, the body would proceed acccording to this latter, 

 describing the line P, and might, after leaving the point /, des- 

 cribe just such a curve as it would have described, if it had been 

 projected from .E, according to C, with the same velocity ; so 

 that it would elevate itself to a certain point, and then return td 

 the surface in some other point /, when the motion under similar 

 circumstances might be again renewed. 



312. A ricochet motion, therefore, depends upon the position 

 of the obstacle against which the body in question strikes. But 

 if the obstacle be flexible or yielding like the earth, water, &c., 

 this motion may take place even when the surface is perfectly 

 horizontal. Indeed, by the vertical velocity QC, the body tends Fig.153 

 to bury itself, and does bury itself more or less, according to the 

 nature of the obstacle ; while with the velocity PC it plows the 

 earth, and forms a furrow, the depth of which increases till the 

 vertical velocity QC is destroyed. Then by the remaining ve- 

 locity in a horizontal direction, it drives before it the matter 

 which lies in its way, and in working for itself a passage, it in- 

 clines in the direction from which it experiences the least resist- 

 ance, and the surface of the furrow becomes, with respect to the 

 body, what CE was in the last case. Now as the remaining pro- Fig 152 

 jectile force, other things being the same, is so much the greater 

 according as the depth of the furrow is -less, and as this depth 

 depends upon the vertical velocity QC which will be so much the 



less, according as the angle .MCP, or the angle of projection RAZ, 

 is less, it will be seen how the smallness of the angle of projec- 

 tion is favourable to this sort of motion. 



313. The figure of the body also, is of great importance. 

 If, for example, the question related to a motion upon water, and 

 the body were of a spherical shape, the velocity MC must be 

 such that the vertical velocity QC may be destroyed before the 

 vertical diameter of the body is entirely immersed, since, when 

 the body is once covered, the resistance of the water would act 

 equally in every direction, and there would be nothing to change* 



