g2 CHARGES OF GREATEST EFFICACY FOR ARTILLERY AT SEA. 



perfectly nonelastlc and affording no resistance to the body 

 but what arises from their inertia. If a denotes the first or 

 initial velocity ; x the distance of the gun from the object ; 

 e zz 2*71828 the number the hyperbolic log. of which is 



unity ; and b ~ - ., „ where N and n represent the re- 

 spective specific gravities of the ball and medium, we shall 

 have 



bx 

 a := Vc 



(See Dr. Hutton's elegant Exercises on Forces, Prob. 31, 

 and most works on fluxions and mechanics). Hence by the 

 law of variation of the charges, and proper substitution, 

 the true expression for the charge in question will be 

 3 « j: 



i> D s ItiOO* 

 for a perpendicular impact, and 



3 nx 

 S dv^w c 4ND 

 2 Da/i600* ~ 

 for an oblique one ; /being the sine of the angle of inci- 

 dence; the space to be described in this case being the 

 hypothenuse of a right angled triangle; when the effect is 

 the same. 



Example. 



Charge for a Resuming the first of the foregoing examples; what roust 

 iL''r"rH^%=!' ^^ ^^^*^ *^'^^''S^ ®^ gunpowder to cause the shot to produce 



the same effect in the vessel when fired at the distance of 



300 feet from it > 



Substituting for the several letters in the general expres- 

 sion for the charge 



3nx 

 Sdv^wc 4 NB 

 2D5 1600* 

 llitir proper numerical values, namelv 



S 5= 



100 yardi dis- 

 tance, 



