67 



imparted by gravity to a body falling through a space of 772 feet is 

 223 feet per second ; six times this, or 1338 feet per second, would not be 

 an inordinate velocity for a rifle ball ; but if this ball was composed of 

 lead, this velocity would raise its temperature 30° ; with six times this 

 velocity, its temperature would increase about 36 times, or 1080°, with 

 a velocity 1338 feet per second, quite sufficient to fuse the lead if con- 

 centrated in the ball itself ; but the fact is, it is divided between the target 

 and the projectile, and in the case of the iron projectiles only one-fourth 

 of this amount, or 320°, would represent the heat. Mr. Joule, of Manches- 

 ter, has shown that if indeed all this heat in the target, after concussion, 

 and in the projectile, and latent in the gun itself, were combined, the 

 force represented would be sufficient to propel it back along the pro- 

 jected trajectory into the gun again. The concussion produced by these 

 heavy pieces of ordnance is very great ; and the lateral and longitudi- 

 nal strains on the timber of the ship, such as to render the stability of 

 the vessel a fact of the greatest importance : the vertical line being in 

 a state of fluctuation produces an immersion, and consequent emersion, 

 greater or less according to the stability of the vessel. Mr, Peake has 

 shown that the height of the metacentre above the centre of gravity of 

 displacement of the immersed portion of the body may be represented 

 by the following formulae* : — 



GF . ' 2fy 3 xsm0xdx 1 ICifxdx 



sm 6 3 J B sin 0 3 J D 



from which we deduce 



Jy 3 dx 



a formula of great practical benefit in calculating the relative stability of 

 floating bodies. 



Baron Sane and M. Tupinier used the following formulae for the 

 relative values of the contents of the parallelepipeds of his famous 

 18-pounder frigates and " La Guerriere," an old 3 6 -gun Trench fri- 

 gate : — in " La Guerriere," 



x : L : :y : I : : * : h : : ^^M^; 



r iM.r , jM.r . , AM.R 



* This determines the height of the metacentric point (m) above the centre of gravity 

 (G) of the displacement. 



