326 Charges of greatest Efficacy for Artillery at Sea. 



stances and quantities of resisting surfaces jointly ; or as 

 the resisting forces of the substances and squares of the 



M R D* 



diameters of the impinging spheres : that is, — = — x -=> 

 r o o i ' m r <r 



But in general — = — x — : therefore equating these 



F 

 two values of the whole resisting forces, we obtain -j- x 



Q R D* , F R D* a 



= — x —pr, and — r- = — x -jt- X ~Ir • and since 



q r d* f r d* Q, 



Q ~ IP X N > lt 1S / ~ r X 2*~ X B» X "N" "" 7~ X 



■q x ^: that is, the forces retarding spheres penetrating 



uniform resisting substances are as the absolute strengths 

 of the fibres of the substances directly, and the diameters 

 and specific gravities of the spheres inversely. 



Lemma II. 



The whole spaces or depths to which spheres impinging 



on different resisting substances penetrate; are as the squares 



of the initial velocities, the diameters and specific gravities 



of the spheres directly, and the absolute strengths of the re- 



j ■ . , S V 3 D N r 



sis ting substances inversely : or, — = — r X —7- X — - X ^r. 

 J ' s v* d n R 



For by mechanics we have — =-rxi; and by the 

 J s . v % F " J 



f r D N 



preceding lemma ~- == — x— t- X — , which substituted 



c MX a n 



.... S V 2 D N r 



m the above it becomes — = —r- x — r x — x -rr» 

 s v* d 11 R 



These being premised, I now proceed to resolve the fol- 

 lowing most important 



Problem : 



To find a general formula which shall express the quan- 

 tity of charge for any given piece of ordnance to produce the 

 greatest destruction possible to an enemy's ship at sea; it 

 being supposed of oak substance of given thickness, and at 4 

 distance not affecting the initial vtlocity of the shot. 



t> x u 11 v * s d n 



By Lemma 2, we have, generally, —f = — x if x N X 



■ — . Also the charges of powder vary as the squares of the 



% velocity 



