4 10 Mr. L. Gompertz's Method of defending 



would not be so hard as assumed, the effect would not be exactly 

 as described ; though as there would be a continual tendency 

 for it to be so, according to the hardness of the side, it would 

 be produced to a certain degree, and the ball would accord- 

 ingly continually widen the indentation, and come out at 

 some other point T, instead of I (fig. 2 ) ; and as the new di- 

 rection would, by the yielding of the substance, be less per- 

 j^endicular than when the material was extremely hard, the 

 ball would be the more inclined to follow the curvature of 

 the side, and to return, and the less inclined to fly over the 

 top of the ship ; as the angles of reflection would thereby be- 

 come still more obtuse every time that the indentations it 

 would produce in its course would widen, as just alluded to. 



It seems that the tendency of being reflected by the reaction 

 of the indentation would exist in some degree till the ball was 

 completely buried, allowing the material of the side of the 

 ship to be as deep as the ball ; because, suppose the ball to be 

 partially buried to HM, fig. 2, (above the diameter,) and al- 

 lowing even that it should still be as much inclined to go in 

 its original direction CB as it was at first (though it is evi- 

 dent that it must have acquired some tendency to alter its 

 direction by the blow, &c.), then, to see this clearly, to the 

 diameter xj/, which is parallel to the side of the ship, draw 

 another diameter VK perpendicular to it; it will be obvious 

 that as the ball continued to penetrate, it would be opposed at 

 its whole buried surface HK ; and it is also plain that, if the 

 resistance to the part of the ball between ,r and K tended to 

 press the ball up-iSoards, resistance above this line between x 

 and V would tend to bury it still deeper : but as the whole 

 of the arc .r K would be greater than part of the arc x V 

 (HV being by hypothesis unburied), arc xV would always 

 cause most resistance ; there would consequently be more 

 than a balance of force to press it upwards, which would exist 

 till the ball was wholly buried, but would then cease. 



But both in this case and in case 1, the ball has two modes 

 of acting, either in going up the side, or out of the indenta- 

 tion, that is, by rolling or sliding, both of which would rob the 

 ball of some of its force, by the friction produced ; but the less 

 should be the impediments which cause friction, the more 

 would it be inclined to slide, and the more of them there 

 should be, the more would it be inclined to roll in its course ; 

 but even this would also rob the ball of some of its pro- 

 gressive force, and would be spent in giving a new motion 

 (of rotation) to it, which would assist it to roll up the side of 

 the ship or to roll out of the indentation : but it must be par- 

 ticularly observed, that either the rotary motion of the ball, or 



the 



