i48 LECTURE XIII, 



. a law very different from that which determines its strength, for it is simply 

 proportional to the bulk or weight of the beam, whether it be shorter or 

 longer, narrower or wider, shallower or deeper, solid or hollow. Tims a beam 

 ten feet long will support but half as great a pressure, without breaking, as 

 a beam of the same breadth and depth, which is only five feet in length; but 

 it will bear the impulse of a double weight striking against it with a given 

 velocity, and will require that a given body should fall from a double height 

 in order to break it. 



It is therefore of great consequence in the determination of the form and 

 quantity of the materials to be employed for any mechanical purpose, that 

 we should consider the nature as well as the magnitude of the forces which 

 are to be resisted. Stiffness, strength, or resilience, may be separately or 

 jointly required in various degrees. For a cicling, stiffness would be princi- 

 pally desirable ; for a door, strength; for the floor of a ball room, resilience; 

 for a coach spring, resilience and flexibility, that is, resilience witliout stift- 

 pess. An observatory should be as stiff' as possible, a ship as strong as pos- 

 fsible, a cable as resilient as possible. 



It is a common remark that a floor which shakes is the strongest ; and, im- 

 probable as it appears at first sight, it may perhaps be founded in truth: for 

 if the absolute strength of a stiff' and a shaking floor were equal, the shaking- 

 floor would bear the effiects of motion with the least injury. It is possible 

 that a stiff" floor, which "would support a numerous assembly, might give way 

 at a ball; while a more resilient one, which would be suited for dancing, 

 might be destroyed by a crowded concert. 



A coach spring, divided into plates, has the same power of resisting, with- 

 out being broken, the momentum of the carriage, arising from sudden eleva- 

 tions and depressions, as. it would possess if it formed one entire mass, 

 ' while its greater flexibility allows it to regulate these motions in a much more 

 gradual and gentle manner. A single piece of timber may perhaps sometimes 

 have too much of the flexibility of a coach spring, its strata sliding in some 

 degree on each other: in such a case its stiff'ness and strength may be in- 

 creased by binding it very firmly with hoops. . 



