218 LECTURES. 



all sifles, the law of diminution is the same as that which has been 

 given for liquids. The degree of compressibility may also be deter- 

 mined by the use of Oersted's apparatus. Explanation of this. 



In rods and wires drawn, in the direction of their axes, the elonga- 

 tion within certain limits is just in proportion to the force applied. 

 When the force is removed the body resumes its ordinary dimensions. 



With a force which exceeds the limits ol elasticity^ the position of 

 the molecules is permanently changed, and the body is said to take a 

 set. After this the molecules will oscillate around their new position 

 of equilibrium and the body will again be perfectly elastic, within, 

 however, a different limit. 



The elastic force of wires of different substances may be found bj 

 the use of Gravesand's apparatus. Explanation of this. 



In stretching a rod or a wire the diameter is diminished one-fourth 

 of the extension in length, and therefore the whole volume is in- 

 creased . 



When the stretching force approaches the limit of cohesion, the 

 dilatation becomes very irregular. 



On the principle of taking a set depends the malleability and duc- 

 tility of bodies, or the properties of being extended and modeled by 

 the hammer, and of being drawn out into wire. 



Illustrati(ms. Gold is one of the most malleable substances; pla- 

 tinum one of the most ductile. A flat sheet of copper may be beaten 

 into a hollow globular vessel, with a small opening at the top, with- 

 out seam or joint. The rolling, coining, and stamping of metal 

 depend on the same princi2)le. Frequent annealing is necessary 

 during the process. 



(117.) Elasticity of Bending. — In the case of plates and rods the 

 force of bending is just in proportion to the degree of bending, and 

 within small limits the body in this respect is perfectly elastic. This 

 fact was discovered by Dr. Hooke in 1660, and expressed by the 

 phrase 



" Ut tensio sic vis." 



Experimental illustrations of this law. Weights suspended from 

 the middle, and also from the end of a flexible bar. Elongation of a 

 spiral spring. 



It follows from this law that all the vibrations of a thin plate fas- 

 tened at one end are isochronous. Proof of this — the force increases 

 in proportion to the distance to be passed over. 



It was this relation that suggested to Dr. Hooke the application of 

 the hair-spring to a watch. On the same principle also depends the 

 operation of the extemporary weighing machine, the spring balance, 

 and the dynamometer. 



Effect ot loading the spring ; the time of vibration must be as the 

 weight. 



In bending a rod the molecules on the concave side are pressed 

 nearer together, while those on the opposite side are drawn further 

 apart; between these a line must exist called the neutral axis, in 

 which the distance of the molecules is unchanged. These inferences 

 from the molecular hypothesis shown to be true by means of polarized 



