120 LECTURE XIII. 



firmness from the accumulation of weight, which makes the resistance of 

 their lower parts to any lateral motion almost insuperable. 



When a hard body penetrates another, or when a substance is ground 

 away by the attrition of another, the force which opposes the motion, is 

 to be considered, like the force of friction, as a uniformly retarding force. 

 There is no reason for imagining the stiffness of a bar, whether longer or 

 shorter, to depend on the velocity of the body that bends it, and the space 

 through which it may be bent, without breaking, is also limited only by 

 the toughness of the materials. In the same manner, when the internal 

 parts of a solid are broken and displaced by the penetration of another, or 

 its external parts abraded by its attrition, the resistance is the same, what- 

 ever the velocity may be, and the space described by the body before its 

 velocity is destroyed, is always proportional to the square of that velocity, 

 or to the energy which results from a combination of the proportions of 

 the velocity and the momentum. 



LECT. XIII. ADDITIONAL AUTHORITIES. 



Passive strength. Buffinger on the Strength of Beams, Comm. Petr. iv. 164. 

 Muschenbroek, Systeme de Physique, par Lafond, Par. 1760. Buffon on the 

 Strength of Timber, Hist, et Mem. de Paris, 1738, p. 169, H. 54; 1740, p. 453 ; 

 1741, p. 292. Duhamel on do. ibid. 1742, p. 335 ; 1768, p. 534, H. 29. Jurin 

 on the Elastic Force of Springs, Ph. Tr. 1744, p. 46. Emerson's Fluxions, 343, 

 Mechanics, 4to, 1758. Euler, Novi Com. Petr. 1757. Acta Petr. 1758. Belidor, 

 Architecture Hydraulique, I. ii. 92. Jo. Bernoulli on the Extension of Threads, 

 &c. Hist, et Mem. de Berlin, 1766, pp. 78, 108. Coulomb on the Force of Tor- 

 sion, Hist, et Mem. de Paris, 1784, p. 229. Gauthey on the Strength of Stones, 

 Rozier's Journal, iv. 402. Dupin sur la Flexibilite, la Force, et 1'Elasticite des 

 Bois, Journal de 1'Ecole Poly technique, x. 137. Rennie, Ph. Tr. 1818. Barlow 

 on the Strength of Timber, 1824 ; Iron, 1835. Do. do. Second Report, 1835. 

 Tredgold on the Strength of Iron, Lond. 1824. Hodgkinson's Memoirs of the Lit. 

 and Phil. Soc. of Manchester, vols. iv. and v. 



Friction. Amontons on the Resistance of Mach. Hist, et Mem. 1699, p. 206, 

 H. 104 ; 1700, p. 47 ; 1703, H. 105 ; 1704, pp. 173, 206. Parent, do. ibid. 1700, 

 H. 149 ; 1704. Sauveur on the Friction of Ropes coiled round a Cylinder, ibid. 

 1703, p. 305. Varignon, do. ibid. 1717, p. 195, H. 68. Euler on Friction, Hist, 

 et Mem. de Berlin. 1748, pp. 122, 133. Novi Com. Petrop. vi. 233; xx. 304, 327. 

 Bernoulli, ibid. xiv. i. 249. Hedin, Dissertatio Physico-Mechanica de Frictione, 4to, 

 Upsal, 1770. Ximenes, Teoria e Pratica delle Resistenze de' Solidi ne' loro Attriti, 

 2 vols. 4to, Pisa, 1782. Library of Useful Knowledge, Mechanics, Third Treatise. 

 Morin, Nouvelles Experiences sur le Frottement, 3 vols. 4to, Paris, 1843. The 

 newest and best authority. 





