32 LECTURE V. 



the rotation of the ball in such a manner that its axis coincides at first with 

 the path of the ball, so that the same face of the ball is turned in succession 

 every way. For the ordinary purposes of gunnery, an estimation governed 

 by experience is found to be the best guide ; at the same time there is no 

 doubt but that some assistance may be obtained from theory and from ex- 

 periment. Those who are desirous of pursuing the subject may find much 

 information relating to it, collected by Professor Robison, in the article 

 'Projectile' of the Encyclopaedia Britannica. 



LECT. IV. ADDITIONAL AUTHORITIES. 



Central Forces. Hooke, Birch's History of the Royal Society, ann. 1664-6, ii. 

 69, 90. Huygens de vi centrifuga, Op. post ; de causa gravitatis, 1690. Keill, Ph. 

 Tr. 1708, p. 174; 1714, p. 91. Demoivre, Ph. Tr. 1717, p. 622. Maclaurin, 

 Geom. Organ. 4to, 1720. Louville, Hist, et Mem. de 1'Acad. de Paris, 1720. Mau- 

 pertuis, ibid. 1732, p. 343, H. 112. Montigny, 1741, p. 280, H. 143. Bosco- 

 vich, Com. Bon. II. iii. 262. Waring, Ph. Tr. 1788, p. 67. Manchester Memoirs, 

 iv. 369 ; v. 101. Trembley, Hist, et Mem. de 1'Acad. de Berlin, 1797, p. 36. 

 Brinkley, Trans, of the Royal Irish Academy, viii. 215. Lagrange, Miscellanea 

 Taurinensia, ii. II. and iv. IV. Airy on Gravitation, 1834. 



On Projectiles and Gunnery. Frisius, Cosmographia, iv. Antwerp, 1584. Digges 

 on the Art of Great Artillery, 4to, 1624. Halley, Ph. Tr. 1686, p. 3 ; 1695, p. 68. 

 Bernoulli, Comm. Physico-Math. Paris, 1710. Keill, Ph. Trans. 1715, p. 91. 

 T. Simpson, ibid. 1748, p. 137. Robins, ibid. 1743, xlii. 437; and Mathematical 

 Tracts, 2 vols. 1761. Borda, Hist, et Mem.deFAcad. de Paris, 1769, p. 247, H. 116. 

 Glenie, History of Gunnery, Edin. 1776. Brown, The True Principles of Gunnery, 

 4to, 1777 (partly a translation from Euler). Hutton, Ph.Tr. 1778, p. 50 ; Tracts, 4to, 

 1786, v. 3. Pringle, A Discourse on the Theory of Gunnery, 4to, 1778. Thompson 

 (Count Rumford), Ph. Tr. 1781, p. 229 ; 1797, p. 222. Inman, An Introduction to 

 Naval Gunnery, Portsea, 1828. 



LECTURE V. 



ON CONFINED MOTION. 



WE have hitherto considered the principal cases of motion, either un- 

 disturbed, or simply subjected to the action of an accelerating, retarding, or 

 deflective force. We now proceed to examine the effects of an additional 

 modification, which is introduced when the motion is limited to a given 

 line or surface of any kind ; the body either being supposed to slide on the 

 surface of a solid actually extended, or being confined to an imaginary sur- 

 face by its attachment to a thread, or still more narrowly restricted by 

 means of two threads, which allow it to move only in a given line. Sus- 

 pension is the most convenient mode of making experiments on confined 

 motion ; but it is not always easy to cause the body to remain in the sur- 

 face that is required ; and to confine it in this manner to a perfectly plane 

 surface is impossible. When we suffer a body to slide along any surface, 

 there is a loss of force from friction, from the production of rotatory 

 motion, or from both these causes combined. The effect of friction is 



