330 HISTORY OF MECHANICS. 



may be remarked that Newton, having established the laws of Curvi- 

 linear Motion independently, has, in a great part of his Seventh Sec- 

 tion, deduced the simpler case of the Rectilinear Motion from the more 

 complex problem, by reasonings of great ingenuity and beauty. 



Sect. 3. — Establishment of the Second Law of Motion. — Curvilinear 



Motions. 



A slight dem'eu of distinctness in men's mechanical notions enabled 

 them to perceive, as we have already explained, that a body which 

 traces a curved line must be urged by some force, by which it is 

 constantly made to deviate from that rectilinear path, which it would 

 pursue if acted upon by no force. Thus, when a body is made tc 

 describe a circle, as when a stone is whirled round in a sling, we find 

 that the string does exert such a force on the stone ; for the string is 

 stretched by the effort, and if it be too slender, it may thus be broken. 

 This centrifugal force of bodies moving in circles was noticed even by 

 the ancients. The effect of force to produce curvilinear motion also 

 appears in the paths described by projectiles. We have already seen 

 that though Tartalea did not perceive this correctly, Rivius, about the 

 same time, did. 



To see that a transverse force would produce a curve, was one step ; 

 to determine what the curve is, was another step, which involved the 

 discovery of the Second Law of Motion. This step was made by 

 Galileo. In his Dialogues on Motion, he asserts that a body projected 

 horizontally will retain a uniform motion in the horizontal direction, 

 and will have, compounded with this, a uniformly accelerated motion 

 downwards, that is, the motion of a body falling vertically from rest ; 

 and will thus describe the curve called a parabola. 



The Second Law of Motion consists of this assertion in a general 

 form ; — namely, that in all cases the motion which the force will produce 

 is compounded with the motion which the body previously has. This 

 was not obvious; for Cardan had maintained," that " if a body is moved 

 by two motions at once, it will come to the place resulting from their 

 composition slower than by either of them." The proof of the truth of 

 the law to Galileo's mind was, so far as we collect from the Dialogue 

 itself, the simplicity of the supposition, and his clear perception of the 

 causes which, in some cases, produced an obvious deviation in practice 



11 Op. vol. iv. p. 490. 



