Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/214

 as in the greater, the velocity is greater onely in the bigger wheel, for that its circumference is bigger; there is no man that thinketh that the cause of the extrusion in the great wheel will encrease according to the proportion of the velocity of its circumference, to the velocity of the circumference of the other lesser wheel; for that this is most false, as by a most expeditious experiment I shall thus grosly declare: We may sling a stone with a stick of a yard long, farther than we can do with a stick six yards long, though the motion of the end of the long stick, that is of the stone placed in the slit thereof, were more than double as swift as the motion of the end of the other shorter stick, as it would be if the velocities were such that the lesser stick should turn thrice round in the time whilst the greater is making one onely conversion.

This which you tell me, Salviatus, must, I see, needs succeed in this very manner; but I do not so readily apprehend the cause why equal velocities should not operate equally in extruding projects, but that of the lesser wheel much more than the other of the greater wheel; therefore I intreat you to tell me how this cometh to pass?

Herein, Sagredus, you seem to differ much from your self, for that you were wont to penetrate all things in an instant, and now you have overlook'd a fallacy couched in the experiment of the stick, which I my self have been able to discover: and this is the different manner of operating, in making the projection one while with the short sling and another while with the long one, for if you will have the stone fly out of the slit, you need not continue its motion uniformly, but at such time as it is at the swiftest, you are to stay your arm, and stop the velocity of the stick; whereupon the stone which was in its swiftest motion, flyeth out, and moveth with impetuosity: but now that stop cannot be made in the great stick, which by reason of its length and flexibility, doth not entirely obey the check of the arm, but continueth to accompany the stone for some space, and holdeth it in with so much less force, and not as if you had with a stiff sling sent it going with a jerk: for if both the sticks or slings should be check'd by one and the same obstacle, I do believe they would fly aswell out of the one, as out of the other, howbeit their motions were equally swift.

With the permission of Salviatus, I will answer something to Simplicius, in regard he hath addressed himself to me; and I say, that in his discourse there is somewhat good and somewhat bad: good, because it is almost all true; bad, because it doth not agree with our case: Truth is, that when that which carrieth the stones with velocity, shall meet with a