Waterbury evening Democrat., 1889-02-14
OOOOO

arc of a circle it has no part of the curve of that figure. It is figure described | as generated by the revolution of circle upon plane.
 Its properties are described in some
 mathematical orks, but we desire here | to call attention to one circumstance
 only, the unequal motion of the point by
 which the figure is described. In other
 words it is that if, when a wagon is
 moving uniformly forward, we trace
 the motion of any point of the tire from
 the time it leaves the ground until it re-
 turns to it again, we shall find that it
 moves through very unequal spaces in equal times.
 | The motion increases from the time
 the point leaves the ground until it
 reaches the highest point, and decreases again until it reaches the ground at the end of its revolution. The upper half I therefore Of the wheel moves much faster than the lower. This seems par | adoxical, but it is strictly true, as any one may satisfy himself in a moment by setting up stake by the side of a wheel and moving the wheel for | ward a few inches. When, however. l we come to think of the matter, we must know that such will be the case, or how could the wheel turn? Move the lower | part as fast as the upper and the wheel must drag. One moment we see a given point directly at the back part of the
 wheel and at the next 1t is in front; how
 did it change places but by out-traveling 1 the other parts In a moving wheel no
 part ever moves backward, as in a stand
 ing one.
 | If the circumference of wheel were
 marked at every 10 degrees and then
 rolled uniformly forward while the point at the first degree would trace the
 cycloidal curve, and if the diameter of
 the wheel were divided into 1 1000 parts,
 the portions of the curve described in
 the several equal times would be (reject-
 ing fractions less than tenthsl 1.6, s2.s,
 SIS, 52.4, 66.S, S06. 93.S, 106.2, 117.S,
 1886, 134.4, 147.2, 154.S, 1912, 1864,
 170.4, 172.9, 1743, which carries us to
 the highest point of the figure; and the
 same numbers reversed in regular order
 will carry us forward to the ground
 again. From this it appears that though the motion continues to increase until
 the mark reaches the highest point, and then decreases to the ground again, it is
 not uniform ratio. In the last 10 de-
 grees the generating point passes through
 more than 23 times the distance it
 does in the first 10 degrees, and hence on
 an average moves 23 times as fast, yet
 the last degree as compared with the first would show far greater relative
 motion: and this would be increased as
 the parts compared are diminished. PROF JAMES CHISHOLM. Prof Chisholm has made a very plausi- ble if not very clear explanation of his
 claim, and one that the average lay mino who is less familiar with the jugglery o1
 figures and the mysteries of geometry can hardly be expected to disprove. We
 think, however. that he makes the mis
 take of regarding all above the hub as the top, while considering as the bottom
 only the portion of the wheel that touch
 es the ground. Under such condition,
 his thesis would be proved at once But taking any given point of the tire f that is exactly opposite another it would
 seem impossible that one point, whether , it be at the time at the top or bottom , should move faster than the other, elss it would lot keep its position in the tire , and the uniformity of the wheel woult be destroyed. At any point of the wheel: revolution the points keep uniformly op , posite to each other, and this 1t would
 seem they could not do if they failed tt move at the same rate of speed. It | , this fact that leads the average mind tt
 the conclusion that the wheel moves uni
 formly and that consequently the tol
 does not move faster than the bOttom-s
 conclusion which we think most natura despite Prof Chisholm's ingenious theo
 ". In this connection we might stat. that Superintendent Crosby and Proi
 Hovey support our position.-ED DEM OCRAT.
 Prof Hovey's Idea of It. , In regard to the question which Ina: l been discussed in the DEMOCRAT as tc l whether there is any difference in tht } rate of motion at different points of the l circumference of a wagon wheel, would say that the position taken by . the editor is correct, viz: there can b. = no difference. The tire may be take1 a to represent the circumference. Now thi , is rigid body and the cohesion between = it's particles is very great and is sufh cient to overcome any tendency to accel : eration or retardation due to friction O.
 any other cause; if this cohesion wer,
 not sufficient to produce thls effect, on' = part or another of the tire would get il :. advance of the rest or be left behind S and the tire would break. However, i I is true that any point within the tir II