538 



SCIENCE. 



[N. S. Vol. XXIV. No. 617. 



The corpol-atioii of the institute has re- 

 cently met a disastrous defeat in^its attempt 

 to form a merger with Harvard University 

 against the wishes of the faculty and alumni. 

 Should it be so ill-advised as to elect a presi- 

 dent without consultation with the faculty, 

 it is to be hoped that Professor West will not 

 accept until he assures himself of their ap- 

 proval. It is indeed quite possible that the 

 election will be welcomed by the faculty, and 

 that they will obtain a president beyond re- 

 proach — in which case science will have cap- 

 tured a captain from the enemy's camp. 



J. McKeen Cattell. 



SPECIAL ARTICLES. 



A SIMPLE METHOD OF ILLUSTRATING UNIFORM 



ACCELERATION. 



The following method of illustrating in the 

 presence of a class (or as a simple laboratory 

 exercise) the principle of uniformly accel- 

 erated raotion exceeds in simplicity, accuracy 

 and interest any that I have hitherto found. 



A ball rolling down a groove in an inclined 

 planlc and at the same time vibrating across 

 the groove has a constant acceleration in one 

 direction, while its transverse vibrations are 

 pendular motions that mark the time. If the 

 groove be painted black and well polished, 

 lycopodium dusted on the groove will preserve 

 a very sharp trace of the motion of the ball. 

 When the powder has been blown off by a 

 wave of a fan the trace comes out with the 

 distinctness of a sharp chalk line. The dis- 

 tances traversed in successive vibrations of 

 the ball are raeasured along a white thread 

 stretched accurately in the middle of the 

 groove (or along a white paint line). The 

 two motions should start simultaneously in 

 the middle of the groove; this may be secured 

 by allowing the ball to roll initially along a 

 transverse brass strip extending to the middle 

 of the groove. 



The frictional resistance to the motion of 

 the ball is negligible and the constancy of 

 the ratio of linear distance to square of num- 

 ber of vibrations depends only on the accuracy 

 of the measurements and the straightness of 

 the plank. 



To illustrate the principle of constant accel- 

 eration the actual period of vibration of the 

 ball is not required; but it may be found by 

 observation or by timing a short pendulum 

 that vibrates in unison with the ball. The 

 linear acceleration of the ball can readily be 

 shown to be 5/7 g sin (inclination of plank). 

 The vibrating ball is a simple pendulum of 

 length equal to the distance from the center 

 of the ball to the center of curvature of the 

 groove; but, to calculate the period, 5/7 g 

 must be used instead of g. 



Several other points of interest may be 

 noted. The record may be obtained by dust- 

 ing the powder on the groove after the ball 

 has rolled down. The record can only be 

 completely removed by a damp cloth. The 

 track of the ball on the powder is very curious 

 and interesting, consisting of a ridge of 

 powder with a clearing on each side. A 

 very striking lecture experiment is to use fine 

 sulphur powder instead of lycopodium; if the 

 plank be raised to a vertical position, and 

 brought down sharply on the table the record 

 will appear instantaneously. If the plank be 

 horizontal, the path of the ball will be a nearly 

 perfect simple harmonic wave. If the grooved 

 plank be placed on an inclined-plane plank, 

 the coefficient of kinetic friction between the 

 two may be deduced from two records, the 

 first with the grooved plank held at rest, the 

 second with the grooved plank in sliding 

 motion. 



I have found a groove five feet long, four 

 inches wide and of four inches radius and 

 a steel ball one and a half inches in diam- 

 eter very satisfactory. The groove could be 

 chipped out in a moment on a molding ma- 

 chine with knives of sufficient size; but, in 

 the absence of such facilities, a number of 

 longitudinal saw cuts of graduated depth, 

 made by a circular saw, will render it easy to 

 chisel the groove out by hand. 



The International Instrument Co., of Cam- 

 bridge, Mass., will supply the above apparatus 

 on order. 



A. WiLMER Duff. 



WoECESTEB Polytechnic Institute, 

 Worcester, Mass. 



