in the first of them. If the velocity acquired at the end of the first interval be v, shew that after a long lapse of time the velocity approaches a uniform velocity 2v. 40. Three smooth equal perfectly elastic billiard balls A, B, C are placed with their centres in the angular points of an equilateral triangle; shew that it will be impossible, with another equal ball, to cannon off A on to B,—A itself striking C,-unless the diameter of each ball be equal to half a side of the triangle. 41. A particle of given elasticity e is projected down a smooth vertical cylinder of indefinite length, but terminated by a horizontal plane at its lower end; the particle initially remaining in contact with the cylinder. If it be projected at a height h from the bottom with velocity V at an <a with the vertical, then after the time it will be moving uniformly with velocity V sin a. 42. Two perfectly elastic balls A and B impinge upon each other. First A impinges upon B at rest and goes off in a direction making an 0 with the line joining their centres : then B impinges upon A at rest and at the same angle of incidence, and goes off at an e'. Prove that 0+0= 180o. Prove also that if the balls be imperfectly elastic, and the angles of incidence in the two cases be a and a', then 43. Two equal balls, one perfectly elastic, the other inelastic, are dismissed by the same horizontal blow from the top of a flight of uniform steps, so that each falls just on the margin of the first step: shew that the number of steps cleared by the elastic ball in its successive flights is the series of successive odd numbers,—and that the two balls reach the bottom of the steps simultaneously. 44. From a point in the lower one of two parallel horizontal planes a ball of elasticity e is projected at an angle a,—is reflected by the upper plane, and again reflected by the lower one; the distance between the planes being th th that due to the velocity V of projection. If v be the velocity of the ball in rebounding for the mth time from the lower plane, By the same Author. A TREATISE ON OPTICS. 304 pp. (1859). Crown 8vo. IOS. 6d. The present work may be regarded as a new edition of the Treatise on Optics, by the Rev. W. N. Griffin, which being some time ago out of print, was very kindly and liberally placed at the disposal of the author. The author has freely used the liberty accorded to him, and has rearranged the matter with considerable alterations and additions-especially in those parts which required more copious explanation and illustration to render the work suitable for the present course of reading in the University. A collection of Examples and Problems has been appended, which are sufficiently numerous and varied in character to afford an useful exercise for the student: for the greater part of them recourse has been had to the Examination Papers set in the University and the several Colleges during the last twenty years. Subjoined to the copious Table of Contents the author has ventured to indicate an elementary course of reading not unsuitable for the requirements of the First Three Days in the Cambridge Senate-House Examinations. 23, HENRIETTA STREET, COVENT GARDEN, W.C. London and Cambridge. MACMILLAN AND CO.'S DESCRIPTIVE CATALOGUE OF CAMBRIDGE CLASS BOOKS. The Works in this Series of CAMBRIDGE CLASS-BOOKS FOR THE USE OF SCHOOLS AND COLLEGES, which have been issued at intervals during the last ten years, are intended to embrace all branches of Education, from the most Elementary to the most Advanced, and to keep pace with the latest discoveries in Science. Of those hitherto published the large and ever increasing sale is a sufficient indication of the manner in which they have been appreciated by the public. A SERIES of a more Elementary character is in course of publication, a list of which will be found on page 2 of this Catalogue. 2500 19: 10: 63. |