An Appendix is added, containing certain geometrical properties of the cycloid, which it was necessary to assume; and a number of problems, selected principally from recent Examination Papers in the Senate-House and S. John's College. I have to thank those friends who have in many ways assisted me in this work, especially Professor Sandeman, M.A. of Queens' College, who permitted me to make unlimited use of his valuable treatise mentioned above, Mr W. H. Besant, M.A. of S. John's College, Rev. N. M. Ferrers, M.A. of Caius College, and Mr E. Wilson, M.A. of Trinity College. Determination of the unit of velocity, and of the measure of any 6. Transformation of the measure of a velocity to other units of space and Resolved part of a given velocity in any given direction 13. Measure of a variable velocity 14. Relation between space, time, and variable velocity 17. The parallelogram of velocities, &c. is true for variable velocities IO SIONS FOR VELOCITIES AND ACCELERATIONS IN CERTAIN DIREC- 29. Method to be pursued in order to determine any motion 30. Relations between acceleration, space, time and velocity 35. Tangential and normal velocities and accelerations PAGE Time of oscillation in this case General case of rectilinear motion (II.) Curvilinear motion. Three pairs of equations to determine it Acceleration ∞ distance: determination of the path Determination of the constants from the initial circumstances Determination of the constants in terms of the axes of the path 94. The idea of motion a geometrical one ᎪᎡᎢ . PAGE 96. The science of force is statics. Fundamental law of force; by means of 97. Experimental laws necessary to reduce dynamics into the geometrical 98. Axiom to determine the motion of a particle 99. Object of the experimental laws of force, and manner of arriving at them ib. (2) This is not altered by any initial motion in that direction. (3) Nor by any initial motion in any other direction. (4) The acceleration produced varies as the intensity of the force. (5) It is independent of any other force acting in the same direction. 109. Definition of the motional effect of a force, momentum, and vis viva. ib. ib. 63 I12. Atwood's machine 64 |