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.

4.

Determination of the unit of velocity, and of the measure of any

velocity

6. Transformation of the measure of a velocity to other units of space and

12.

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

Acceleration and retardation

18.

20.

Determination of the unit of acceleration and of the measure of an

acceleration

21.

The sign

to an acceleration indicates retardation

22.

Variable acceleration

23. Relation between velocity, time, and variable acceleration

26. Parallelogram of accelerations

27. Transformation of the measure of an acceleration to other units of space

and time

PAGE

I

ib.

IO

ib.

ib.

II

CHAPTER II.

OF THE MOTION OF A POINT IN GENERAL.

ART.

ANALYTICAL EXPRES-

SIONS FOR VELOCITIES AND ACCELERATIONS IN CERTAIN DIREC-
TIONS.

29. Method to be pursued in order to determine any motion

30. Relations between acceleration, space, time and velocity
32. Expressions for velocities and accelerations in direction of the axes of
x, y, and z

33. Radial and transversal velocities

34. Radial and transversal accelerations

PAGE

14

ib.

15

ib.

16

17

37. Dimensions of the measure of a velocity or acceleration.

19

35. Tangential and normal velocities and accelerations

CHAPTER III.

OF THE MOTION OF A POINT AFFECTED BY A CONSTANT ACCELERA-

TION, THE DIRECTION OF WHICH IS ALWAYS THE SAME.

48. Investigation of the above by means of the differential calculus .

25

CHAPTER IV.

OF THE MOTION OF A POINT AFFECTED BY AN ACCELERATION, THE

DIRECTION OF WHICH ALWAYS PASSES THROUGH A FIXED POINT.

50. The two kinds of this motion

51. (I.) Rectilinear motion, acceleration ∞ distance

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

Velocity = (semi-conjugate diameter)

Determination of the axes from the initial circumstances

2π

75.

Period =

90.

Normal acceleration measuring the tendency to proceed in a

straight line

ib.

92. Distinction between material and immaterial things, by the possession of

95. Generalization of the idea of force: method on which a force must be

estimated

51

94. The idea of motion a geometrical one

ᎪᎡᎢ .

PAGE

96. The science of force is statics.

Fundamental law of force; by means of

which statics is reduced into geometry

52

97. Experimental laws necessary to reduce dynamics into the geometrical

science of motion

98. Axiom to determine the motion of a particle

99. Object of the experimental laws of force, and manner of arriving at them ib.

ib.

53

CHAPTER VI.

OF THE DYNAMICAL LAWS OF FORCE, COMMONLY CALLED THE

LAWS OF MOTION.

(1) A constant force produces a constant acceleration in its own

direction.

(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.

(6) And of any force acting in any other direction.

(7) All this is true for variable forces.

109. Definition of the motional effect of a force, momentum, and vis viva.

ib.

ib.

63

I12.

Atwood's machine

64