186 THE CONTINUITY OF MOTION. 



trine of the Continuity of Motion will be entirely mis- 

 apprehended. 



§ 56. As expressed by Xewton, the first law of motion 

 is that " every body must persevere in its state of rest, or of 

 uniform motion in a straight line, unless it be compelled to 

 change that state by forces impressed upon it." 



AVith this truth may be associated the truth that a body 

 describing a circular orbit round a centre which detains it 

 by a tractive force, moves in that orbit with undiminished 

 velocity. 



The first of these abstract truths is never realized in the 

 concrete, and the second of them is but approximately 

 realized. Uniform motion in a straight line, implies the 

 absence of a resisting medium; and it further implies the 

 absence of forces, gravitative or other, exercised by neigh- 

 bouring masses: conditions never fulfilled. So, too, the 

 maintenance of a circular orbit by any celestial body, im- 

 plies both that there are no perturbing bodies, and that there 

 is a certain exact adjustment between its velocity and the 

 tractive force of its primary: neither requirement ever 

 being conformed to. In all actual orbits, sensibly elliptical 

 as they are, the velocity is sensibly variable. And along 

 with great eccentricity there goes great variation. 



To the case of celestial bodies which, moving in eccen- 

 tric orbits, display at one time little motion and at another 

 much motion, may be joined the case of the pendulum. 

 With speed now increasing and now decreasing, the pen- 

 dulum alternates between extremes at which motion ceases. 



How shall we so conceive these allied phenomena as to 

 express rightly the truth common to them? The first law 

 of motion, nowhere literally fulfilled, is yet, in a sense, 

 implied by these facts which seem at variance with it. 

 Though in a circular orbit the direction of the motion is 

 continually being changed, yet the velocity remains un- 

 changed. Though in an elliptical orbit there is now accel- 



