LECTURES 



197 



(33.) In the consideration of motion tlie ideas of space and time 

 are necessarily involved. 



Time is considered as a quantity consisting of parts which can be 

 compared or measured. 



Imperfectly measured by a succession of ideas. 



Circumstances which vary the apparent rapidity of the lapse of time. 



(34.) In the exact measurement of time, the following axiom is as- 

 sumed — In the operations of nature the same effects under the same cir- 

 cumstances are always produced in equal times. 



Examples : The fall of a stone from the same height to-day and yes- 

 terday ; the successive vibrations of a pendulum ; flowing of equal 

 quantities of sand ; the revolutions of the earth on its axis. 



(35.) Uniform motion is that in which equal spaces are passed over 

 in equal times. • • i 



Motion of the earth on its axis perfectly uniform. From this is de- 

 rived the principal unit of time— the day ; the subdivisions of which 

 give the lesser divisions. 



By the whirling mirror less than the to irV o u^li part of a second can 

 be measured, and yet great physical changes are produced in this in- 

 terval. 



(36.) The velocity or rate of motion of a moving body, is the ratio 

 of the space described to the time of describing it. Illustrations. 



Velocity, time, and space, are heterogepeous quantities, and are 

 therefore compared numerically. 



Unity of time and of space— hour, mile — second, foot. 



The 'relations of uniform motion are expressed by the following 

 equations ; 



S=YT; T=|; V= |. (1.) 



(37.) Variable motion is that in which equal spaces are not described 

 in equal times. 



The velocity may be constantly increasing or constantly decreasing. 

 Two cases of each kind : 1. Variation equal in equal times ; 2. Vari- 

 ation unequal in equal times. 



INERTIA. 



(38.) That property of matter by which it tends to retain its state, 

 whether of rest or motion. [La Place.] 



(39.) It has been established by a wide induction that a body at rest 

 cannot of itself begin to move and that a body in motion cannot change 

 its velocity nor its direction of motion luithout the action of some extra- 

 neous cause. 



This is called the law of Inertia. (See Mechanics.) 



It may be otherwise stated as follows : 

 • A body at rest tends to remain continually at rest ; a body in free 

 motion tends to move continually (1) with a uniform velocity, and 

 (2) in a straight line. 



