INSTRUMENTS ILLUSTRATING KINEMATICS. 63 



which have received a great deal of attention on account of their 

 frequent occurrence in nature ; such as Parabolic Motion, Simple 

 Harmonic Motion, Elliptic Motion. We propose to say a few 

 words in explanation of each of f hese. 



Parabolic ^e motion of a projectile, that is to say, of a body 

 Motion. thrown in any direction and falling under the influence 

 of gravity, was investigated by Galileo ; and this is the first pro- 

 blem of Kinetics that was ever solved. We must confine our- 

 selves here to a description of the motion, without considering 

 the way in which it depends on the circumstance of the presence 

 of the earth at a certain distance from the moving body. Galileo 

 found that the path of such a body, or the curve which it 

 traces out, is a parabola ; a curve which may be described as the 

 shadow of a circle cast on a horizontal table by a candle which 

 is just level with the highest point of the circle. 



It is convenient to consider separately the vertical and the hori- 

 zontal motion, for in accordance with a law subsequently stated in 

 a general form by Newton, these two take place in complete 

 independence of one another. So far as its horizontal motion is 

 concerned, the projectile moves uniformly, as if it were sliding on 

 perfectly smooth ice ; and, so far as its vertical motion is con- 

 cerned, it moves as if it were falling down straight. The nature of 

 this vertical motion may be described in two ways, each of which 

 implies the other. First, a falling body moves faster and faster as 

 it goes down ; and the rate at which it is going at any moment is 

 strictly proportional to the number of seconds which has elapsed 

 since it started. Thus its downward velocity is continually being 

 added to at a uniform rate. Secondly, the whole distance fallen 

 from the starting-point is proportional to the square of the number 

 of seconds elapsed ; thus, in three seconds a body will fall nine 

 times as far as it will fall in one second. The latter of these state- 

 ments was experimentally proved by Galileo ; not, however, in the 

 case of bodies falling vertically, which move too quickly for the 

 time to be conveniently measured, but in the case of bodies fall- 



