INSTRUMENTS ILLUSTRATING KINEMATICS. 65 



called on the Continent, and lately also in England, the Differen- 

 tial Calculus ; because the difference between two values of the 

 varying quantity is mentioned in one of the processes that may be 

 used for calculating its fluxion. The inverse problem, Given that 

 the velocity is proportional to the time elapsed, to find the dis- 

 tance fallen, is a particular case of the general problem, Given 

 how fast a body is going at every instant, to find where it is at 

 any instant j or, Given the fluxion of a quantity, to find the quan- 

 tity itself. The answer to this is given by Newton's Inverse 

 Method of Fluxions ; which J[s also called the Integral Calculus, 

 because in one of the processes which may be used for calculating 

 the quantity, it is regarded as a whole (integer) made up of a 

 number of small parts. The method of Fluxions, then, or Differ- 

 ential and Integral Calculus, takes its start from Galileo's study of 

 parabolic motion. 



Harmonic ^ e anc i en ^ s ? regarding the circle as the most perfect of 

 Motion, figures, believed that circular motion was not only simple, 

 that is, not made up by putting together other motions, but also 

 perfect, in the sense that when once set up in perfect bodies it 

 would maintain itself without external interference. The moderns, 

 who know nothing about perfection except as something to be 

 aimed at, but never reached, in practical work, have been forced 

 to reject both of these doctrines. The second of them, indeed, 

 belongs to Kinetics, and will again be mentioned under that head. 

 But as a matter of Kinematics it has been found necessary to 

 treat the uniform motion of a point round a circle as compounded 

 of two oscillations. To take again the example of a clock, the 

 extreme point of the minute-hand describes a circle uniformly j but 

 if we consider separately its vertical position and its horizontal 

 position, we shall see that it not only oscillates up and down, but 

 at the same time swings from side to side, each in the same period 

 of one hour. If we suppose a button to move up and down in a 

 slit between the figures XII. and VI., in such a way as to be 

 always at the same height as the end of the minute-hand, this 



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