T/i T/ \ / v f 



THE HUMAN MOTOR 



T 



If / = - * we shall have s = a ; 

 4 



if / = T, s = o, and so on. The 

 curve is repeated periodically like 

 the movement, and is called 



TA " sinusoidal." Thus the move- 



men that has for its equation 



s = a sin 27c is shown by the 



diagram above ; there we see clearly 

 F '- 10 the amplitude and the period of trie 



movement, and we can ascertainjthe character of the oscillations. 

 Let us take a simple rule, that of the movement 



s = vt. 



The moving point occupies the two positions M and M' in the 

 time t and t'. Take the lengths OP and OP' proportional to the 



time on the line of the abscissae, and 

 the lengths PM and P'M' (fig. 11). 

 proportional to the spaces traversed, 

 on the axes of the ordinates. The 

 line OMM' will give the diagram or 

 the curve of the movement. Knowing 

 the equation of a movement it will 



I, always be possible to represent it by 



a graph. For this squared paper 

 FI. 11 should be used. Generally, in equations 



analogous to s = vt, there are two variables, s and t, 

 space and time, that is to say, y and x. Their relation constitutes 

 the law of the phenomenon considered. Thus the height p of a 

 barometer diminishes in proportion as a mountain is climbed. 

 The variation of one of the heights determines that of the other ; 

 from this is derived the term " variable." Therefore, if one 

 of the variables is known, owing to their relation, the value of 

 the other can be calculated. The known quantity is described 

 as the independent variable and a function / obtained therefrom. 

 There can be several independent variables. For example, the 

 barometric height is a function of the height of the ascent h, and 

 of the temperature T of the air, etc. 

 We write: $=/(*), 



p=f(h, T)..., 

 to designate the above-mentioned functions. 



But when there are two independent variables, we take 

 three axes of rectangular co-ordinates to represent the variation 

 of the function. We shall not insist upon this complex method, 

 but shall say that, to find the law of a phenomenon, we must 



