82 M. A. P. Sundell on Absolute 



1. Various physical conceptions have resulted from the 

 endeavour of physicists to represent the results of their re- 

 searches mathematically as simply as possible, and to extend 

 them. Most physical conceptions, even if not required for 

 this special purpose, are at any rate absolutely necessary for 

 a satisfactory formal demonstration of physical laws. If, for 

 example, we seek to represent the law of a given uniform 

 motion mathematically, the equation 



•=<* (1) 



is sufficient ; in which 8 represents the distance described in 

 the time t, and c is a constant dependent on the units employed 

 for s and t. If by means of this equation we determine the 

 value of the constant c by means of the distance described in 

 a given time, we are then able to calculate the distance for any 

 time /. The equation (1) may then be regarded as the ma- 

 thematical representation of the law of the given motion. But 

 with the value found for the constant, the equation can be 

 used only for this particular motion, and not for any other 

 uniform motion. But for any other motion of the same kind, 

 an equation of the same form may be used,Jbut with a different 

 value of the constant c. It is in fact impossible to give a 

 general formula for uniform motion with only the two con- 

 ceptions of distance and time. But if we employ also a third 

 conception, h, proportional to the ratio of distance to time, Ave 

 obtain the formula e 



*=4 (2) 



which is sufficient for any uniform motion. This conception 

 (Ji) is of course that of velocity. If from any particular uni- 

 form motion we determine the value of the constant c, we are 

 able to calculate from the formula (2) the value of any one of 

 the three quantities when the values of the two other quantities 

 are given. 



Equation (2) may be regarded as the general formula of 

 uniform motion ; but it may also be regarded, on the other 

 hand, as an equation defining the conception of velocity, if we 

 take the conceptions of space and time as already in an}- way 

 defined. Each new conception in physics may be defined by 

 an equation containing this new quantity, together with other 

 quantities previously defined. Thus, for example, the con- 

 ception of acceleration may be defined by the equation 



which relates to uniformly accelerated motion with zero initial 





