84 M. A. F. Sundell on Absolute 



velocity of light as the unit of velocity, we must put * = 40000, 

 tssl } Ti—\\ hence c = jtt^tt. Equation (2) becomes there- 

 fore /i=TAjwr, or 6' = 40000 ht; which holds good for any 



uniform motion so long as distance, time, and velocity are 



expressed in the units chosen. But if we take as unit of 



length a quadrant of the earth's meridian (1350 geographical 



miles) without changing the other units, then we must put 



40000 800 ... , ,. . 27 



«= i ocr> = s^Ti and the constant c has now the value 37^:. 

 1350 27 ' 800 



As the constants of the equations thus change with the units, 

 so, conversely, by choosing appropriate units, particular values 

 may be given to the constants. If we choose the units so as 

 to make certain constants equal to unity, the corresponding 

 equations assume the simplest form, and the constants disap- 

 pear from them. Units so chosen are termed absolute units, 

 and form an absolute system. If we assume that p (the num- 

 ber of equations) is smaller than q (the number of quantities), 

 then we may eliminate all the constants by choosing the units 

 properly; q—p units remaining undetermined, and p units 

 having values determined by the condition that each constant 

 is equal to unity. But if we wish to have more than q—p 

 units, say q—p + x undetermined, then x constants must be 

 retained, which are then to be considered as independent con- 

 ceptions. Let us take a few examples. The four conceptions 

 distance, time, velocity, and acceleration are connected by 

 the equations (2) and (3). If we wish to eliminate the two 

 constants, we must take as unit of velocity the velocity of the 

 uniform motion in which unit distance is described in unit 

 time ; the unit of acceleration must be the acceleration of a 

 uniformly accelerated motion in which the velocity increases 

 or diminishes in unit time by unit velocity. 



Then equations (2) and (3) may be written as follows: — 



*=?> (8) 



•=*' W 



and similarly equations (4) and (5) become 



''=§> ( 10 > 



dh t , . s 



