432 Prof. H. Helmholtz on Systems of Absolute 



is put not merely proportional, but equal to the value of 

 (7% . m 2 /r 2 ). Since the force and the length r are to be mea- 

 sured by known methods, the value of the product (wij . m 2 ) 

 is thereby determined in absolute measure ; and therefore, if 

 from other facts the ratio (m x /m 2 ) can be determined, m x and 

 m 2 can each be separately determined. 



Exactly the same principle is also applied by Gauss, at the 

 commencement of his memoir "Allgerneine Lehrsatze in 

 Beziehung auf die im verkehrten Verhaltnisse des Quadrats 

 der Bntfernung wirkenden Anziehungs- und Abstossungs- 

 krafte " *, to electrical quanta and gravitating masses. Al- 

 though he has not in the latter two cases carried the prin- 

 ciple into practical effect, it would be justifiable to designate 

 all three methods by his name as that of their mental author. 

 That which refers to electricity gives the electrostatic system 

 as -it has hitherto been employed. The third, referring to 

 gravitating masses, will probably in future play an important 

 part, when we have succeeded in accomplishing more exact 

 determinations of the force of gravitation. If, like Maxwell, 

 we denote by angular brackets the dimensions of the expres- 

 sion enclosed in them, by M a mass, by L a length, and by T 

 a time, according to Gauss the attraction between two heavy 

 masses m at the distance r is 



H-ff£] «£]-&]■ 



On the left stands a density, on the right a function of the 

 time. If, therefore, as hitherto, we put the absolute density 

 of water equal to unity, while the unit of mass is determined 

 in gravitation-measure, a time-measure is thereby given which 

 is independent of the probably variable rotation of the earth, 

 and only a single measure, the metre, is left to be handed 

 down by tradition. But even this could be absolutely defined 

 if we availed ourselves of an invariable velocity, for instance 

 the velocity of light in free Eether. 



Thus, for example, the period of revolution T of a small 

 satellite revolving close to the surface of a sphere of pure 

 water of normal density D, would, independently of the radius 

 of the sphere, in gravitation-measure be 



T2— ??T 

 D' 



and the velocity of light 



* Resultate aus den Beobachtumjen des maynetischen Verema L839, 



