430 Prof. H. Helmholtz on Systems of Absolute 



It is quite clear, therefore, that the remarkable expression 

 (1) found by Mr. Darwin is not peculiar to his special hypo- 

 thesis of a viscous earth, but can be deduced equally well 

 from the totally distinct hypothesis of an absolutely rigid 

 earth retarded by the tidal action of a liquid ocean. 



I was led by this result to consider the case of the earth- 

 moon, separating (as I believe they did) from the central 

 solar mass in the form of a swarm of discrete masses of mete- 

 oric iron and stone, each one having the temperature of the 

 cold of interstellar space, or not much above it. Translating 

 this conception into mathematical language, I find that the 

 equation of continuity belonging to the hydrodynamical 

 theory applies equally well to the meteoric theory, viz. 



vy=v'y', (7) 



where v, v' are the velocities at any two points, and y, y' are 

 the depths of the ocean or meteoric swarm at the same points. 



The depth of the swarm or ocean without jostling or friction 

 will be least under the moon and greatest at right angles to 

 the moon, and the velocities will be inversely. Hence the 

 chances of jostling among the meteorites when disturbed by 

 the moon's tidal action will be proportional to the velocity, 

 being greatest where the velocity is greatest and the area of 

 passage least, and vice versa. 



This consideration reduces the meteoric problem to that of 

 the hydrodynamical problem, with a friction proportional to the 

 velocity, and gives equations in all respects similar to those 

 derived by Mr. Darwin from the hypothesis of a viscous earth. 



On the meteoric hypothesis, if the jostling of the stones be 

 slow they may cool almost as fast as they are heated, and the 

 result will be a cool earth and almost indefinite time at the 

 disposal of geologists. 



XL VIII. On Systems of Absolute Measures for Electric and 

 Magnetic Quantities. By Prof. H. Helmholtz*. 



PHYSICISTS have hitherto been obliged to employ two 

 different systems of electrical absolute measures, the 

 electrostatic and electromagnetic ; while for magnetic quantities 

 only one has always been made use of — namely that introduced 

 by Gauss, in which only the parts of the metre and the gramme 

 employed as the units of length and mass have changed. 

 Indeed the employment of those two systems of electrical 

 measures could not be dispensed with, for practical reasons, 

 because the determination of the factor which had to be used 



* Translated from Wiedemann's Anncden, 1882, no. 9. vol. xvii. pp. 12-54. 



