28 RECORDS 



foundations of the earth are far from stable, we can hardly ex- 

 pect such lines to become systematically shorter or longer in so 

 brief a terrestrial interval as a million years. Better still, prob- 

 ably, is the check on the invariability of the meter afforded by 

 Professor Michelson's measurement of it in terms of the wave- 

 lengths of particular rays emitted by the metal cadmium.^ In 

 this, apparently, we have a cosmic standard, although it remains 

 to be proved that the wave-lengths used will remain invariable 

 in the unexplored parts of the universe into which we are 

 journeying along with the solar system at the rate of some 

 kilometers per second. 



Our standard of mass is likewise connected directly with 

 various masses which may serve as checks on its stability, and 

 indirectly with the masses of definite volumes of many substances. 

 It is especially well known in terms of the mass of a cubic deci- 

 meter of water at a standard temperature. It is less definitely 

 known in terms of the atomic masses of the so-called elements, 

 and it is roughly known in terms of the enormous though slowly 

 varying mass of the earth." But, on the whole, our standard 



1 See Tome XI, Travaux et Meiiioires dii Btireazi Inteimational des Poids et 

 Mesjires, Paris, 1895. ]t is remarkable that the ratios of the three wave-lengths 

 used to the meter were measured with a precision requiring seven significant figures, 

 the uncertainty amounting to a few units only in the last figure. Thus the values of 

 the wave-lengths used (designated as red, green and blue respectively) are as fol- 

 lows, in microns, or millionths of a meter : 



0.643,847,2, 

 0.508,582,4, 

 0-479,991, 1- 



2 If we could measure the gravitation constant with a precision extending to five 

 significant figures, the mass of the earth would at once become known to the same 

 degree of precision, provided only that the law of gravitation is exact to the same 

 number of figures. For I have shown that the product of that constant and the mean 

 density of the earth is known with a precision expressed by five significant figures. 

 Thus, calling the gravitation constant k and the mean density of the earth p, 



/■p = 36,797X io-"/'(second)2. 



This relation may be otherwise expressed by the following theorem : Let r be the 

 periodic time of an infinitesimal satellite which would revolve about the earth close 

 to the equator (assuming no atmospheric resistance). Then the theorem asserts that 



where re is the ratio of the circumference to the diameter of a circle. The value of 

 r is I hour, 24 minutes, and 20.9 seconds. See Astronomical Journal, Vol. XVIII., 

 No. 16. 



