June 20, 1902] 



SCIENCE. 



965 



or longer in so brief a terrestrial interval 

 as a million years. Better still, probably, 

 is the cheek 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 re- 

 mains to be proved that the wave lengths 

 used will remain invariable in the unex- 

 plored parts of the universe into which we 

 are joumejdng along with the solar sys- 

 tem at the rate of some kilometers per 

 second. 



Our standard of mass is likewise con- 

 nected directly with various masses which 

 may serve as cheeks on its stability, and 

 indirectly with the masses of definite vol- 

 umes of many substances. It is especially 

 well known in terms of the mass of a 

 cubic decimeter 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, t But on the 



* See Tome XI., Travaux et MSmoires du Bureau 

 International des Poids et Mesures, Paris, 1895. 

 It 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 respec- 

 tively) are as follows, in microns, or millionths 

 of a meter: 



0.643,847,2, 



0.508,582,4, 



0.479,991,1. 



f If we could measure the gravitation constant 

 with a precision extending to five significant fig- 

 ures, the mass of the earth would at once become 

 known to the same degree of precision, provided 

 only that the law of gra^•itation is exact to the 

 same number of figures. For I have shown that 

 the product of that constant and the mean den- 

 sity of the earth is known \vith a precision ex- 

 pressed by five significant figures. Thus, calling 



whole, our standard of mass must be re- 

 garded as less secure, than our standard of 

 length, although the prototype kilograms 

 are less likely to change in mass with 

 the lapse of time than the prototype meters 

 are to change in length; for while such a 

 general variation in volume as is knovrai to 

 occur in metals, especially alloys, need not 

 affect the former, it would almost certainly 

 affect the latter. 



Our unit of time is also known with a 

 definiteness that meets in most cases the 

 highest demands of science at the present 

 epoch. The period of rotation of the 

 earth, or the sidereal day, is the standard 

 interval of time, though it has been found 

 convenient for many purposes to use the 

 shorter interval of a mean solar second, of 

 which there are 86,164.1 in a sidereal day. 

 That the earth rotates with wonderful 

 regularity is a fact of the highest impor- 

 tance to science. Without that regnilarity 

 the development of sidereal and planetary 

 astronomy, with all they have entailed, 

 would have been impossible except by the 

 discovery of some other equally trust- 

 worthy timekeeper. But the laws of me- 

 chanics, which show us plainly why the 

 earth rotates with such remarkable regu- 

 larity, also show us that its period of rota- 

 tion is subject to sources of disturbance, 

 some tending to increase and some tending 

 to decrease that period, whose effects, 

 the gravitation constant k and the mean density 

 of the earth p, 



ip = 36797X10"" /(second)' 



This relation may be otherwise expressed by the 

 following theorem : Let t 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 



fcpr2=35r 



where tt is the ratio of the circumference to the 

 diameter of a circle. The value of r is 1 hour, 

 24 minutes, and 20.9 seconds. See Astronomical 

 Journal, Vol. XVIII., No. 16. 



