964 



SCIENCE. 



[N. S. Vol. XV. No. 390. 



ards of length and mass which are now 

 universally adopted in science are the me- 

 ter and the kilogram respectively, care- 

 fully intercompared copies, or ' proto- 

 types,' of which have been distributed by 

 the' international bureau of standards to 

 the nations contributing to the cost thereof, 

 l^he United States possesses two copies of 

 each of these prototypes, and they are, as 

 a matter of fact, our effective working stand- 

 ards, even for the pi-oduetion of standard 

 yards and pounds. It is to be hoped, there- 

 fore, that the end of the barbaric system 

 of 'weights and measures' we have inher- 

 ited from an unscientific ancestry is near 

 at hand, and this not so much in the inter- 

 est of men of science as in the interests of 

 those less well fitted to struggle with the" 

 ingenious intricacies of the British system. 

 These ' prototype meters and kilograms 

 are known in terms of the adopted stand- 

 ards, and hence in terms of one another, 

 with a degree of precision which verges 

 close to the limits of the constancy of 

 matter itself. Thus the lengtlis of the 

 meters are known with an uncertainty ex- 

 pressed by a probable error of only one 

 part in five millions. This degree of refine- 

 ment corresponds to about one hundredth 

 of an inch in a mile, or to about nineteen 

 miles in the mean distance of the earth 

 from the sun. But this admirable pre- 

 cision is greatly surpassed by that of the 

 kilograms, whose uncertainty falls to 

 one part in five hundred millions. It is well 

 ImoAvn, of course, that the operation of 

 weighing by means of the balance secures 

 a precision superior to that of every other 

 species of physical mejisurement ; but it is 

 not easy to visualize directly the five- 

 hundred-millionth part of a kilogram. 

 One may get a tolerably definite idea of 

 this magnitude, however, by observing that 

 with the degree of precision in question it 

 would be essential in comparing two kilo- 

 gram masses to keep the pans of the bal- 



ance closely at the same level, for a centi- 

 meter difference in their altitudes would 

 be appreciable by reason of the variation 

 of the attraction of the earth with distance 

 from its center.* 



For present purposes, therefore, our 

 standards of length and mass leave little, 

 if anything, to be desired. But it is a mat- 

 ter of great importance to the future pro- 

 gress of science that these standards be 

 preserved for an indefinitely long period; 

 and although such a contingency seems 

 remote enough now, one can hardly sup- 

 press the query as to what would happen 

 to us if our standards should be lost, or if 

 they should unexpectedly prove unstable 

 with the lapse of time. It is quite certain 

 that our standard of length could be re- 

 covered with a high degree of precision if 

 such a calamity should befall us during 

 the next ten thousand, or possibly during 

 the next hundred thousand years. Numer- 

 ous bars of other metals than the alloj' 

 used in the construction of the prototype 

 meters are known in terms of the latter. 

 Many base lines scattered at widely sepa- 

 rated points of the earth's surface are 

 also known in terms of the meter with a 

 precision of about one part in a million; 

 and although the foundations of the earth 

 are far from stable, we can hardly expect 

 such lines to become systematically shorter 



* Denoting the mass of a kilogram by mi 

 and the mass of the earth by to,, the weight of 

 nil by tr, and the distance from the balance to 

 the earth's center by s (since the earth is nearly 

 eentrobaric ) , the Newtonian law gives 



:A;- 



whence the relation of a small change A to in ic 

 to the corresponding change A s in s is expressed 



by 



Aw „ As 



Since Aw/io is here 1/500,000,000, and since s 

 is about 630,000,000 centimeters, As==F 0.63 centi- 

 meter. 



