RECORDS 27 



dred millions. It is well known, of course, that the operation 

 of weighing by means of the balance secures a precision superior 

 to that of every other species of physical measurement ; 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 pre- 

 cision in question it would be essential in comparing two kilo- 

 gram masses to keep the pans of the balance closely at the same 

 level, for a centimeter difference in their altitudes would be ap- 

 preciable 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 matter 

 of great importance to the future progress of science that these 

 standards be preserved for an indefinitely long period ; and al- 

 though such a contingency seems remote enough now, one can 

 hardly suppress 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 recovered 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. Numerous bars of other metals than the alloy used in 

 the construction of the prototype meters are known in terms of 

 the latter. Many base lines scattered at widely separated 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 



1 Denoting the mass of a kilogram by tn^ and the mass of the earth by Wj, the 

 weight of ;«j by w, and the distance from the balance to earth's center by s (since 

 the earth is nearly centrobaric), the Newtonian law gives 



whence the relation of a small change Aw in w to the corresponding change -i^ in 

 s is expressed by 



Aw Aj 



w s 



Since Arcz/w is here 1/500,000,000, and since s is about 630,000,000 centimeters, 

 Aj ^ =p 0.63 centimeter. 



