Polytechnic Association. 937 



When I was in Paris, in 18G7, this iron meter bar was sent over to 

 me to be compared with the standard there (which is only used once 

 in ten years to verify the other standards, lest the comparison should 

 injure the ends), and the difference actually observed, with the delicate 

 instruments used in the comparison, was only .00017 millimeter, or 

 l-160,000th of an inch, a difference that could not be determined at 

 all except by these marvelous mechanical and optical means. 



But even were the standard meter l-200th of an inch in error ; 

 what difference does it make ? If you know how much more or less 

 it is than l-10,000,000th of a quadrant, it can be re-established with as 

 much certainty as if it were that exact quantity. By the law of Eng- 

 land the length of the yard was established by comparison with the 

 length of the pendulum ; and hence it could be restored, although it 

 was shorter than the pendulum. 



There are but few natural dimensions which are invariable ; but 

 there are several which have been proposed as standards of measure- 

 ment. 



One of these is- derived from the velocity of light. How are we to 

 determine it ? One method is by comparison of the observed times 

 of the eclipses of Jupiter's satellites with the times given by calcula- 

 tion. It is found that these appear to occur earlier when the earth is 

 nearest to the planet ; and that the difference arising from the motion of 

 the earth is about eight and one-fourth minutes for a progress through 

 a space equal to the distance of the sun from the earth. But how are 

 we to know how far off the sun is ? Our only means is by comparison 

 of its distance with the diameter of the earth ; and thus the magni- 

 tude of the earth becomes, after all, the real standard. 



Another method of determining the velocity of light was contrived 

 by Foucault, which was certainly very ingenious. It consisted of a 

 measurement by a filar micrometer of the deviation of a ray of light 

 passing over a given space, and reflected by a rapidly revolving mirror 

 Hence, in order to obtain the result, it was necessary to determine 

 with very great accuracy, three things ; the distance traversed by the 

 light, the velocity of the rotation, and the amount of deflection ; a pro- 

 cess requiring so many delicate adjustments as to be obviously unfit 

 to be relied upon to furnish a standard of measurement. 



The length of the pendulum has been proposed as a natural stand- 

 ard. But what is the length of a pendulum ? A pendulum, in theory, 

 is a point having weight, suspended by a line which has no weight. 

 But a pendulum in practice is a heavy body suspended by a rod ; and 

 the length of the practical pendulum is the distance between the 



