OF ARTS AND SCIENCES. 301 



one exception, a very close accordance. Mr. Airy concludes this part 

 of his report as follows : — 



" First, there is no evidence whatever of a general preponder- 

 ance of excess from the New Measures above the excess from the 

 Old Measures; the signs -f- ar) d — being intermixed, in the dif- 

 ferences, in all possible ways, and the mean of the whole being 

 less than d .50. Secondly, the only instance which fairly supports 

 the conclusion deduced from Cast-steel D is the first of all, namely, 

 Bronze 1*2. Cast-steel D was compared on April 13, 14, and 16; 

 Bronze 12, on April 26, 27, 28, and May 1; Bronze 39 (the next), 

 on April 30. The conclusion, I think, is inevitable, that Bronze 28 

 really was shortened at the beginning of April ; that it recovered its 

 exact length before April 30; but that this recovery took place with 

 some fluctuations, so that on May 1 it was subject to nearly the same 

 error as be-fore. Bronze 21, observed June 2G, exhibits a similar dis- 

 cordance. What circumstances can have produced these changes, or 

 how far the later fluctuations are apparent rather than real, I am 

 wholly unable to conjecture." 



1 believe that the explanation of the phenomena observed by Mr. 

 Sheepshanks will be found to fall under the following : — • 



First, two bars of different materials, having different shapes and 

 different masses, have a variable coefficient of expansion with respect to 

 each other, which is a function of the time of exposure to a given tem- 

 perature. 



Second, the more violent the change of temperature, the greater ivill be 

 the variation in the length of the bars before they assume their normal 

 condition under a constant temperature. 



All of the bronze bars had the same mass. The iron bars and the 

 steel bars, on the other hand, not only had a different mass, but they 

 were subject to a different degree of specific heat. Their conductive 

 power was also different. They also had a different absorptive power. 

 The difficulty with the observations of Mr. Sheepshanks was. that they 

 were not sufficiently continuous. They did not extend over a sufficient 

 length of time to enable him to discover the slow changes which were 

 going on in the length of the bars through the heat already absorbed, 

 and which was not indicated by his thermometers. 



This paper has been already extended so far beyond the limits pro- 

 posed that it is inexpedient to give even a resume of all the observa- 

 tions which I have made bearing upon this point. It will be seen from 

 the following brief account, that it is absolutely necessary to investi- 

 gate the performance of two standards which are to be compared un- 



