464 
LIEUT.-COL. A. E. CLARKE ON STANDARDS OF LENGTH. 
or, both being at 62°, 
M 8 =M 0 +54-55 + 0-37. 
It is unfortunate for the success of these comparisons that the expansion of neither 
of the metres is known by direct experiment. We can arrive at a value of the expansion 
of M 0 through its comparison with Y 55 , but the expansion of Y 55 is known only indirectly. 
This last bar has been compared with two iron bars, each of which has had its expansion 
determined by direct experiment. The first of these bars is the Indian 10-feet steel 
standard. The expansion of Y 55 , as derived from this source, is 
6-650. 
But the expansion of this same yard, as inferred from the 10-feet bar OF (see ‘ Compa- 
risons of Standards,’ pages 90 and 227), is 
6-514. 
The discrepancy between these two is very considerable, especially when, as in the 
present case, it has to be multiplied by 30. We have, however, no alternative but to 
adopt the mean as the expansion of Y 55 , namely 6-582. By page 106 of the ‘ Compa- 
risons of Standards,’ the expansion of a yard of the Ordnance metre is less than this by 
0-411 ; that is, the expansion of the metre for 30° Fahr. is 
6-171 x 30x 1-09375 = 202-48. 
Consequently the length of the metre at 32° (see ‘Comparisons of Standards,’ p. 110) 
= 1-09355096Y m , 
with a probable error of perhaps *00000250. 
Thus the length of the American metre at 32° is (Y 55 being at 62°) 
1-09359533Y SS . 
We may arrive at the length of the American metre otherwise than by using the 
inferred expansion of the Ordnance metre. For it is stated, in the Report referred to, 
that in the comparisons of the sum of the six iron metres with the six-metre standard at 
different temperatures, no variation in the difference of length was found corresponding 
to different temperatures ; that is, the expansion of the iron metres was equal to the 
expansion of the standard six-metre bar. Now the coefficient of the expansion of the 
standard was found by very careful experiments to be 
•00000641. 
Hence the actual expansion of one of the metres between 32° and 62° would be 
30x0-41x1-0936=210-30. 
Hence M„ being at 32°, and M 0 at 62°, 
M„=M 0 + 54-55— 210-30 
=1-09359769Y 55 . 
