468 
LIEUT. -COL. A. R. CLARKE ON STANDARDS OR LENGTH. 
The Double Toise Q. — This is a bar similar in every respect to P, but without the 
defect in the terminal surfaces. Eighteen comparisons were made in March 1868 at 
temperatures from 45° to 46°, and twenty-two comparisons in September 1869 at tem- 
peratures between 58° and 61°. These observations, reduced by least squares, give the 
result, 
Q=2T 0 — 360-00 + 0-40; 
and this, when compared with the length we have determined for P, viz. P = 2T 0 — 323*90, 
is in tolerable accordance with M. Struve’s determination of the lengths of these bars. 
According to M. Struve, P — Q=0'-01370, which, expressed in millionths of a yard, is 
P— Q=33-80, 
while the difference, as determined at Southampton, is 
P— Q=36T0. 
But there is not the same accordance if we compare the difference between Q and two 
lengths of the Prussian toise denoted B'. The length of 2B' (Struve, ‘Arcdu Meridien 
. . . ,’ tom. i. p. lxxiii) is 
2B'=1727-99S28; 
and this exceeds the length of Q, namely 1727*97 386, by 0 1, 02442, which, expressed in 
millionths of a yard, is 
2B' — Q= 60*25 =2T 10 —Q. 
But, according to the observations made at Southampton (‘ Comparisons of Standards,’ 
page 273), 
2T 10 =2T 0 — 309*04, 
which, compared with the length of Q determined above, gives 
2T lo -Q=50*96, 
showing a discrepancy of 9-29 millionths of a yard, as though Q had increased in length 
between the comparisons at Pulkowa and at Southampton. 
In order to throw some light upon this discrepancy, in the autumn of 1871, just two 
years after the comparisons of Q detailed in the preceding paragraph, some further 
observations were made of Q, the comparisons between it and two lengths of the 
Ordnance toise being made with the utmost care and circumspection, and the tempe- 
rature being remarkably uniform during the whole time. The result of these ten com- 
parisons was 
Q=2T 0 - 355*74+0*33. 
In combining our two results for the length of Q we shall not make use of their pro- 
bable errors, as manifestly they are delusive on account of the existence of some constant 
source of error. If we are content to take the mean, it is 
Q=2T 0 — 357*87; ' 
but to this Ave cannot assign its probable error. 
