452 
LIEUT. -COL. A. R. CLARKE ON STANDARDS OF LENGTH. 
The difference of the expressions we have given for \_k g] and [c g] gives 
[^]=3^Y m +3'97; 
consequently the length of the half klafter is 
In order to determine the probable error of this result, it is necessary to form the 
algebraic expression for [a d], which involves all the observations and operations. It is 
found to be this : — 
[a d]= 
3 733 V 
3600 ^55' 
133 ~ 
'6 00 u g ‘ 
6 7 rv* I ry 
10 0 
3 /i i 7 :y 
1 0 1 0 ‘*'7 
-x. 
+ iWo v+x+rf — x,. 
This compound error is formed from seven independent operations. The first term 
in x g depends on the subdivision of the standard foot into two 6-inch spaces ; the second, 
involving the terms in x b and x c , on the determination of the errors of the different inch 
lines on one half of the foot ; the third, the terms in x 6 x 7 , on the division of one of the 
inches into tenths ; the fourth, x k , on the division of one of the tenths into hundredths ; 
the fifth, in v, on the comparison of the standard foot with the standard yard ; the sixth, 
in x, on the comparison of the standard yard with the half klafter ; and the seventh, 
x 1 — x,, on the comparison of the small spaces on the half klafter with the foot. Taking 
the different component probable errors in this same order, we get the quantity 
± v/{(-008) 2 +(-045) 2 +(-052) 2 +(-085) 2 +(-011) 2 +(-085) 2 + (-076) 2 }, 
which is equal to +0T58. 
The length of Y 55 at 61°-25 is (see ‘ Comparisons of Standards,’ page 276) 4-886 less 
than its length at 62°, and at 62° it is less than a true yard by 0-40 ; hence the length 
of the half klafter at 61°*25, 
K, =1-03693714 g + -00000016, 
where ^ is a true yard. 
During the comparisons the bar was supported on two knife-edges, at one fourth and 
three fourths of its length. The positions of these supports are marked on the bar. 
The Pulkowa Copy of the Klafter. 
This is a bar of steel (apparently) 0-55 inch in breadth and 1-06 inch in depth, but 
not very evenly planed. On its under surface are fixed small brass pieces at one fourth 
and three fourths of its length, on which it is supported during comparisons. Its upper 
surface has seven inlaid plates of silver, on each of which is engraved a dot. The 
extreme dots are one toise apart. Near one of the end dots is the klafter dot. Two 
other dots mark the half klafter and the half toise. The two remaining dots subdivide 
the half klafter into thirds or Vienna feet. We shall use the symbol K' for the length 
of the klafter on this bar. 
The klafter and the half klafter were mounted side by side in a box for comparison, 
their middle points being opposite one another. The microscopes II and K being 
