LIEUT.-COL. A. R. CLARKE OK STANDARDS OF LENGTH. 
455 
Comparison between the Pulkowa and Milan Klafters. 
The Milan klafter was compared with the Pulkowa copy in May, June, and July, 1869. 
Both surfaces of the former were compared — -that is, both the distance [1.3] and the 
distance [I . II]. The klafter distance [1 . 3] was compared with the Pulkowa klafter 
ten times between May 3rd and 6th, at a temperature of about 53° — five times on June 
12th and 14th, at about 58° — and five times on July 3rd and 5th, at near 60°. 
The distance [I . II] was compared with the Pulkowa klafter eleven times between 
May 7th and 11th at a temperature of about 53°, and nine times on June 10th and 11th 
at about 58°. 
The reduction of these observations by the method of least squares shows that the 
probable error of one comparison was 
+ 0-674 \/ — 989 = + 1-08, 
which is somewhat large; and for final results at 61°-25, 
K'=K?.3+20-86±0-43, 
K'=K''.„+ 5-52 + 0-43. 
We have now determined directly the lengths of the Pulkowa and Milan klafters, and 
also by direct observations their difference. It remains to examine as to the consistency 
of these results ; they are, in fact, these : — 
K' -21+ =162-44 + 0-38, 
K". 3 -2Kj =139-64 + 0-56, 
K' - K". s = 20-86 + 0-43, 
which are not consistent, as the difference of the first and second exceeds the third by 
1-94. If we adjust the three results by least squares, we get 
K' =2Ki+162-01, 
K?.3=2K, +140-59. 
But these results are not perfectly satisfactory, as from the manner in which they have 
been derived we cannot express their probable errors. In order to do this, it is necessary 
to reduce in one system of equations, by the method of least squares, all the following 
comparisons, namely : — 
27 between K' li2 and I+, 
27 between K 2 . 3 and K., 
24 between K . 2 and I+, 
24 
20 
20 
between K 2i3 and 
between Ki < 3 and 
between K' li3 and 
3 p 2 
I+, 
2 7 
k;.s, 
Ki. n , 
