LIEUT. -COL. A. E. CLAEKE ON STANDAEDS OE LENGTH. 
453 
mounted at the distance of half a klafter apart, the order of observation at each visit 
was this : — 
1st, the thermometers ; 
2nd, the half klafter ; 
3rd, the first half of the Vienna klafter ; 
4th, the second half of the Vienna klafter ; 
5th, the half klafter ; 
6 th, the thermometers. 
The “first half” of the Vienna klafter is that which is on the same side with the toise 
dot: we shall denote it by K' I2 , and the second half by K 2-3 ; so that K' K2 + IV i3 =K'. 
The klafter and half klafter were compared twenty times in September 1867, at tem- 
peratures varying between 61°-3 and 64 0, 7, and seven times in January 1868, at tempe- 
ratures varying between 37° and 38°-6. 
The reduction of these comparisons by least squares, putting x -\-fy and x' -\-fy for the 
excess of the first and second halves of the klafter over the half klafter at the tempera- 
tures 61*25 +/*, leads to a system of equations, 
$=n(x+x!) + 2(f )y-(j)-(j<), 
0 = (/ )(x+a!) + 2(/ 2 )j/ -(fj)- ( fj '), 
0 =n(x-x')+ (j')-(j) ; 
and the substitution of the numerical values gives 
x = -f- 80*03, 
+ = + 83-88, 
y = - 0-593. 
If we assumed as true the equation Ki.. 2 +K 2 . 3 =K', we should arrive at the result, 
K'=2K,+163-91: 
but this is not so ; for an examination of the alignment of the dots shows that the centre 
dot is considerably misplaced. In order to measure the quantity, a very fine silk thread 
was stretched tightly just above the surface and close to the dots. Measurements were 
then made, and with this result, that the centre dot is 553 micrometer-divisions (one 
division =Y 2 ^oo inch) off the line joining the end dots of the klafter: it is also very 
slightly above the line joining the end dots ; but this deviation is much smaller, and not 
large enough to produce any error. Now the 553 divisions correspond to about 1240 
millionths of a yard. If we write S for this deviation, it is clear that the distance of the 
extreme dots is less than the sum of the two portions by 
S 2 
IK’ 
3 p 
MDCCCLXXIII. 
