450 
LIEUT. -COL. A. E. CLARKE ON STANDARDS OE LENGTH. 
This is on the supposition of the klafter and the yard being both at the temperature 
of 62°. 
The standard temperature of the Vienna klafter is 61 0, 25 Fahrenheit, or 16 0, 25 Cen- 
tigrade, and this temperature is therefore adopted for the half klafter ; consequently we 
require the length of [kg'] at the same temperature. Now the comparisons made 
between the standard foot and the standard yard Y 65 give this result, 
F=^Y 55 — 0-36 + 0-104, 
the foot and yard being both at 61°-25. Hence, at the same temperature, 
M=^Y 65 + l-24 + 0-118. 
The space \b c] of 4 inches on the half klafter was compared with the space [c g] of 
4 inches on the standard foot. The value of this space is, both the foot and the yard 
being at 61°-25, 
M=AY m -2-73±0-062. 
The space [5 d] of 36 inches was compared with the standard yard Y 55 twenty times 
between March 19th and 27th, 1866, at temperatures varying from 41 0, 6 to 43°*7 — sixteen 
times between June 25th and July 2nd, the temperature varying from 62 0- 7 to 6 7°*4 — 
and six times in September 1867, at about 64°, — in all forty-two comparisons. 
Reduced by the method of least squares the result is 
[b <f]=Y 55 +0T7+(7— 61 0, 25) -0224. 
The reciprocals of the weights of the determinations of the quantities 0T7 and ‘0224 
are 0-03204 and 0-00018 respectively; and the sum of the squares of the forty-two errors 
of observation is 
2(e 2 )= 19-949. 
Hence we find the probable error of a single comparison to be 
+ 0-674 a/ 19 ‘ 949 = + 0-476. 
— V 42 — 2 — 
The probable error therefore of 0-17 is 
+ 0-476 v /-03304= + 0-085; 
and at the temperature of 61°*25, 
[b ^]=Y 65 -J- 0-17 + 0-085. 
The 4-inch space [5 c] on the half klafter was compared with the space \_c g] on the 
foot fifteen times between April 13th and 19fch, 1866, at temperatures varying between 
47° and 49° — ten times between June 9th and 13th, the temperatures varying from 60° 
to 62° — and six times in September 1867, at the temperature of 58°. 
The 5"33-inch space [a c] was compared with the space [kg'] on the foot ten times in 
April 1866, at a temperature varying little from 46° — fifteen times in June of the same 
year, at temperatures varying little from 60° — and five times in September 1867, the 
temperature being 62° or 63°. 
