LIEUT. -COL. A. R. CLARKE ON STANDARDS OF LENGTH. 
461 
Let tlie distances of the zeros of the four micrometers H, I, J, Iv he 
H I=P : I J=Q : JK=R. 
Then, remarking that the screw-heads of Ii and I were to the left, and those of J K 
to the right, we have 
P + Q+R=S +*/*+/£, 
P=T + ah-hi, 
Q=Y+b'i+(j, 
R=T— c'j-\-dk, 
where h, i,j , k are the values of one division of the respective microscopes. Hence we 
aet 
8=2X+Y+{a-e)h+{V-l)i+(c-d)!j+(d-f% 
where S, T, F represent the length of the Spanish bar, the toise, and the 4-inch space 
on the foot respectively. This expression gives us the actual difference of length of the 
bars at the time of comparison. The foot being in the same box with the toise, it is 
assumed that its temperature is the same as that of the toise. 
The comparisons of the Spanish bar with the toise extend over seven days in October, 
three days in November, and three days in December 1869, in all twenty-three compa- 
risons. The readings of one observer lead to the result, the bars being all at 61°*25, 
S=2T 0 + 4I+499-63, 
and those of the other to the result, 
S=2T 0 + 41+ 499-58; 
and taking the means of the corresponding readings of the two observers, the result is 
S=2T 0 + 41+499-60 + 0-23. 
The 4-inch space 41 actually used was the space \_c g]. The value of this space is, 
see page 450, at the temperature of 61°-25, 
Consequently 
2-73 + 0-06. 
2T, + [ej]=4-37443869Y„ + 0-42; 
so that finally we have, the Spanish bar being at 61 0, 25 and the yard at 62°, 
S = 4-37493829Y 55 +0-48. 
Comparisons with four lengths of the Ordnance Metre . 
In order to effect this, five microscopes were adjusted in line at one metre apart. Ten 
comparisons were made in October and November 1869. The readings of one observer 
lead to the result, 
S=4M 0 — 58-81, 
3 Q 
MDCCCLXXIII. 
