462 LIEUT. -COL. A. E. CLAEKE ON STANDAEDS OF LENGTH. 
those of the second observer to the result, 
S=4M 0 - 60-62; 
and, taking the means of the corresponding readings of the two observers, 
S=4M o -59*72±0*65, 
both bars being at 61°*25. 
Now the ratio of 4M 0 at 61°-25 to Y B5 at 62° is 
4M o =4*377499376Y S8 ±0*64 ; 
consequently the Spanish bar at 61°-25 is 
S=4*37493404Y 55 ±0*91. 
The two results we have now arrived at as to the length of S differ by 4*25 + 1*03.* 
If we combine them with regard to their probable errors, we get finally 
S=4-37493737Y 55 . 
By page 280 of the ‘ Comparisons of Standards,’ it appears that at 62° 
Y ss = *91439143 iH; 
whence the length of the Spanish bar is, expressed in metres, 
8=4-00040524 iH. 
We now compare this with the result obtained by Colonel Ilanez at Madrid; accord- 
ing to the certificate accompanying the bar, its length at the temperature of 21-935 
Centigrade is 4-0006526 metres, and the rate of expansion is *000043193 metre for each 
degree Centigrade ; hence the length of the bar at 61°-25 Fahrenheit, according to the 
Spanish observations, is 
4-0004071 
From this it appears that the length of the metre, as given by the Spanish bar, agrees 
with great precision with that inferred at Southampton from the comparisons of the 
Belgian and Prussian toises. 
The difference between the two lengths obtained for the Spanish bar, first through 
the tcise, and secondly through the metre, suggested the direct comparison of those 
bars one with the other by means of the approximate relation 
Toise+2 inches = 2 metres. 
For this purpose five microscopes were adjusted in line in the order H, K, G, I, J, at 
the distances HG=GI=one metre, HK=5 inches, I J = 3 inches. Then the compa- 
rison was effected by observing in succession ; — 
1st, the Ordnance toise under K and J ; 
2nd, the Ordnance metre under G and I ; 
3rd, the Ordnance metre under FI and G ; 
4th, 5-inch space [af] on foot under H and K ; 
5th, 3-inch space [a d] on foot under I and J. 
