456 
LIEUT. -COL. A. E. CLAEKE ON STAND AEDS OF LENGTH. 
where it is to be remembered that K , li2 +K 2i3 =K , + T48. Now let 
K;. 2 -K, =u+fy, 
k;. 3 -k, =v+fy 9 
k". 2 — Kj =++/y, 
Ko.3 — Kj =v'+f'y', 
Ki , .„-K li3 =^. 
Then, further, if K' and K" _ 3 be compared at the temperature 61°-25 + <?, 
K' — K" i3 =u-{-v— u' — + + 2 ey— ‘ley' — 1 -48 ; 
and if K 7 and 1+,, be compared at temperature 61 0- 25 Tc, 
K'-Kl u =u+v~u'-v'-a:+2e'y-l^y'-l'4:S. 
Thus we have a system of 142 equations to solve, which finally give a group of seven 
equations resulting in the following quantities : — 
u =+79-97, 
v = + 83-81, 
+= + 67*08, 
+ =+73-26, 
x — +15-28, 
y — - 0-6115, 
y' = ~ 0-0759; 
and consequently at 61°-25 the lengths of the klafters — 
K' =2Ki+m +-r —1-48=162-30, 
K".3 =2Ki++++ =140-34, 
Ki' in =2Ki+++++^ =155-62. 
The reciprocals of the weights of the determinations are 
•0624, 
-0892, 
-1426. 
The sum of the squares of the 142 errors is 326-82 ; consequently the probable error 
of a single equation is +T05, and the probable errors of the determinations of K', 
K+ 3 , and Kj n are respectively, 
1+ +1-05 x / : 0624= + 0-26, 
K+3 +1-05 x / t 0892 = + 0-31, 
K'(.„ .... +1-05 x/T426= + 0-40. 
