812 
ME. W. HOPKIXS’S EXPEEi:\IEXTAE EESEAECHES 
Equations (1.), (2.) and (3.) will determine and in terms of and r, and the 
other quantities involved. They may be written 
P 
(-) 
«2 
Adding them together, we have 
or writing ty — r — — r) for ty — 
PK\PK_yP_h-7_-^ 
k^'k^~^q t'^—T 
_^i-4 
^2-’- 
or if hy-\-h^=Ji, and ^,=^ 2=^5 
q — T ^\ky ^ 2 / 
P. 
h-t'^ _P± 
L — 7 k ' 
(^■) 
If (^,), (t' 2 ) and (r) denote the values which ty, and r would have m an experiment 
with an undivided block of equal length and of the same substance, we shall have 
and therefore 
ph {ty)-{Q 
k 
(art. 1, equation ( 0 .)). 
P^ h-h {h)-{k) 
q 4 -t {Q-{7) 
(5.) 
7. To apply this formula to the experimental determination of I took two equal 
blocks of the same piece of sandstone. One of these was spht transversely, and the expe- 
riments conducted as hereafter described (see page 845). The undmded block gave 
(b) ~ (^2) q-| C 
(1) In the first experiment with the divided block, one portion of it was placed in 
close contact with the other, without cement of any kind between them. This gave 
b-b 
^ 2 -’' 
= • 44 , 
