THE 110YAL ARTILLERY INSTITUTION. 
321 
Again, 
272 . cos a _ DO _ sin BKO 
W ~ KO ~ sin KDO 
__ COS 0 
sin (0 —■ 0) 5 
jg_ 7F* cos 0 
2 cos a . sin (0 — 0) 
Prom the triangle DA C, 
F _ ^ __ v^3 _ DC' 2 
72 ^ 7 ) - 7 - 
\/2 2 — 2 2 cos 2 a sin 2 0 
_ 
(») 
Also, 
since DC = BO sin 0 = 2 cos a sin 0; 
. *. jP z= 72 -\/l — cos 2 a . sin 2 0 
_ 7T cos 0 \/l — cos 2 a . sin 2 0 
2 cos a . sin (0 — 0) 
_77^ cos 0 sec 2 a —■ sin 2 0 
2 sin (0 — 0) 
TV_ BC __ 2 cos a sin 0 1 
72 “ 52 2 J 
. •. TV = 72 cos a sin 0 
__ /F sin 0 . cos 0 
2 sin (0 — 0). 
(3) 
(4) 
We can approximate to greater accuracy by writing (7F + w) for /Tin 
w 
the values for T, 22, and F— as we may suppose - to act at A or B —and 
(V 
we have 
w 
TV — — = 72 cos a sin 0 ; 
2 
7V = 
W -f w sin 0 cos 0 w 
2 * sin (0 — 0) 2 ’ 
(5) 
The above expressions may also be obtained by referring the forces acting 
on the sheers to OC, OA, and OK, as co-ordinate axes of x, y, and z respec¬ 
tively. We can resolve along OC and OK, and take moments about OA or 
BA. The method employed above is, however, simpler. 
Lever Sheers. 
Lever sheers consist of a long heavy spar, AH (see Pig. 13), with one end 
resting on the ground, and the other supported on two short spars, crossed 
and securely lashed together* 
