MINUTES OE PROCEEDINGS OE 
322 
Let W = weight of gun and tackle, 
L = length of spar AH, 
l — length AH, projecting beyond the point of support, 
a = radius of spar, 
Z a = inclination of spar AH to horizon, 
R = normal reaction at end II. 
The strain caused by the weight suspended from A, acting vertically, may 
be resolved into two forces—(1) AB, at right angles to the spar, tending to 
break it across, and also to cause the other end H to fly up; (2) the force 
BC, acting in a direction parallel to the spar, and tending to force the end II 
into the ground. 
It is evident that the triangles BAC, BEH are similar. 
From the triangle BAC, 
AB = AC . cos BAC 
= W. cos a . (1) 
Also, by the principle of the lever, 
R = AB . — W cos a y . (2) 
JJll Ju 
To find the load which the spar will safely bear—from Fenwick's 
“ Mechanics of Construction," p. 63—we have 
PI = ^$7ra 3 , or P — 
SlTcfi 
~w 
where P is the “breaking weight." If p be the ratio of “safe load" to 
“ breaking weight," 
tit $7 ra 3 ,„v 
W COS a = p —— . . (3) 
4£ 
The butt end of the spar AH is heavily weighted, and is usually sunk a 
little in the ground, resting against a board or slab of wood, to prevent the 
earth from yielding to the pressure of the force represented by PC. A rear 
guy is also employed, to prevent the short cross spars, or sheers, from failing 
to the front; the pressure of the lever at D prevents them from inclining to 
the rear. 
Derrick. 
If time and materials are available, a derrick should be constructed as 
follows :—One large spar or square beam is placed vertically, passing through 
a horizontal slab of wood, and sunk several feet in the ground. In the slab, 
which is further fastened to the beam by cleats, a hollow is made to receive 
the foot of the spar forming the derrick, the top of which is attached to that 
of the main beam by tackle. One or two guys are needed, to control the 
head of the derrick ; the main beam is also supported by guys—one directly 
in rear, and at least one on each side. 
In the following investigation, we shall suppose the tensions of the side 
guys to be resolved along the plane of the paper, taken as the vertical plane 
