436 APPLIED MECHANICS 
while it is immersed in the liquid, its loss of weve is equal to the weigl i 
of the liquid which it displaces. ‘f 
371. Floating Bodies.—A consequence of the result of the preceding} r 
. Article is that when a body floats in a liquid the weight of the body is 
equal to the weight of the liquid which it displaces. Another obvious _ 
result is that when the floating body is at rest, the straight line which — 
joins the centre of gravity of the body and the centre of gravity of the — 
displaced liquid is vertical. The centre of gravity of the displaced liquid q 
is called the centre of buoyancy. The resultant fluid pressure on the 
body acts vertically upwards in a line through the centre of buoyancy. 
Fig. 713 shows a floating body slightly displaced from its position — 
of equilibrium. CG is the line joining the centre of buoyancy and the” 
centre of gravity of the body when the body is in 1 
its position of equilibrium. ©’ is the new position 
of the centre of buoyancy. The body is now under 
the action of two vertical forces, each equal to the 
weight of the body, one acting downwards through 
G, and the other upwards through C’. If the vertical 
line through C’ meets the line CG or that line pro- Fig. 712 
duced at M, the point M is called the metacentre of oa 
the floating body. The equilibrium of the floating body is evidently q 
more stable the higher the point M is above G, the centre of gravity as 
the body, and the equilibrium is unstable when M is below G. “ 
372. Weight of Water.—The weight of a cubic foot of water varies — 
with the temperature, as shown in the following table :— 
— 
Temp. Cent. Bier seats S| 6, 4° | 16°67°| 40° | 60° | 80° | 100° | 
» ahr. : A . | 32° | 39-2° | 62° | 104° | 140° | 176° | 212° 1s 
Weight in Ibs, of 1 cubic foot | 62°34 | 62°35 | 62°28 | 61°87 | 61°31 | 60°59 | 59°76 a 
be : 
A 
The above weights are for pure distilled water free from air. 
At the temperature 62° Fahr., and the barometer at 30 inches, a cubic 
foot of distilled water, freed from air, weighs 0-046 lb. more than vies 7 
nearly saturated with air. : 
A gallon of water at 62° Fahr. weighs 10 Ibs. 
Exercises XXVII. 
1. Referring to Fig. 704, p. 432, if the diameter of the larger piston is 12 
inches, and the diameter of ‘the other is 14 inches, what is the force Ww when » 5 
is 150 lbs, ? = 
2. A vertical tube 3 feet long, and having an internal diameter of 1 inch, is” 
filled with equal volumes of water and mercury. Assuming that the weight of 
the mercury is 13°56 times the weight of the water, calculate the pressure il 
Ibs. per square inch at the bottom of the tube due to the head of liquid. A 
what is the weight of water in the tube? 
3. What pressure, in lbs. per square inch, corresponds to 160 feet head 
water, and what head of water, in feet, corresponds toa pressure, of 180 Ibs, per 
square inch? 
4. Feed water is pumped into a boiler from a tank. 4 ust before starting 
feed-pump the levels of the water in the boiler and tank are 38°5 inches 
