13. Equivalent expressions of quantity. When the value of a quantity is known in terms of one unit, it is a simple matter to find its value in terms of a second unit. Thus to find the number of square feet in 3210 sq. in., write

1 ——— 144

=

no. of sq. ft. —————————— no. of sq. in.

=

x ———— 3210

,

since there are 144 sq. in. in a square foot; hence                               to 144 on D, set index of C;                               opposite 3210 on D, read x = 22.3 on C; that is, there are 22.3 sq. ft. in 3210 sq. in. Again consider the problem of finding the number of nautical miles in 28.5 ordinary miles. Since there are 5280 ft. in an ordinary mile and 6080 ft. in a nautical mile, write

5280 ———— 6080

=

no. of naut. mi. —————————— no. of ord. mi.

=

x ——— 28.5

,

make the corresponding setting and read x = 24.75 naut. mi. EXERCISES

1.	An inch is equivalent to 2.54 cm. Find the respective length in cm. of rods     66 in. long,     98 in. long, and     386 in. long. Note the proportion:   in. —— cm.  :  1 ——— 2.54  =  66 —— x  =  98 —— y  =  386 ——— z  .
2.	One yd. is equivalent to 0.9144 meters. Find the number of meters in a distance of   (a) 300 yd.   (b) 875 yd.   (c) 2.78 yd.  Hint. yd. —— m  :  1 ———— 0.914  =  300 —— x  =  875 —— y  =  2.78 ——— z  .
3.	If 7.5 gal. water weighs 62.4 lbs., find the weight of   (a) 86.5 gal. water,   (b) 247 gal. water,   (c)  3.78 gal. water.
4.	31 sq. in. is approximately 200 sq.cm. How many square centimeters in   (a) 36.5 sq. in.?   (b) 144 sq. in.?   (c)  65.3 sq. in.?
5.	If one horsepower is equivalent to 746 watts, how many watts are equivalent to   (a) 34.5 horsepower,   (b) 5280 horsepower,   (c)  0.832 horsepower?
6.	If one gallon is equivalent to 3790 cu. cm., find the number of gallons of water in a bottle which contains   (a) 4250 cu. cm.,   (b) 9.68 cu. cm.,   (c) 570 cu. cm. of the liquid.
7.	The intensity of pressure due to a column of mercury 1 inch high (1 inch of mercury) is 0.49 lb. per sq. in.     If atmospheric pressure is 14.2 lb. per sq. in., what is atmospheric pressure in inches of mercury?     What is a pressure of 286 lb. per sq. in. in inches of mercury?     What is a pressure of 128 inches of mercury in lb. per sq. in.?
8.	If P, represents the pressure per square unit on a given quantity of a perfect gas and V, the corresponding volume, then for two states of the gas at the same temperature P1/P2 = V2/V1. The volume of a gas at constant temperature and pressure 14.7 lb. per sq. in. is 125 cu. in.   (a) Find the respective pressures at which the volumes of the gas are          300 cu. in.,          250 cu. in.,          75.0 cu. in.    (b) Find the respective volumes of the gas under the pressures:          85 lb. per sq. in.,          55 lb. per sq. in.,          23 lb. per sq. in.,          10 lb. per sq. in.