71. A solution is to be evaporated until the reading is 55 Tw. Compute the specific gravity when this point is reached.

72. Specific Gravity by Baumé's Hydrometer.

(a) The specific gravity of a liquid heavier than water at 15.55° C. equals 145 divided by the difference between 145 and the Baumé reading.

(b) The specific gravity of a liquid lighter than water at 15.55° C. equals 140 divided by the sum of 130 and the Baumé reading. Write both formulas.

73. Compute the specific gravity of a solution heavier than water, which reads 55 Bé.

74. When sulphuric acid has a specific gravity of 1.842 what will be the Baumé reading?

75. Compute the Baumé reading for a liquid whose specific gravity is .95.

76. In a liquid lighter than water at 17.5° C., the reading is 45 Bé.

Compute the specific gravity of the liquid.

The

77. Specific Gravity by Pyknometer. specific gravity of a liquid by the pyknometer may be computed from the following law:

Weight of bottle and liquid - weight of bottle Sp grp= Weight of bottle and water - weight of bottle

Simplify the second member of the equation, and formulate both the original equation and the simplified equation.

10 ccm 20°c

FIG. 55. Pyknometer or Specific Gravity Bottle.

78. Volume of Dry Air. Mendeléeff gives the following formula for the volume of dry air at any temperature and pressure, when saturated with watery vapor:

in which VD = volume of dry air in cubic centimeters, V1 = saturated volume of air in cubic centimeters, P=barometric pressure of saturated air in millimeters, Pa=barometric pressure of the aqueous vapor in millimeters at the given temperature, Centigrade.

Copy the formula and write the law.

79. Compute the volume of dry air in a saturated volume of 52.4 cc at 15.3° C under a pressure of 748.5 millimeters, the pressure of aqueous vapor at this temperature being 12.9 millimeters.

80. Dry Volume at 760 mm. and 0°. The volume of dry air in cubic centimeters under a barometric pressure of 760 millimeters at a temperature of 0° C., equals the moist volume times the given pressure in millimeters divided by 760, times 273 divided by the sum of 273 and the given temperature.

Formulate and compute the dry volume in problem 79 at 760 millimeters and 0°.

CHAPTER II

RESOLUTION AND COMPOSITION OF FORCES

SECTION 1, PROJECTION. SECTION 2, GRAPHICAL RESOLUTION. SECTION 3, RESOLUTION BY COMPUTATION. SECTION 4, FUNCTIONS OF AN OBTUSE ANGLE, AND EXAMPLES. SECTION 5, RESULTANT.

"Whenever an idea is constantly recurring the best which can be done for the perfection of language and consequent advancement of knowledge is to shorten as much as possible the sign which is used to stand for that idea.'

DE MORGAN.

§ 1. PROJECTION

38. Definition. Under headings draw this figure to an enlarged scale in the work-book.

R

FIG. 56.

From R draw a perpendicular to OA, terminating in OA at V. Then OV is the right-angled or orthogonal projection of OR on OA.

Specify this under the figure.

Draw the same figure again in the work-book and from

A draw a perpendicular to OR, terminating at C.

What then is OC? (Write answer immediately under the figure.)

Draw Fig. 57 to an enlarged scale in the work-book.

B

FIG. 57.

From R and L draw perpendiculars to AB. The segment of AB lying between the feet of these perpendiculars is the projection of LR on AB.

Specify this under the figure.

Observe that in orthogonal projection perpendiculars are drawn to the line on which projection is to be made.

Draw the figure again in the work-book and project AB on RL.

Specify the projection.

Draw Fig. 58 to an enlarged scale in the work-book and draw perpendiculars to AB from O and R, terminating in AB at V and T.

R

FIG. 58.

Then VT is the projection of OR on AB.

Specify the projection.

Draw Fig. 59 to an enlarged scale in the work-book and from

-A

FIG. 59.

R draw a perpendicular to OA produced, terminating at V. Then OV is the projection

of OR on OA.

Specify the projection.

Write the definition of the orthogonal projection of one line on another.

39. Examples. In the following examples draw each. figure to an enlarged scale and make both projections as in the work required for Fig. 56, specifying the projection under each.