4. Answer for other places marked on the map such questions as are asked in problems 2 and 3 for Omaha, for St. Paul, and for Dodge City.

The circle Sq Nr (Fig. 1) represents the earth and the curved lines represent the hourly meridians running from the equator, qr, and con

verging toward the poles S and N. If O represents some place in the northern hemisphere, Sq Nr`is the meridian of the place and BQPR may be imagined to represent the meridian of the sky (hour circle of the sun), on which the sun, T, is situated. The hour circle of the sun in the apparatus is held in place at A. If now the crank F is turned so as to carry q forward and downward through E to r, the sun's meridian standing stationary, the motions which cause the differences of time and the changes of day and night may be understood, by recalling that only the half of the globe which is turned to the sun is light (in day). SGN denotes the prime meridian.

5. As the globe is standing in Fig. 1, what time is it at O? At places on the 105th meridian? On the 60th meridian? On the 15th meridian east* of Greenwich? On the 45th east?

* Remember that east is the direction toward which the globe is turning, that is eastward means from E toward G through r and around to E again.

6. If the meridian SGN is continued around on the other side of the globe, what will its number be?

7. Knowing that a place on the earth, as O, turns round through 360° in 24 hr., how long does it require the space between any two adjacent meridians of Fig. 1, p. 197 to pass under the sun's hour circle?

8. If a man should start from some place on the prime meridian (say London) on Friday noon and move westward just as fast as the globe turns eastward, what time (by the sun) would it be to him during his journey all the way round the globe? What hour and day would a Londoner call it when the traveler returned 24 hr. later?

The problem raises the question, "Where should the traveler have changed his date so that his date might agree with that of his starting place when he returns?" The answer is, "It has been agreed that the date should change at the 180th meridian." When vessels cross this meridian from the east toward the west they add a day to their reckoning. If they cross at noon on Friday, Friday noon instantly becomes Saturday noon. Crossing from the west toward the east, they repeat a day. In the case mentioned, the 24-hour period from Friday noon would "be done over again." The 180th meridian is for this reason called the Date Line. Trace it on the earth in a Geography.

9. The date begins on the 180th meridian of longitude and travels westward around the earth. Supposing the day begins at midnight, give the date and hour on the 180th meridian, when it is Wednesday, Oct. 15, 10 P.M., standard time, in Chicago; in Washington; in Denver; in San Francisco.

10. The U. S. Supreme Court has decided that legal time at any place is the local time of the place. A man in Akron, O., insured his house at 11:30 A.M. "standard" (90th meridian) time and the house took fire at that moment and was destroyed. The policy stated that the insurance would be in force at and after 12 o'clock (noon)

of the day of insuring. The difference between Akron local time and 90th meridian time is 33 minutes. Would the law require the insurance company to pay the policy? Give reason for your answer.

11. If every place on the earth has the time of that meridian of the map, p. 190, nearest to it, when it is 3:25 P.M. in England what will be the time of the following places? (1) Washington. (2) Boston. (3) New Orleans. (4) Denver. (5) Rio Janeiro. (6) Cuba. (7) Japan. (8) Philippine Islands.

MENSURATION

§114. Areas, Roofing and Brickwork.

1. Give a rule for computing from its dimensions the area of a square; a rectangle; a parallelogram; a triangle.

Fig. 1 represents a plot of the streets and blocks of a part of a certain city. The streets are all 75 ft. wide

between sidewalks. The numbers written on the lines indicate their lengths in feet. The dotted lines show how to divide up the areas into parts for computation.

2. If $240 per foot of frontage on both 3d, and 4th streets, was paid for block B (Fig. 1, p. 201), how much did the block cost per square foot? Per square yard?

3. Find the area in square yards of other parallelograms, such as O, P, etc., of Fig. 1, p. 201.

4. Find the area in square feet of the following triangles of Fig. 1, p. 201; E; G; I; J; K; L; abc.

Other areas of Fig. 1, p. 201, require a knowledge of trapezoids. A four-sided figure (a quadrilateral) like Fig. 1, having one pair of parallel sides is called a trapezoid.

Trapezoid

FIGURE 1

The altitude of a trapezoid is the distance square across between two parallel sides (called the bases).

5. Study the trapezoids of Fig. 2, and find how to get the length of EF, the line connecting the middle points of the two non-parallel sides, from the lengths of the two bases. After computing EF, find for each trapezoid a rectangle whose area equals the area of the trapezoid. Find the areas of the trapezoids of Fig. 2.

The lengths a, b, and c of the last trapezoid are called its dimensions.

NOTE.the sum of x and y is written (x + y). n times the half sum is written an (x + y)

6. How does the sum of the bases of a trapezoid compare with the base of a parallelogram having an altitude

FIGURE 1

and area equal to the altitude and area of the trapezoid (Fig. 1)?

7. Supposing a, b, and c are the dimensions, in feet, of the trapezoids of Fig. 1, what are the areas of these trapezoids?

8. Find the areas in square feet of C; of D; of M; of N; of H (Fig. 1, p. 201).

9. Calling Z the area of any trapezoid, whose bases are b and c and whose altitude is a, write an equation showing how to find Z from a, b, and c.

10. Find the area in square yards of A, B, N, S, T, Fig. 1, p. 201.

A square of roofing means a 10' square of roof surface, or 100 sq. ft. A shingle is said to be laid 4", 42", or 5" to the weather when the lower end of each course of shingles on the roof extends 4", 4", or 5" below the course next above it.

ient scale, of the development of the roof shown on the

left.

12. If 1000 shingles laid 4" to the weather cover a square of roofing, how many shingles will be needed to cover a square, if laid 5′′ to the weather? 41" to the weather? 3" to the weather? 31′′?

13. The dimensions on the development (Fig. 2) being in feet, find the cost of the shingles, laid 4′′ to the weather,