107. Effects of the Rotation of the Earth on Its Axis. We have spoken of the instant at which the earth's axis is most inclined toward the sun's rays, or the summer solstice; and of the instant at which it is the least inclined, or the winter solstice. Two other instants are of equal importance. These are the two instants in each year at which the line connecting the centre of the sun and the centre of the earth is at right angles to the earth's axis, and are called, as they occur in the spring or in the autumn, the Vernal or the Autumnal Equinox.

Diagram 4, on page 248, represents the earth at either equinox. The points N and S in the diagram are the two ends, or Poles, of the earth's Axis, the point N being the end which points to a certain bright star called the North Star. The line in the diagram composed of the points on the earth's surface which are half way between the two poles is called the Equator. Suppose the earth to make a complete rotation at either equinox. During what part of the rotation will every point on the surface of the earth be exposed to the sun's rays?

What, then, will be the length of the day and of the night at every point on the earth's surface?

The vernal equinox of 1901 was on March 21, at 2 h. 23 m. A. M.; and the autumnal equinox on Sept. 23, at 1 h. 9 m. P. M. What, nearly, was the length of the day and of the night on each of these dates?

At nearly what hour did the sun rise and set on each date?

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The direction the earth is turning on its axis, or from which the sun appears to be moving in its course, is called East; and the direction from which the earth is turning, or in which the sun appears to be moving, is called West, Think of the figure representing the earth in Diagrams 1 and 2 as turning in a direction opposite to the direction in which the hands of a watch would turn if held between yourself and the diagram. Examine the diagrams and give the direction

Of Newfoundland from Vermont.

Of Newfoundland from Italy.

Of Italy from China.

Of China from Vermont.

Of Alaska from Vermont.

Of California from Chicago.

Each diagram represents the earth at one of the equinoxes. At what time, then, does the sun rise at each locality represented in the diagrams?

When it is sunrise in Vermont what time is it

When it is noon at Chicago what time is it
In Vermont?

In Newfoundland?

In Alaska?

In California?

When it is midnight in Vermont what time is it

In Italy?

In Newfoundland?

In Alaska?

In California?

In Chicago?

2. Diagram Showing Time in Other Localities at I P. M. in New England.

When it is a certain hour in any locality what will be the relative time at any locality to the east? to the west? Give a general principle concerning the relative solar times of two localities.

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Lines drawn on the surface of the earth directly from pole to pole are called Meridians, this name being given from the fact that all points in the same meridian have their mid-day, or noon, at the same instant.

Lines drawn on the surface of the earth parallel to the equator are called Parallels of Latitude. The angular distance of a locality from the equator is called its Latitude, and its angular distance from a standard meridian its Longitude. The standard meridian in most general use is that passing through the Astronomical Observatory at Greenwich, near London.

Latitude is reckoned from the equator to the poles, and longitude from a standard, or Prime, meridian, to the meridian half way around the earth. What, then, is the greatest latitude a place can have? the greatest longitude?

How, evidently, shall we find the difference in the latitude of two places that are on the same side of the equator, or the longitude of two places that are in the same direction from the prime meridian?

One of two localities is a given number of degrees north of the equator and the other a given number of degrees south of the equator. How shall we find their difference in latitude?

One of two localities is in 85 degrees east longitude and the other in 89 degrees west longitude. How shall we find their difference in longitude?

One locality is in 45° east longitude, and the other in 145° west longitude. We wish to find their difference in longitude. Suppose that we add the two longitudes. What sum shall we obtain ?

How many degrees are there in a half circumference? in an entire circumference?

If, then, it is 185 degrees from the first locality to the second in one direction, how many degrees must it be in the other direction?

One locality is in 170 degrees east longitude, and another in 160 degrees west longitude. We wish to find their difference in longitude.

How far is the first locality from the meridian of 180 degrees?
How far is the second locality from this meridian?
How many degrees apart, then, are the two localities?

In what two ways may we find the difference in longitude of two places on opposite sides of the prime meridian when the sum of their longitudes is more than 180 degrees?

* *

Through how many degrees does the earth turn in a day? How many hours are there in a day?

Through how many degrees, then, does the earth turn in an hour?

What, then, is the difference in the longitude

Of Vt. and Newfoundland?

Of Vt. and Italy?

Of Italy and China?

Of Vt. and China?

Of Cal. and China?

Of Vt. and California?

Of Vt. and Alaska?
Of Chicago and Italy?
Of Cal. and Italy?

Of Alaska and Italy?

The longitude of Chicago is about 88° west. What, then, is the longitude

Of California?

Of China?

Of Newfoundland?
Of Vermont?

Of Alaska?

Of Italy?

NOTE. Find on a map the longitude of the preceding localities. Observe that the longitude you obtain for Alaska is that of the western part of the Aleutian Islands.

108. To Find Difference in Longitude when Difference in Time is Given.

A difference of an hour in the solar time of two localities is produced by a difference of how many degrees of longitude ? How, then, shall we change difference in time expressed in hours to difference in longitude expressed in degrees?

A difference of a sixtieth of an hour in time is produced by a difference of how many sixtieths of a degree of longitude? A difference of a minute of time, then, is produced by a difference of how many minutes of longitude?

How, then, shall we change difference in time expressed in minutes of time to difference in longitude expressed in minutes of longitude?

A difference of a sixtieth of a minute of time is produced by a difference of how many sixtieths of a minute of longitude? A difference of a second of time, then, is produced by a difference of how many seconds of longitude?

How, then, shall we change difference in time expressed in seconds of time to difference in longitude expressed in seconds of longitude?

We wish to find what difference in longitude will produce a difference of a given number of hours, minutes, and seconds in time.

By what must we multiply the given number of seconds of

time to obtain the number of seconds in the required difference in longitude?

By what must we divide our product to reduce it to the next higher denomination?

Multiplying by 15 and dividing by 60 is equivalent to dividing by what number?

How, then, might we at a single step have changed the given number of seconds of time to minutes of longitude?

How, following the same method, may we at one step change the given number of minutes of time to degrees of longitude?

Suppose our minutes of time to be 39 and our seconds of time to be 46. What is the largest multiple of 4 less than 39? less than 46?

How many of our seconds of time, then, can we change to an integral number of minutes of longitude? how many of our minutes of time to an integral number of degrees of longitude?

What shall we do with the remaining seconds of time? with the remaining minutes of time?

Give a rule for finding the difference in longitude expressed in degrees, minutes, and seconds that will produce a given difference in time expressed in hours, minutes and seconds.

The difference in the time of New York and of Honolulu is 12 hours less 6 h. 24 m. 36 sec., or 5 h. 35 m. 24 sec.

The difference of an hour in time is produced by a difference of 15 degrees in longitude, and the difference of any part of an hour is produced by 15 times that part of a degree. Therefore, to find the difference in the longitude of the two localities expressed in degrees, minutes, and seconds we multiply by 15 their difference in time expressed in hours, minutes, and seconds.

A difference of 24 seconds of time is produced by a difference of 15 times 24 seconds of longitude, or of of 15 times 24, or ¦ of 24, or 6, minutes of longitude.

A difference of 35, or 32 plus 3, minutes of time is produced by a difference of 15 times (32 plus 3) minutes of longitude.

15 times 3 minutes of longitude, plus the 6 minutes of longitude previously obtained, are 51 minutes of longitude.