to the west of the first meridian. But if he observe an eclipse taking place at 12 o'clock at night, for instance, which his almanac states will appear in London at 8 o'clock the same evening, it is evident that he is four hours in advance of London time, and consequently four times fifteen or sixty degrees to the eastward of the first meridian."

We have seen how the circumference, diameter, and general magnitude of the earth have been determined; and we have been made acquainted with the means by which the relative and actual positions of places on its surface may be ascertained-we shall now show how the distance between any two places on globes or maps may be found.

b

1. If the places are on the same meridian, but in different hemispheres, we have only to multiply the sum of their latitudes by 60 for geographical, or by 691 for English miles, to find the distance between them. For instance, if one of the places is 20° north, and the other 10° south of the equator, the distance between them in degrees of latitude is evidently 30, which, multiplied by 60, gives us 1,800 geographical, or, by 691, 2,073 English miles.

What is said here is merely in illustration of the principle, as this method of finding the longitude is found to be impracticable at sea, in consequence of the motion of the vessel. For, in order to observe these eclipses, it is necessary that the telescope should be perfectly steady. Besides it would be requisite, either that the vessel should remain at the place at which the time was regulated by the sun, till the eclipse occurred; or that the distance she may have moved east or west during the interval should be known and taken into account. eclipses of the moon and of the sun are better adapted for this purpose, but they are of rare occurrence.

The

The longitude at sea may be found when the moon is visible, by taking her angular distance from the sun, or from one of nine conspicuous stars which lie near her orbit or path. The distance of the moon from the sun, and from these nine stars, is given in the Nautical Almanac for every three hours of Greenwich time; and the general principle is, that the difference between Greenwich time as noted in the Almanac, and the time at the place where the longitude is sought, when converted into degrees, will be the longitude of the ship. This is called the LUNAR METHOD of finding the longitude. bOr, in round numbers, by 70, the result, of course, will be a little in excess.

• There is no more difficulty in this than in answering the following questions:-If one town is 20 miles due north, and another 10 miles due south from Dublin, what is the distance between these two towns? (30.) But if one town is 10 miles due north from Dublin, and another 30 miles from it in the same direction, what is the distance between these two towns? (20.)

2. If the places are on the same meridian, and in the same hemisphere, the difference between their latitudes, multiplied by 60 for geographical and 69 for English miles, gives us the distance between them. For instance, if one of the places is 10° and the other 30° north latitude, we have only to subtract 10 from 30, and multiply the difference as before.

If the places are on the same parallel, their distance from each other in degrees is found in like manner-that is, by adding their longitudes, if in different hemispheres or by subtracting them from each other, if in the same hemisphere But their distance in miles is found not by multiplying by 60, as in reducing the degrees of latitude, but by the number of miles contained in a degree of longitude on that parallel under which the places in question lie.* For instance, if one of the places is ten degrees east, and the other twenty degrees west of the first meridian, it is evident that the sum of their longitude (10° E. + 20° W. = 30°) gives their distance from each other in degrees of longitude; but if the places are on the same side of the first meridian, the one say 20° and the other 40° east of it, it is equally evident that the difference in their longitude (40°— 20° — 20°) gives their distance from each other in degrees of longitude. And it is clear from what has been said that to reduce these degrees to geographical miles, we must multiply not by 60, except at the equator, but by the number of miles contained in a degree of longitude in that particular latitude in which the places in question lie. By referring to the table, we find that the number of miles in a degree of longitude in our latitude (Dublin) is about 36 miles. If we wish, therefore, to find the distance in miles between Dublin and Manchester, for instance, which are nearly under the same parallel, we have merely to multiply the difference between their longitudes (6° 20′ and 2° 14') by 36, and the result will be about 148 miles.

=

But when, as is generally the case, two places are on different parallels and different meridians, we have merely to take the distance between them with a pair of compasses or piece of tape, and measure it on the equator, or graduated scale to be found on every map. This, if referred to the

• The number of miles in a degree of longitude in every latitude is found in the table mentioned, page 53.

equator, will give us their distance, nearly, in degrees, which, as they are degrees of a great circle, we may reduce to miles by multiplying by 60. We say degrees of a great circle, because it is evident that the shortest distance between any two points on the globe is an arc of the great circle which joins them; and we measure this arc on the equator or on a meridian; because, as all great circles are equal, it is immaterial which we adopt as a measure. For example, if the distance thus taken between two places on a globe or map is found when carried to the equator, or the graduated side of the map, to contain 10, 20, or 50 degrees, their distance in geographical miles will be 10, 20, or 50, multiplied by 60. By means of the scale referred to we are enabled to find the distance at once in miles, without ascer taining the number of degrees of a great circle intercepted between the places.

The instructor should now exercise his pupils in measuring, and calculating the distance between any two given points or places on the earth's surface, as laid down in their maps. The table in page 53 will enable them to convert the degrees of longitude into geographical miles, which they can easily reduce into English miles. They should also be exercised in converting longitude into time, and vice versâ.

QUESTIONS FOR EXAMINATION ON CHAP. IV.

Pages 45, 46.-How is the magnitude of a spherical body ascertained? 2. Meaning of the terms diameter and circumference? 3. How is the length of the circumference of the earth ascertained? 4. How, the length of the diameter ? 5. The length of a degree on the earth's surface? 6. Why is the equator a great circle? 7. How does it divide the globe? 8. Can you explain the circles in the diagram?

Pages 47-50.-The latitude of a place? 2. In what latitude is the entire northern hemisphere? 3. In what, the southern? 4. Does the latitude of a place give you its precise position? 5. What other measurement is necessary? 6. What is a meridian? 7. First meridian? 8. On what is latitude measured? 9. How many degrees in the quadrant of a circle? 10. How many miles in the quadrant of a meridian circle ? 11. How is latitude measured? 12. What is meant by the universal meridian? 13. Parallels of latitude? 14. Why called parallels? 15. Why parallels of latitude? 16. How many usually drawn? 17. How many might be drawn?

a Great Circle.-See note, page 31.

Pages 51-53.-What is longitude? 2. The first meridian? 3. All nations count latitude from the same place; is there the like unanimity with respect to longitude? 4. How is this explained? 5. On what circles is longitude measured? 6. Why is longitude reckoned on the equator? 7. Are the terms longitude and latitude properly applied to a spherical body? 8. Why originally applied to the earth? 9. Are they, strictly speaking, applicable to the earth? 10. Why was the Mediterranean Sea so called? 11. The latitude of a place really s? 12. In what way are the meridians made to assist in determining the longitude? 13. The length of a degree depends upon? 14. If a circle is 360 feet in circumference, what will be the length of a degree? 15. Why? 16. The length of a degree on the earth's surface? 17. Why is a degree on the equator longer than a degree on any of the parallels? 18. Why are the degrees of longitude of unequal length? 19. Why the degrees of latitude, generally speaking, of equal length ? 20. How are the degrees of latitude reduced to miles? 21. How the degrees of longitude? 22. Can you state the nature and use of the table referred to?

Pages 53, 54.-How far is longitude counted round the globe? 2. How far is latitude? 3. The extremes of latitude, north and south? 4. If one person is 180° E. longitude, and another 180° W. longitude, and on the same parallel, how far are they from each other? 5. How do you show this? 6. Strictly speaking, are the degrees of latitude of equal length? 7. Can you describe the principle of Sir Isaac Newton's theory as to the true form of the earth? 8. Can you give the proofs and illustrations added in the note ? 9. A degree of a meridian near the polar circles is how much longer than a degree of the same meridian near the equator? 10. The cause of this? 11. The consequence of this? 12. In what direction do the degrees of latitude get longer? 13. Is the difference worth taking into account practically? 14. The degrees of longitude become shorter in what direction, and in what proportion? 15. How do you show that the latitude of a place in the northern hemisphere always corresponds to the altitude of the polar star, as observed from that place? 16. In what part of the earth would we be, if the polar star were in our zenith? 17. What would its altitude and our latitude be in this case? 18. At 45° N. latitude what is the altitude of the polar star? 19. At 530? 20. At the equator? 21. In what part of the earth would a person be, from which, if he moves, no matter in what direction, he is going southward? Pages 55-59.-How measure a degree upon the earth's surface? 2. How find the circumference and diameter of the earth? 3. How much is the equatorial diameter of the earth longer than the polar? 4. How may the latitude of a place be found by the meridian altitude of the sun? 5. Why does our zenith distance from the celestial equator give us our latitude? 6. Why does the distance between the celestial equator and the poles of the heavens correspond to the distance between the terrestrial equator and the poles of the earth? 7. In what part of the earth would we be, if the celestial equator were in our zenith? 8. Where, ifit coincided with our rational horizon? 9. What would be our latitude in each of the preceding cases? 10. What would be our latitude if our zenith were 45° from the celestial equator? 11. What is DECLINATION, and to what does it correspond? 12. How may our zenith distance from the celestial equator be found 13. What is the

sun's declination on the 21st of June? 14. When is the sun's south declination greatest? 15. When has the sun no declination? 16. How may the latitude of a place be found by taking the meridian altitude of the moon, or of any fixed star, whose declination is known?

Pages 61-64.-How is longitude found at sea? 2. Why is time earlier towards the east? 3. And why in the proportion of one hour to 15 degrees? 4. When it is 10 o'clock with us, what will be the hour with persons residing 15 degrees to the east of us? 5. What with persons residing 45 degrees to the west of us? 6. How do you show this? 7. By knowing the difference in the time of any two places we can determine? 8. And by knowing the difference in their longitudes we can determine? 9. How many meridians usually drawn upon globes and maps? 10. Why 24? 11. If a meridian is drawn through every 10 degrees, every meridian corresponds to how much time? 12. What is meant by a chronometer? 13. The use of it in determining the longitude? 14. If it is 12 o'clock by our watches, as regulated by the sun, and only 10 by the chronometer, which gives London time, what is our distance from the first meridian, and in what direction is it from us— or, in other words, what would be our longitude? 15. Suppose it were 4 o'clock by the chronometer when it is 2 by us, what would be our longitude? 16. Why other methods for finding the longitude resorted to? 17. In what way have the eclipses of Jupiter's satellites been made available for the purpose? 18. Can you give an instance? this method practicable at sea? 20. Why not?

19. Is

14. How

Pages 64-66.-How is the distance between two places on a globe or map found? 2. If on the same meridian and in the same hemisphere ? 3. If in different hemispheres? 4. If on the same parallel and on the same side of the first meridian? 5. If on different sides of the first meridian? 6. How are the degrees of latitude reduced to miles? 7. How the degrees of longitude? 8. Can you state the principle of the lunar method? 9. In what part of the earth may the degrees of longitude be multiplied by 60 to bring them to miles? 10. Why? 11. Strictly speaking, is the equator greater than a meridian circle? 12. In the latitude of Dublin how many miles in a degree of longitude? 13. How find the distance between Dublin and Manchester? find the distance between any two places on a globe or map without regard to their latitudes or longitudes? 15. The shortest distance between any two places on a globe? 16. Why, if carried to the equator will this give the distance between them? 17. In maps on which the equator is not represented, how measure the distance between any two places? 18. Given the difference in time between any two places, how may the difference in their longitudes be found? 19. And vice versâ? 20. The length of a degree of longitude at the equator? 21. At th poles? 22. In latitude 45° ? 23. In latitude 53°? 24. In latitude 60°? 25. At the polar circles"