6. Multiply 4 by 75 by logs. 7. Multiply 75 by 60 by logs. 8. Multiply 701 by 9 by logs. 9. Multiply 1074 by 2 by logs. 10. Multiply 7000 by 1 by logs. 11. Multiply 476 by 682 by logs.

12. Multiply 3746 by 6168 by logs and decimals. 13. Find the product of 38, 1.74, 96 and 0756 by logs. 14. Find the product of 376, 0069, and 1.476 by logs.

15. Find the product of 2·4, 008, ·62, and 3·1. 16. Divide 66 by 3 by logs.

17. Divide 777 by 11 by logs.

18. Divide 1728 by 144 by logs. 19. Divide 1000 by 1000 by logs. 20. Divide 1010 by 101 by logs. 21. Divide 87469 by 364 by logs.

22. Divide 37 by 02 by logs and decimals.

23. Divide 76 by 874 by logs.

24. Divide 10 by 5.86 by logs and decimals.

25. Divide 6748 by 00763 by logs.

26. Divide 34761 by 2.674 by logs and decimals.

27. Required the square of 46, of 94, of 163, and of 0075 by logs.

28. Required the cube of 47, of 63, of 109, and of 00861 by logs.

29. Required the square root of 4796, of 746937, and of 6470 by logs.

30. Required the cube root of 36472, of 62154, and of •7564 by logs.

31. What is the cost of 243 yards at 9s. 3 d. per yard, by logs and decimals?

32.

What is the cost of 3 tons, 2 cwt. 3 qrs. at 4s. 6d. for 7 lbs. by logs?

33. If 1000 yards cost £70. 15s. what does 1 foot cost at the same rate?

34. If of a lb. cost 4s. 8d. what will 27 lb. cost.

ELEMENTARY PRINCIPLES AND DEFINITIONS.

See MRS. TAYLOR'S EPITOME, pp. 49 and 172.

NAVIGATION is the art of finding the latitude and longitude, or the place of a ship at sea, and of determining her course and distance. A ship's place at sea is determined by what is technically called account or dead reckoning, or Astronomical Observation, the former method is called Navigation, the latter Nautical Astronomy.

Before a pupil can well understand the following definitions, he must turn to his Epitome for a full account of the Earth, her figure, and the situation of the respective circles drawn on her surface, and likewise for a more extensive account of her motions and other phenomena.

1. The Earth's Axis is the diameter about which it revolves, the extremities of which diameter are called the Poles of the Earth, one of which is called the North, the other the South pole.

2. The Equator, known to seamen generally as the Line, is a great circle, at an equal distance from the poles, and divides the Earth into two equal parts, called the Northern and Southern

hemispheres. Like all other great circles it is divided into 360 equal parts or degrees, and these are sub-divided into 60 equal parts called miles or minutes, and each minute is again divided into 60 equal parts called seconds.

Meridians are great circles cutting the Equator at right angles and passing through the Poles. Every place on the globe may be supposed to have a meridian passing through it. Places lying due north and south of each other, are said to be on the same meridian.

The meridian passing through the Royal Observatory at Greenwich is, by English Geographers called the first meridian, and all tables in the Nautical Almanac, and other English Astronomical tables, are adapted to that meridian.

Each country may however reckon that meridian which passes through their own principal observatory, their first meridian, thus, the French consider their first meridian to be that which passes through the Royal Observatory at Paris. Each meridian in reference to a place through which it passes may be considered to divide the earth into two equal parts, called the Eastern and Western hemispheres.

The Latitude of a place is an arc of the meridian which passes through it, and is either north or south according as it is north or south of the Equator. The latitude is reckoned from the Equator to the Poles, therefore the greatest latitude a place can have will be 90°.

Parallels of Latitude are small circles parallel to the Equator, every place on the Earth's surface may be supposed to have a parallel of latitude passing through it.

The difference of latitude is the distance between any two places, shewing how far they are north or south of each other, and is an arc of the meridian intercepted between their respec

tive parallels of latitude. The greatest possible difference of latitude between any two places is therefore 180°.

To find the difference of latitude between any two given places ;

Rule: If the latitudes are both of the same name, that is both

north or both south, subtract the less from the greater and the remainder will be the difference of latitude; but if one be north and the other be south, add the two together and their sum will be the difference of latitude.

1. What is the diff. of lat. between Hong Kong and Bombay?

Lat. of Hong Kong
Lat. of Bombay......

2. What is the diff. of lat. between Sydney and Sinca

pore?

......

22° 15'N.
18 49N.

Lat. of Sydney
Lat. of Sincapore

33° 52 S.

1

17N.

The Co-latitude of any place, is the complement of the latitude of that place to 90°.

The Longitude of any place is an arc of the equator contained between the first meridian and the given place, it is called east or west according as the given place is east or west of the first meridian. Longitude being reckoned both to the right and left of the first meridian, till it reaches that point of the equator intersected by the opposite part of the same meridian, commonly called the opposite meridian, can never exceed 180°.

The difference of longitude between two places is an arc of the equator, intercepted between their respective meridians, shewing how far they are to the eastward or westward of each other, and can never exceed 180°.

To find the difference of longitude between two given places ;

Rule: When the given longitudes are of the same denomination, subtract the less from the greater; but when they are of different denominations add them together, the sum or remainder will be the difference of longitude; but, as the difference of longitude signifies the less arc of the Equator intercepted between the two meridians, when the longitudes are of different denominations and their sum exceeds 180°, that sum must be subtracted from 360°, to find the difference of longitude.

A ship in north latitude sailing northerly or in south latitude sailing southerly, increases her latitude, but in north latitude sailing southerly, or in south sailing northerly she decreases her latitude; the same observations apply to the longitude.

For further illustration of this subject, see "the Epitome."