9. Arc.-A part of the circumference of a circle.

10. Complement of an Arc or Angle.-Its difference from 90°. 11. Supplement of an Arc or Angle.-Its difference from 180°.

12. The Poles.-The points where the earth's axis meets the surface.

13. Equator.-A great circle of the earth 90° distant from the poles.

14. A Meridian.-Half a great circle extending from pole to pole of the earth.

15. Parallels of Latitude.-Circles whose planes are parallel to the plane of the Equator.

16. Tropics.-Two parallels of latitude distant 23° 28' on each side of the Equator: Cancer on the north, and Capricorn on the South.

17. Difference of Latitude.-The arc of a meridian intercepted between the parallels of latitude on which the places stand.

18. Prime Meridian.-The meridian from which longitudes are measured; in this country it is the meridian of Greenwich.

19. Longitude.-Distance in arc east or west of the meridian of Greenwich. It is measured on the Equator, or on a graduated parallel. p+ 180°

20. Difference of Longitude.-An arc of the Equator intercepted between two meridians of longitude (Fig. 16).

P and P' are the poles.

EQ is the equator.

PAP' and PBP' are meridians.

POP' the prime meridian.

LL', TT, RR' are parallels of latitude.

TT' is tropic of Cancer.

RR' is tropic of Capricorn.

XY is difference of latitude when places are on same side of equator, on parallels LL' and TT'.

XZ is difference of latitude when places are on opposite sides of equator, on parallels LL' and RR'.

OA and OB are Longitudes of places on meridians PAP' and PBP'.

AB is difference of longitude, between places on meridians PAP' and PBP'

21. Meridional Parts.-The distance from the Equator in geographical miles of a given latitude on Mercator's Chart (Fig. 17).

22. Departure. The distance in geographical miles between two places in the same latitude. In the traverse table, it is the number of miles of easting or westing made on a given course and distance.

23. Nautical Mile.-The one-sixtieth part of a degree measured on a meridian. It varies slightly with the latitude, and its mean value is taken at 6080 feet.

24. Rhumb Liné.-A line which makes equal angles with all the meridians it crosses.

25. Zenith. The point in the heavens vertically over the observer's head.

26. Nadir. The point in the heavens diametrically opposite to the Zenith.

27. Equinoctial. A great circle in the heavens 90° from the celestial poles.

28. Ecliptic.-A great circle in the heavens representing the sun's annual apparent path.

29. First Point of Aries.-The point where the sun crosses the Equinoctial about the 21st of March.

30. Celestial Meridian of Observer.-The vertical circle which cuts the Horizon in the true North and South points (Fig. 18).

31. Azimuth. The bearing of an elevated object reckoned

from the N. or S. point.

32. Amplitude. The bearing of an object when rising or setting, reckoned from the E. or W. point.

33. Vertical Circles.-Circles passing through the Zenith and Nadir, and therefore perpendicular to the Horizon. They are also called "altitude circles" and "azimuth circles."

34. Prime Vertical.-The vertical circle which cuts the Horizon in the true East and West points.

35. Declination.-Distance in arc north or south from the Equinoctial measured on an Hour Circle.

36. Polar Distance.-The distance in arc from the elevated pole, and therefore the complement of the Declination, measured on an Hour Circle.

37. Hour Circles.-Halves of great circles which pass through the celestial poles, one hour being equal to 15° (Fig. 19).

38. Right Ascension.-Distance eastward from the first point of Aries measured on the Equinoctial and expressed in Time. 39. Hour Angle.-The angle at the pole between the observer's Celestial Meridian and an Hour Circle.

40. Civil Time. The time used in civil life. The day begins at midnight, and is divided into two parts of twelve hours each, a.m. from midnight to noon, and p.m. from noon to midnight.

41. Astronomical Time.-Time used for astronomical calculations. The day begins at noon, and the hours count from 0 to 24.

42. Mean Time.-The Westerly hour angle of the Mean Sun, it is the time shown by a correctly going timepiece.

The Mean Sun is an imaginary body which is supposed to move along the equinoctial with the average velocity of the True Sun in the ecliptic.

43. Apparent Time.--The Westerly hour angle of the true Sun. 44. Equation of Time.-The difference between Mean and Apparent Times; and therefore used to convert one time to the other.

The Equation of Time is least about April 15th, June 15th, August 31st, and December 24th; and greatest about February 10th, May 14th, July 26th, and November 2nd in each year.

45. Sidereal Time.-The Westerly hour angle of the first point of Aries (Fig. 20).

46. Visible Horizon.-The circle which bounds the observer's view at sea.

47. Sensible Horizon.-A plane touching the Earth at the observer's position and extended to the Heavens.

48. Rational Horizon.-A plane passing through the Earth's Centre parallel to the Sensible Horizon and extended to the Heavens.

49. Artificial Horizon.-A horizontal reflecting surface used for observing altitudes in the absence of a good sea-horizon.

50. Dip. The angular depression of the Visible horizon below the Sensible, due to the observer's elevated position.

51. Observed Altitude. The angular height of an object above the Visible horizon as measured by a Sextant.

52. Apparent Altitude. The angular height of an object above the Sensible horizon, found by correcting the observed altitude for Index Error and Dip.

53. True Altitude. The angular height of an object above the Rational Horizon, found by correcting the Apparent Altitude for Refraction and Parallax (Fig. 21).

AB is visible horizon.

MOA = angle OA makes with sensible horizon is Dip.

AOX observed altitude.

MOX = apparent altitude.

XCN= true altitude.

FIG. 21.

M

Sensible Horizon

Rational NHorizon

54. Refraction. The error of altitude caused by the bending of rays of light in passing through the atmosphere (Fig. 22).

55. Parallax is the angle at the centre of the object subtended by the earth's radius at the position of the observer. It is a correction for reducing an observation to the earth's centre (Fig. 23).