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37. The Culmination of a body is the passage of its centre over the meridian of a place. This is also called the Transit of the body over the meridian.

The circumpolar stars pass the meridian twice in every diurnal revolution; once above, and once below the pole. These meridian passages are called respectively, Upper and Lower Culminations.

38. The Hour Angle of a body is the angle contained between the meridian and a declination circle through the centre of the body. Thus MPS is the hour angle of a body at S.



39. The Astronomical Clock is a clock constructed with great care and accuracy, and furnished with a compensating pendulum : that is, a pendulum with a rod so formed by a combination of materials, that its length is not sensibly affected by changes in the temperature of the air.

40. A Chronometer is a balance watch, constructed with various improvements and refinements of modern art, so as to insure great precision in its movement.

41. The rate of a clock or chronometer is its gain or loss in twenty-four hours. If it gains half a second in twenty-four hours, its rate is 0.5 sec.; if it loses 1.4 sec. in that time, its rate is 1.4 sec.

42. The Vernier is a divided arc or line, moveable along another graduated arc or line,* and serving to determine the values of fractional parts of the divisions of the latter. It is an appendage to various astronomical instruments, and to some others.

To explain the principle on which the vernier is constructed, let AB, Fig. 9, be an arc of a circle divided into degrees and subdivided into 20' spaces, and let the vernier arc CD, be taken equal

* Sometimes the vernier has a fixed position and the graduated arc is moveable

19 20


in length to nineteen of these spaces and be divided into twenty equal parts. Each vernier space will then be of a space on the graduated arc. Hence if the line marked 0 on the vernier, called the zero of the vernier, coincide with a division line on the arc, as in the figure, it is evident the first division line of the vernier must fall behind the next division line of the arc, by 20 part of a space on the arc, that is by 1'; the second division line of the vernier must fall behind the following one on the arc by 2'; and thus on. Consequently, if the vernier is moved forward till one of its division. lines coincides with a division line on the arc, the zero must then be as many minutes forward of a division line on the arc, as is expressed by the number of the vernier division line. We may, therefore, for any position of the vernier, determine the place of the zero, which is the object required, by observing which of the vernier division lines coincides, or is the nearest to coincidence, with one on the arc, and adding the corresponding number of minutes. to the degrees and minutes denoted by that division line on the arc, which next precedes the zero of the vernier. Thus in Fig. 10, the zero of the vernier stands forward of 15° 20' on the graduated arc, and the eighth division line of the vernier coincides with a division line of the arc. Hence the arc indicated by the vernier is 15° 28′.

By making the vernier equal in length to fifty-nine divisions on the arc, instead of nineteen, and dividing it into sixty equal parts, it would evidently serve to read off, or indicate the fractional part of a division to the accuracy of of 20', that is to 20′′.


The reading of the vernier, that is, the precision with which it will indicate the arc, is varied according to the size of the instrument. In instruments of large size it is sometimes made to read to single seconds.

43. The Reading Microscope is an appendage frequently attached to instruments, instead of the vernier, and for the same object. It is commonly regarded as determining the arc with greater precision than the vernier.

In the body of the microscope a small frame is placed, across which are two spiders-lines intersecting each other in an acute angle. This frame with its spiders-lines is moveable by means of a screw having a graduated head. It may, therefore, by turning

the screw, be moved till a division line of the graduated arc is seen to bisect the acute angle formed by the spiders-lines. When this is done, the number of whole turns of the screw gives the minutes, and the part of a turn as indicated by the graduated head gives the additional seconds, intercepted between the first position of the zero of the microscope and the division line.

44. A Transit Instrument is an instrument used for observing transits of the heavenly bodies over the meridian. It is made of various sizes, the length of the telescope forming a prominent part of it, varying from about twenty inches to ten feet. Those of the larger sizes are made to rest on stone piers, and are called fixed instruments. The smaller ones are placed on moveable stands, and are called portable instruments.

In Fig. 11, which represents a portable transit instrument, AB is a telescope firmly connected with an axis CD, which is at right angles to the optical axis of the telescope. The horizontal axis CD, terminates in two cylindrical pivots which rest in angular notches in pieces of metal called Y's. The Y's are attached to the upper ends of the upright pieces FF of the stand; one of them admits of a small lateral motion by means of a screw a, and the other, by means of a screw, not seen in the figure, admits of a small vertical motion. A graduated circle H is firmly fixed on the extremity of one of the pivots which extends beyond its Y for this purpose, and must, therefore, revolve as the telescope is turned to different altitudes. The double vernier index e, e, which may be placed in a horizontal position by means of a spirit level f, serves to direct the telescope to a given altitude.

The spirit level E, which rests on the pivots of the axis, is used in conjunction with the foot screw b of the stand, or with the screw that gives a vertical motion to one of the Y's, to place the axis in a horizontal position. When thus placed, the level is removed, and the telescope has then a free motion for all altitudes.

In the tube of the telescope near to the eye end A, a flat ring is placed, across the middle of which a spiders-line is fixed in a horizontal position. This is crossed at right angles by five equidistant parallel lines, as represented in Fig. 12. The ring is moveable by means of screws which connect it with the tube, and may be so

adjusted, that the middle vertical line shall pass exactly through the optical axis of the telescope; the horizontal line at the same time passing through it, or very nearly so. To render the lines visible at night, a lantern I is placed opposite one end of the horizontal axis. The axis is hollow, and the light of a lamp in the lantern falls on a reflector placed in the tube of the telescope, at an angle of 45° with the axis, and is thence reflected so as to illumine the lines. The reflector has an aperture in its middle, sufficiently large to allow a free passage to the light from the body viewed.

When the direction of the meridian at any place is known, if the stand of the instrument be placed on some firm support, and turned till the optical axis of the telescope is nearly in that direction, it may be brought to be exactly so by means of the screw a, which moves one of the Y's, and the pivot of the horizontal axis resting in it. When this is done and the axis made truly horizontal, the middle vertical spiders-line will move in the plane of the meridian as the telescope is turned to different elevations; and consequently when a star or other heavenly body is bisected by that line, it must be on the meridian.

In transit observations it is usual to observe the time of the passage of the body over each of the vertical lines, and to take the mean of these times, as being generally more accurate than the observed time of the passage over the middle line. But if the observations are good, the difference between the mean and the middle time will never amount to a second. When the observed body is the sun, moon, or a planet, the times of passage of both the western and eastern limbs are observed; the mean of which gives the time of passage of the centre. If only one limb is visible, the time of passage of the centre is found by applying the computed interval of time occupied by the semi-diameter in its transit, to the observed time of passage of the visible limbs.

45. A Transit Circle or Meridian Circle is an instrument used for observing the meridian altitude, zenith distance, or polar distance of a heavenly body. It is an important instrument, differing from the simple transit instrument, in having, instead of the circle H, a much larger and very accurately graduated vertical circle

firmly connected with the telescope and axis, and consequently revolving as the telescope revolves. It is nearly represented in its principal parts by the upper part of Fig. 13, to which reference is made in the next article.

A Mural Circle is a meridian circle of large size, having its axis extending through a massive stone pier; the circle and telescope being fixed on one extremity of the axis, and a counterpoise on the other. In this, as in the transit instrument, provision is made for giving slight horizontal and vertical motions to one end of the axis. The angle is read off by stationary microscopes or verniers, usually six in number, attached to the pier.

The Mural Quadrant is a modification of the mural circle; a quadrant being substituted for the complete circle. This instrument is now rarely used, as the circle, though smaller, affords much more accurate results.

The Zenith Sector is an instrument used for measuring the meridian zenith distances of stars, that culminate within a few degrees of the zenith. In this instrument the graduated arc does not exceed 20°. It can, therefore, be made with a much larger radius than either the circle or quadrant, and admits of a more minute subdivision in the graduation of the arc.

The diameter of the mural circle at the National Observatory at Washington is 5 feet. The largest mural circles that have yet been constructed, are 8 feet in diameter. The celebrated zenith sector of Dr. Bradley, formerly at the Greenwich Observatory, and now at the Cape of Good Hope, has an arc of 123 feet radius.

46. An Altitude and Azimuth Instrument is an instrument used for observing, at the same time, both the altitude and azimuth of a body in any part of the heavens.

In Fig. 13, which represents the instrument, the circular plate C has on it a graduated azimuth circle. This plate is attached to a tripod stand supported by three feet screws, two of which are shown at A and B. Firmly connected with the tripod, is a vertical axis, which passes through the centre of the azimuth plate and through two collars in the conical piece E, which projects upwards from the plate D. The whole of the instrument above the azimuth plate C is moveable about this vertical axis, and its position at any

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