The

pillar FG, which carries the telescope HK, and a graduated semicircle PQ; and these turn together on an axis at F. upper portion of the block being disposed as in the figure, when the pivot on which it turns is in the plane of the meridian, its superior surface will be parallel to the equator, and the axis FG will be parallel to that of the earth's rotation. The rim AE is graduated in hours, &c. like the dial of a clock, and the telescope, while it has a movement on the axis of its pillar FG, is capable, according as the upper surface of the block is parallel to the horizon or equator, of being turned in altitude or declination about the axis passing through F perpendicularly to that pillar. An index attached to FG, and turning with it on the circle A E, serves to show the movement of the telescope in azimuth or in right ascension, while another index, also attached to FG, shows on the circle PQ its movement in altitude or in declination. The handles M and N enable the observer to give slow motions to the telescope by means of endless screws which turn in notches cut in the circumferences of the circles AE and PQ.

This cylinder, which is called Smeaton's Block, from the name of that engineer, enables the telescope to have the movements of an altitude and azimuth, or of an equatorial instrument; and a micrometer at the eye-piece of the telescope serves for obtaining, by observation, differences in azimuth and altitude, or in right ascension and declination, when two celestial bodies can be seen in the field at the same time.

119. When a micrometer is to be employed for the purpose of measuring arcs of small extent, and angles of position, in the heavens, the whole instrument should be turned on the optical axis of the telescope to which it is attached, till the wire mn (fig. to art. 74.) is parallel to the equator; and then the wires pq and st will be in the planes of two horary circles. The verification of the position of mn is made in the same manner as that of the horizontal wire in the transit telescope (art. 89.), and in this state the index of the micrometer circle EF should be at the zero of the graduations: if not, the error must be ascertained in order that it may be applied as a correction. Then, if (for example) it were required to obtain the angle which a line joining two stars a and b would make with the plane of a horary circle PS passing through one of them; having turned the part carrying the system of wires upon the optical axis of the telescope, till the wire mn

m

b.

-b'.

n

passes through both the stars, or is estimated to be parallel to such line (as in the figure), the index of the micrometer circle will show the value of the angle Pap, which, being corrected if necessary on account of the index error before mentioned, is the complement of the required angle bas.

The wire mn is not in strictness necessary, for the micrometer may be turned so that one of the wires pq shall coincide with the line ab of the stars; then the number of the graduation at the index of the micrometer circle being read, that circle, and with it the whole micrometer, may be turned one quarter round upon the optical axis of the telescope, when the wires pq will be perpendicular to the line ab joining the

stars.

In order to measure the angular distance ab, the whole equatorial instrument must be turned on the polar axis till one of the wires, as pq, passes through the star a (for example); then, turning the micrometer screw which moves the other wire, bring the latter wire to bisect the star b (the first wire continuing to pass through the star a), and read on the screw head belonging to the second wire the graduation which is in coincidence with the index. Again, move the whole equatorial till the first wire bisects the star b, when the second wire will be moved to b' so that ab' will be equal to twice the distance between the stars; and then, by turning the micrometer screw belonging to the second wire, bring the latter wire back to the star a: read the number of revolutions made by this wire, and the parts of a revolution on its screw head; then half the difference between this and the former reading will be the required distance, in terms of the screw's revolutions.

120. The knowledge of the distance ab in seconds of a degree, and of the angle Pab, or its supplement, will enable the observer, by letting fall be perpendicularly on Pa, produced if necessary, to compute ac and be: the former is the difference between the declinations of the stars a and b, and the latter, when reduced to the corresponding arc of the equator, that is, when divided by the cosine of the star's declination (art. 70.), is the difference (in arc) between their right ascensions.

If one of the celestial bodies were the moon, whose declination at times changes rapidly; on making the wire mn of the position micrometer a tangent to the path of the moon's upper or lower edge as she appears to move across the field of view, that wire, instead of being parallel to the equator, would, as in the last example, be in some other position, as mn, and

S

D

m

one of the perpendicular wires, instead of being in the plane of a horary circle PS, would be in the position pq; so that the observed transit of a star moving in the parallel ef of declination would take place at c: then sc will be the apparent difference of declination, measured by the micrometer, between the star and the moon's upper limb; and the angle PSP being given by the micrometer circle, sc the true difference of declination may be found by the formula sc cos. Psp sc. (Pl. Trigon., art. 56.) Again, let the contact of the enlightened edge of the moon at the time of her apparent transit be at d when the upper edge (for example) moves along mn, and let fall dD perpendicularly on PS; then sd being considered as equal to the moon's semidiameter, and the angle Psp or DSd being known, we have (art. 61.), PD and PC being the polar distances of the moon and star, and putting small arcs or angles for their sines, sc sin. Psp

SPd=

sd sin. PSP; also, 8Pc=

sin. PD

sin. PC

the sum of these two angles, or the angle cPd is (in seconds of a degree) the whole error in the observed difference between the right ascensions of the moon and star in consequence of the moon's movement in declination.

121. The Heliometer employed by M. Bessel for the purpose of ascertaining the parallax of the fixed stars is a telescope about 9 feet long and 6 inches diameter, which is equatorially mounted, and the whole instrument is turned by clock-work with a movement equal to the diurnal rotation. The object glass is divided into two parts in the direction of a diameter, and the two halves have a parallel movement along the line of separation by means of screws at the eye end of the telescope. The circular head of each of these screws is divided into one hundred parts, and the divisions are great enough to allow a tenth part of each to be estimated. The circle by which the angles of position are obtained is placed at the object end of the telescope, and it has four verniers by which the angles are read to minutes.

In observing double stars, one of the halves of the object glass is moved till the four images are brought into one straight line, and all appear at equal distances from one another; then each star will have moved, apparently, over twice the interval between the two, and the measure of this interval is ex

pressed by the divisions of the micrometer. The half-object glass is then moved in like manner in the opposite direction; and now the divisions of the micrometer express four times the distance of one star from the other in terms depending upon the unit of the scale. A mean of the readings at the verniers of the position circle expresses the angle of position between a line joining the stars and the hour circle passing through one of them.

122. When a micrometer is used to find the angular position of a star with respect to one which is with it in the field of view, particularly in observations on double and revolving stars, it is customary to distinguish the place of the star whose position is to be determined by the latter being in one of the quadrants of a circle imagined to be described in the heavens about the other star, considered as situated in the centre. The meridian of the station, if the star is on the meridian, otherwise the hour circle passing through the star, is supposed to cut the said circle in two points n and s, which are the northern and southern extremities of a diameter; and another diameter pf is supposed to be at right angles to this: the four quadrants are distinguished by the letters nf (north following), sf (south following), sp (south preceding), and np (north preceding); and they are situated in the manner represented in the figure, which is such a circle described about a star A, and is supposed to be viewed by the naked eye, or in a telescope which does not invert objects. The position of the line joining the stars A and B would be indicated by the angle fAB in the quadrant nf, and the position of the line A B' by the angle fA B' in the quadrant sf: in like manner the position of a line from A in the other semicircle would be expressed by an angle reckoned from p in the quadrant sp or np. The words following and preceding relate to the position of the star B, in right-ascension, with respect to A. This mode of designating a position has, however, been objected to on account of the mistakes to which it is liable; and it has been preferred to express the position by an angle as n AB, reckoned from n quite round the circumference, in the order of the letters nfsp, or from the north, by the west, the observer being supposed to look southwards.

p

A

B

B

123. The late Captain Kater invented two kinds of instruments which he called Collimators, for the purpose of determining the horizontal and zenith points on astronomical circles. Each kind consisted of a telescope which was either made to rest in a horizontal position on a plate of iron floating on the surface of mercury; or it was fixed in a frame,

the lower part of which was an iron ring whose plane was perpendicular to the axis of the telescope, and this ring floated on mercury in an annular vessel, so that the telescope being in a vertical position, the observer looked towards the floor, or towards the cieling of the apartment, through the open space in the centre of the vessel. The former was called a horizontal, and the latter a vertical collimator.

124. In using the horizontal collimator, the vessel, with the telescope floating on the mercury, is placed either on the north or south side of the astronomical circle; and the telescope of this circle being brought by hand nearly in a horizontal position, the axes of the two telescopes are made nearly to coincide in direction, with the object-glass of one turned towards that of the other. The collimating telescope, which is about twelve inches long, is provided with two wires crossing each other at the focus of the object glass, and care is taken moreover that it shall be in the optical axis: now the rays of light in the pencils which diverge from those wires are, after refraction in passing through the object glass, made to proceed from thence parallel to one another; and consequently, falling in this state upon the object glass of the circle, they form in its focus a distinct image of the wires from whence they diverged. Thus the observer, on looking into the telescope of the circle, sees the wires of both telescopes distinctly; and, upon making the points of their intersections coincident, it will follow that a line joining those intersections is parallel to the horizon: consequently the graduation at which the index stands on the circle may be considered as the zero of the instrument when altitudes are to be observed.

The vertical collimator is used in a similar manner, and the wires of both telescopes being made coincident, a line joining them is in a vertical position: the index, therefore, stands then at the graduation which must be considered as zero when zenith distances are to be observed.

125. These floating collimators being unsteady, and the optical axes of their telescopes being seldom exactly horizontal or vertical, a telescope mounted on a stand, with its optical axis carefully adjusted, and furnished with a spirit-level which is capable of being reversed on its points of support, has been used for the like purpose. The disposition of the instrument is similar to that which has been described, and the axis of the telescope is made level by means of foot

screws.

In order to use a collimating telescope for the purpose of finding the error of collimation in a transit telescope the latter must be furnished with a micrometer: the moveable wire in the micrometer must be brought to coincide with the