determine the relative distances and positions of all other objects, however inaccessible, that fall within the range of vision.

7. Angular magnitude—its importance. — It will be apparent, therefore, that ANGULAR MAGNITUDE plays a most prominent part in astronomical investigations, and it is, before all, necessary that the student should be rendered familiar with it.

8. Division of the circle —its nomenclature. —A circle is divided into four equal arcs, called quadrants, by two diameters AA' and BB' intersecting at right angles at

the centre C, fig. 1.

The circumference being supposed to be divided into 360 equal parts, each of which is called a DEGREE, a quadrant will consist of 90 degrees.

Angles are subdivided in the same manner as the arcs which measure them, and accordingly a right angle, such as AC B, being divided into 90 equal angles, each of these is a DEGREE.

If an angle or arc of one degree be di

Fig. 1.

vided into 60 equal parts, each of these is called a MINUTE.

B

If an angle or arc of one minute be divided into 60 equal parts, each such part is called a second.

Angles less than a second are usually expressed in decimal parts of a second.

Degrees, minutes, and seconds of SPACE are usually expressed by the signs °, ', "; thus 23° 30′ 40′′9 means an angle or arc which measures 23 degrees, 30 minutes, 40 seconds, and 9 tenths of a second.

The letters m and 8 are generally used to express minutes and seconds of TIME. Thus, 23h 30m 409, expresses an interval of time consisting of 23 hours, 30 minutes, 40 seconds, and 9 tenths of a second. This symbolical distinction in representing time and space is found not only a practical convenience in computations where both must necessarily appear, but it is also a means of preventing many errors which may easily occur, when one set of symbols is used in both cases.

9. Methods of ascertaining the direction of a visible and distant object.—It might appear an easy matter to observe the exact direction of any point placed within the range of vision, since that direction must be that of a straight line passing directly from the eye of the observer to the point to be observed. If the eye were supplied with the appendages necessary to record and measure the directions of visible objects, this would be true, and the organ of sight would be in fact a philosophical instrument.

The eye is, however, adapted to other and different uses, and constructed to play a different part in the animal economy; and invention has been stimulated to supply expedients, by means of which the exact directions of visible distant points can be ascertained, observed, and compared one with another, so as to supply the various data necessary in the classes of problems connected with astronomy, some of which we shall have occasion hereafter to advert to.

10. Use of sights. The most simple expedient by which the visual direction of a distant point can be determined is by SIGHTS, which are small holes or narrow slits made in two thin opaque plates placed at right angles, or nearly so, to the line of vision, and so arranged, that when the eye is placed behind the posterior opening the object of observation shall be visible through the anterior opening. Every one is rendered familiar with this expedient by its application to fire-arms as a method of “taking aim."

This contrivance is, however, too rude and susceptible of error within too wide limits, to be available for astronomical purposes, though occasionally it is used in large instruments as an assistance in setting for bright objects.

II. Application of the telescope to indicate the visual direction of micrometric wires.-The telescope (0.501) supplies means of determining the direction of the visual ray with all the necessary precision.

If T T', fig. 2, represent the tube of a telescope, T the extremity in which the abject-glass is fixed, and T' the end where the images

of distant objects to which the tube is directed are formed, the visual direction of any object will be that of the line s'e drawn from the image of such object formed in the field of view of the telescope to the centre c of the object-glass, for if this line be continued it will pass through the object s.

But since the field of view of the telescope is a circular space of definite extent, within which many objects in different directions may at the same time be visible, some expedient is necessary by which one or more fixed points in it may be permanently marked, or by which the entire field may be spaced out as a map, by the lines of latitude and longitude.

This is accomplished by a system of fibres, or wires (M. 38) so thin that even when magnified they will appear like hairs. In

instruments of great precision, the web of a peculiar kind of spider is used for this purpose. These wires are extended in a frame fixed within the eye-piece of the telescope, so that they appear when seen through the eye-glass like fine lines drawn across the field of view. They are differently arranged, according to the sort of observation to which the instrument is to be applied. 12. Line of collimation.-In some cases two wires intersect at right angles at the centre of the field of view, dividing it into quadrants, as represented in fig. 1. The wires are so adjusted that their point of intersection c coincides with the axis of the telescopic tube; and when the instrument is so adjusted that the point of observation, a star for example, is seen precisely upon the intersection c of the wires, the line of direction, or visual ray of that star, will be the line s'c, fig. 2, joining the intersection c, fig. 1, of the wires with the centre c, fig. 2 of the object-glass.

The line sc, fig. 2, is technically called the line of collimation. 13. Application of the telescope to a graduated instrument. The telescope thus prepared is attached to a graduated instrument by which angular magnitudes can be observed and measured. Such instruments vary infinitely in form, magnitude, and mode of mounting and adjustment, according to the purposes to which they are applied, and to the degree of precision necessary in the observations to be made with them. To explain and illustrate the general principles on which they are constructed we shall take the example of one, which consists of a complete circle graduated in the usual manner, being the most common form of instrument used in astronomy for the measurement of angular distances.

Such an apparatus is represented in fig. 3. The circle A B C D, on which the divisions of the graduation are accurately engraved, is

connected with its centre by a series of spokes x y z.

At its centre

is a circular hole, in which an axle is inserted so as to turn smoothly

BCD.

in it, and while it turns to be always concentric with the circle A To this axle the telescope a b is attached in such a manner that the imaginary line s' c, fig. 2, which joins the intersection of the wires, fig. 1, with the centre of the object-glass, shall be parallel to the plane of the circle, and in a plane passing through its centre and at right angles to it.

At right angles to the axis of the telescope are two arms, m n, which form one piece with the tube, so that when the tube is turned with the axis to which it is attached, the arms m n shall turn also, always preserving their direction at right angles to the tube. Marks or indices are engraved upon the extremities m and n of the arms which point to the divisions upon the LIMB (as the divided arc is called).

A clamp is provided on the instrument, by which the telescope, being brought to any desired position, can be fixed immovably in that position, while the observer examines the divisions upon the limb to which the indices m and n are directed.

Now let us suppose that the visual angle under the directions of two distant objects within the range of vision is required to be measured. The circle being brought into the plane of the objects, and fixed in it, the telescope is moved upon its axis until it is directed to one of the objects, so that its image shall coincide exactly with the intersection of the wires. The telescope is then clamped, and the observer examines the divisions of the divided limb, to which one of the indices, m for example, is directed. This process is called "reading off." The clamp being disengaged, the telescope is then in like manner directed to the other object, and being clamped as before, the position of the index is again "read off." The difference between the numbers which indicate the position of the same index in both cases, will evidently be the visual angle under the directions of the two objects.

As a means of further accuracy, both the indices m and n may be "read off," and if the results differ, which they always will slightly, owing to various causes of error, a mean of the two may be taken.

It is evident that the same results would be obtained if, instead of making the telescope move upon the circle, it were immovably attached to it, and that the circle itself turned upon its centre, as a wheel does upon its axle, carrying the telescope with it. In this case the divided limb of the circle is made to move before a fixed index, and the angle under the directions of the objects will be measured by the length of the arc which passes before the index.

Such a combination is represented in section in fig. 4, where T is the telescope, p the pieces by which it is attached to the circle a в seen edgewise, the axis of which D works in a solid block of metal.

The fixed index F is directed to the graduated limb which moves before it.

This is the most frequent method of mounting instruments used in astronomy for angular measurement.

14. Expedients for measuring the fraction of a division.It will happen in general that the index will be directed, not to any exact division, but to some point intermediate between two divisions of the limb. In that case expedients are provided by which the distance between the index and the last division which it has passed, may be ascertained with an extraordinary degree of precision.

15. By a vernier. This may be accomplished by means of a supplemental scale called a VERNIER. (P 229.)

16. By a compound microscope, and micrometric screw.-The same object may, however, be attained with far greater accuracy by means of a compound microscope mounted as represented in fig. 5, so that the observer looks at the index through it. A system of cross wires is placed in the field of view of the microscope, and the whole may be so adjusted by the action of a fine screw, that the index shall coincide precisely with the intersection of the wires. The screw is then turned until the intersection of the cross is brought to coincide with the previous division of the limb; and the number of turns and fraction of a turn of the screw will give the fraction of a degree between the index and the previous division of the limb.

Fig. 5.

It is necessary, however, to ascertain previously the value of a complete revolution of the screw. This is easily done by placing the cross-wires which are carried by the micrometric screw, on consecutive divisions of the limb. Dividing, then, the value in arc be