it is the last point they arrive at. We have therefore preferred that course, which begins by stating and classifying appearances of general interest, and by explaining them in a manner consistent with popular observation; especially as we thus very early arrive at conclusions of high importance, which depend on those appearances, and follow from them as necessary consequences, in whatever manner they are themselves finally explained.

This however is not the only object sought in the adoption of the proposed course. One of the most important and laborious exercises of the mind consists in extracting from complicated results the simple principles on which they depend, in developing truth from the mass of confusion which often conceals it. There is no department of science which furnishes so long and so curiously connected a train of this kind of investigation as Astronomy: none in which the process is more curious, or the results more satisfactory. It has also this additional advantage, that it is capable of being made intelligible in its general outlines, almost without reference to mathematical investigation; and with none which requires more than a very limited portion of mathe matical acquirement. It consequently seems to furnish to those, whose attention has not been directed to the severer studies, some opportunity of applying that peculiar discipline to the mind which those studies best furnish, and which moral and metaphysical inquiries, from the more vague and qualified character of the elements on which they depend, almost entirely fail in affording. In speaking of the truths of Astronomy as admitting of explanation, almost without recourse to mathematical investigation, we only mean that the fundamental observations and principles admit of being stated intelligibly, and that much reasoning may be grounded upon them without introducing it. Of course however a science which is conversant entirely with mathematical relations can only be established on mathematical principles. Those therefore who are unacquainted with the elements of mathematics, cannot follow the whole process of the deduction; but they may trace at least its general course, assuming the correctness of those investigations which they are unable to prosecute, but taking their results as the elements of a new train of reasoning, which will, in many cases,

be perfectly intelligible to every one who is acquainted with the common relations of number and quantity. With a view to facilitate such a course, all the more complicated mathematical investigations (of which, however, none run into difficulty, for the fuller development of the subject is reserved for a treatise of a purely scientific character) have, as far as possible, been removed from the text into notes*, and certain portions of the text itself, of too much importance to the general progress of the deduction to he thus removed, are included between brackets, in cases where they have appeared likely to offer difficulty to any class of readers. In these instances care has been taken, wherever the result deduced is of importance to the future course of the reasoning, to state it, if possible, in terms intelligible to those who are unable to pursue its investigation, and thus to enable them to resume the thread of the general argument. With all these assistances, however, it is impossible to remove some degree of difficulty and abstruseness even from the most popular parts of the treatise: a long process of investigation cannot be followed without thought and diligence, and the results of reasoning from their very nature can only be comprehended by some effort of reason and attention.

It may be necessary to remark, that while we profess to deduce our principles from the first and fundamental observations, we do not pretend to follow the historical course of discovery. For our purpose the class of objects which present the most simple phenomena requires the first attention in the historical course of investigation, the most re markable appearances were probably those which first attracted attention, and thus furnished the groundwork of theory. All that we profess to do, is to point out those observations from which we may most readily and conclusively deduce the principles of which we are in search: and in so doing we shall often call attention at an early period to facts and appearances, easily ascertained when the attention of an observer is directed to them, but which probably excited little attention till the progress of science showed their importance.

There are some notes also, which have been inserted in that shape, not on account of their dif

ficulty, but as bearing only an incidental relation to

the text. That there may be no confusion between the two classes of notes, the notes which present any mathematical difficulty will, as well as the similar passages of the text, be included in brackets.

CHAPTER I.

SECTION 1.-First Observations on the Stars-Division into Constellations Daily rotation of the Heavens.

To an observer situated anywhere upon the earth, the heavens offer the appearance of a vast concave vault, in the centre of which he is himself placed, and which is bounded by a plane extending to the sky; this plane is called the horizon, and itself appears circular. In this vault we perceive several different sorts of bodies: the sun visible by day only (for its sinking below the horizon terminates the day, when that word is used in opposition to night); the moon visible either by day or by night; and the stars (among which, for the present, we include the planets and comets) visible generally by night only. All these bodies appear to the eye to be situated in the vault itself: for we have no means, by mere ocular observation at a single place, of estimating their respective distances, and we consequently refer all alike to one imaginary surface in which they appear to be placed, and which, as we find no apparent difference in their distances, we imagine to be spherical. A slight degree of observation will shew that all these objects partake generally of one common motion. The sun and moon, from their great apparent size, and the remarkable changes of their situation and appear ance, more forcibly attract our attention than any others; but the stars, on account of their number and the opportunities which they in consequence afford for comparative observations, as well as from other circumstances which will hereafter be explained, are the preferable objects for the first and fundamental observations.

A very moderate degree of attention is enough to assure us that the stars, with the exception of a few called planets*, from a Greek word signifying wanderers, always hold very nearly the same positions with respect to each other. If we consider a few stars to form a group, we may observe this group night after night, and its shape and appearance will be always the same. There are not anywhere in the heavens different groups of stars of considerable extent, so resembling each other that an observer can be in any danger of mistaking one group

The comets may be considered as a class of planets.

for the other. And as the groups cannot be mistaken, the individual stars composing them may thus be certainly recognized, however any single stars in each may resemble each other in magnitude, colour, and brightness. Being thus able to recognize a star which we have once observed, we may prosecute our observations upon it night after night, and year after year. For the immediate observations of an individual no more than this is requisite ; but when he wants to register their results, or to inform others of their nature, it is evident that he can no longer be satisfied with this mere power of identifying to his own satisfaction the parti cular star which he observes at different times, but he must have some means of distinguishing between the different stars which he has himself observed, and of announcing to others which it is, among all the heavenly bodies, to which he has especially applied his attention. For this purpose we again have recourse to those groups of stars, by which we originally distinguished each particular star from every other. These groups, when divided for the convenience of reference, are called constellations, (i, e. collections of stars,) a name which is also applied to those portions of the heavens which they respectively occupy; and the whole surface of the heavens has been long divided in this manner. The divisions are arbitrary in themselves, and often, perhaps, ill chosen; but as the only real use of them is for the convenience of reference, the one important object is to have a single received standard; and it would consequently be very undesirable to alter them even for the purpose of making what would originally have been a simpler and more distinct division. The surface of the heavens being thus divided into constellations, consisting each of a moderate number of stars, the stars in each are catalogued, and are arranged nearly in the order of their apparent brightness; the brightest stars being designated by the earlier letters of the Greek alphabet, the less bright by the later letters of the same; and if there be more stars in the constellation than there are letters in that alphabet, other alphabets, generally the small Italic and large Roman alphabets, are used to denote the stars next in importance, and if all the stars in the constellations are not thus distinguished, the least considerable of all are catalogued by num

it is the last point they arrive at. We have therefore preferred that course, which begins by stating and classifying appearances of general interest, and by explaining them in a manner consistent with popular observation; especially as we thus very early arrive at conclusions of high importance, which depend on those appearances, and follow from them as necessary consequences, in whatever manner they are themselves finally explained.

This however is not the only object sought in the adoption of the proposed course. One of the most important and laborious exercises of the mind consists in extracting from complicated results the simple principles on which they depend, in developing truth from the mass of confusion which often conceals it.

There is no department of science which furnishes so long and so curiously connected a train of this kind of investigation as Astronomy: none in which the process is more curious, or the results more satisfactory. It has also this additional advantage, that it is capable of being made intelligible in its general outlines, almost without reference to mathematical investigation; and with none which requires more than a very limited portion of mathe matical acquirement. It consequently seems to furnish to those, whose attention has not been directed to the severer studies, some opportunity of applying that peculiar discipline to the mind which those studies best furnish, and which moral and metaphysical inquiries, from the more vague and qualified character of the elements on which they depend, almost entirely fail in affording. In speaking of the truths of Astronomy as admitting of explanation, almost without recourse to mathematical investigation, we only mean that the fundamental observations and principles admit of being stated intelligibly, and that much reasoning may be grounded upon them without introducing it. Of course however a science which is conversant entirely with mathematical relations ean only be established on mathematical principles. Those therefore who are unacquainted with the elements of mathematics, cannot follow the whole process of the deduction; but they may trace at least its general course, assuming the correctness of those investigations which they are unable to prosecute, but taking their results as the elements of a new train of reasoning, which will, in many cases,

be perfectly intelligible to every one who is acquainted with the common relations of number and quantity. With a view to facilitate such a course, all the more complicated mathematical investigations (of which, however, none run into difficulty, for the fuller development of the subject is reserved for a treatise of a purely scientific character) have, as far as possible, been removed from the text into notes *, and certain portions of the text itself, of too much importance to the general progress of the deduction to be thus removed, are included between brackets, in cases where they have appeared likely to offer difficulty to any class of readers. In these instances care has been taken, wherever the result deduced is of importance to the future course of the reasoning, to state it, if possible, in terms intelligible to those who are unable to pursue its investigation, and thus to enable them to resume the thread of the general argument. With all these assistances, however, it is impossible to remove some degree of difficulty and abstruseness even from the most popular parts of the treatise: a long process of investigation cannot be followed without thought and diligence, and the results of reasoning from their very nature can only be comprehended by some effort of reason and attention.

It may be necessary to remark, that while we profess to deduce our principles from the first and fundamental observations, we do not pretend to follow the historical course of discovery. For our purpose the class of objects which present the most simple phenomena requires the first attention in the historical course of investigation, the most remarkable appearances were probably those which first attracted attention, and thus furnished the groundwork of theory. All that we profess to do, is to point out those observations from which we may most readily and conclusively deduce the principles of which we are in search: and in so doing we shall often call attention at an early period to facts and appearances, easily ascertained when the attention of an observer is directed to them, but which probably excited little attention till the progress of science showed their importance.

There are some notes also, which have been inserted in that shape, not on account of their dif

ficulty, but as bearing only an incidental relation to

the text. That there may be no confusion between the two classes of notes, the notes which present any mathematical difficulty will, as well as the similar passages of the text, be included in brackets.

CHAPTER I.

SECTION 1.-First Observations on the Stars-Division into Constellations Daily rotation of the Heavens.

To an observer situated anywhere upon the earth, the heavens offer the appearance of a vast concave vault, in the centre of which he is himself placed, and which is bounded by a plane extending to the sky; this plane is called the horizon, and itself appears circular. In this vault we perceive several different sorts of bodies: the sun visible by day only (for its sinking below the horizon terminates the day, when that word is used in opposition to night); the moon visible either by day or by night; and the stars (among which, for the present, we include the planets and comets) visible generally by night only. All these bodies appear to the eye to be situated in the vault itself: for we have no means, by mere ocular observation at a single place, of estimating their respective distances, and we consequently refer all alike to one imaginary surface in which they appear to be placed, and which, as we find no apparent difference in their distances, we imagine to be spherical. A slight degree of observation will shew that all these objects partake generally of one common motion. The sun and moon, from their great apparent size, and the remarkable changes of their situation and appear ance, more forcibly attract our attention than any others; but the stars, on account of their number and the opportunities which they in consequence afford for comparative observations, as well as from other circumstances which will hereafter be explained, are the preferable objects for the first and funda

mental observations.

A very moderate degree of attention is enough to assure us that the stars, with the exception of a few called planets*, from a Greek word signifying wanderers, always hold very nearly the same positions with respect to each other. If we consider a few stars to form a group, we may observe this group night after night, and its shape and appearance will be always the same. There are not anywhere in the heavens different groups of stars of considerable extent, so resembling each other that an observer can be in any danger of mistaking one group

The comets may be considered as a class of planets.

for the other. And as the groups cannot be mistaken, the individual stars composing them may thus be certainly recognized, however any single stars in each may resemble each other in magnitude, colour, and brightness. Being thus able to recognize a star which we have once observed, we may prosecute our observations upon it night after night, and year after year. For the immediate observations of an individual no more than this is requisite ; but when he wants to register their results, or to inform others of their nature, it is evident that he can no longer be satisfied with this mere power of identifying to his own satisfaction the particular star which he observes at different times, but he must have some means of distinguishing between the different stars which he has himself observed, and of announcing to others which it is, among all the heavenly bodies, to which he has especially applied his attention. For this purpose we again have recourse to those groups of stars, by which we originally distinguished each particular star from every other. These groups, when divided for the convenience of reference, are called constellations, (i, e. collections of stars,) a name which is also applied to those portions of the heavens which they respectively occupy; and the whole surface of the heavens has been long divided in this manner. The divisions are arbitrary in themselves, and often, perhaps, ill chosen; but as the only real use of them is for the convenience of reference, the one important object is to have a single re ceived standard; and it would consequently be very undesirable to alter them even for the purpose of making what would originally have been a simpler and more distinct division. The surface of the heavens being thus divided into constellations, consisting each of a moderate number of stars, the stars in each are catalogued, and are arranged nearly in the order of their apparent brightness; the brightest stars being designated by the earlier letters of the Greek alphabet, the less bright by the later letters of the same; and if there be more stars in the constellation than there are letters in that alphabet, other alphabets, generally the small Italic and large Roman alphabets, are used to denote the stars next in importance, and if all the stars in the constellations are not thus distinguished, the least considerable of all are catalogued by num

bers. These stars being registered on maps of stars, or on celestial globes, or their places being defined in the manner we shall hereafter explain, become known bodies; and any astronomer making observations, on any particular star, may communicate them to any other, who will at once know the star in question, and be able to compare those results with his own observations and conclusions. Besides this mode of distinction, some of the brighter and more remarkable stars have been distinguished by particular names: and a vague classification has been made of stars, according to their lustre, into what are called different magnitudes; the brightest which appear the largest to the naked eye, although none have any ascertainable diameter when viewed through a telescope, being called of the first magnitude, the next class of the second, and so on. The stars of the fifth magnitude are barely discernible by the unassisted eye; and beyond these there are stars of the sixth, seventh, eighth, and even lower magnitudes, which we discover by means of telescopes. The number of stars of each magnitude increases as their brilliancy diminishes: thus in the Astronomical Society's catalogue of 2881 stars, there are only 21 stars above the second magnitude, (18 of which are called of the first magnitude, and 3 between the first and second magnitude), about 50 of the second magnitude and between the second and third, about 180 of the third magnitude, and between the third and fourth; and so on. As an instance of these different modes of characterizing stars, we may take the principal stars of the constellation Orion. The brightest star, a of Orion, is also of the first magnitude, and is sometimes called Betelgeuse, though this name is nearly obsolete; the next, of Orion, is also of the first magnitude, and is called Rigel; then there are four of nearly equal brilliancy, y, d, s, , of Orion, all of the second magnitude, and none having any received name; then follow stars of the third magnitude, then of the fourth, and so in succession.

A map of the stars (comprised in six sheets)

is published under the Superintendence of the Society for the Diffusion of Useful Knowledge, in which these constellations are represented.

These, and many of the names of the stars, were given by the Arabians, who, during the eighth century, and for a long period after, cultivated astronomy more diligently than any other people.

In the map referred to, Orion will be found nearly in the centre of Plate 2. This constellation

Let us now examine what are the appearances presented to an observer in the course of a single bright night. He sees a vast variety of stars distributed about the heavens, and all, at first sight, seeming to be at rest. A very short course of observation, however, proves that this appearance of rest is fallacious. The stars all continue at the same apparent distances from each other, but their positions vary with respect to the horizon and the observer. On one side of the heavens they are seen gradually to rise higher above the horizon, and some stars appear above it, which at first were not seen at all; on the other, they sink towards the liorizon, and some which were originally visible, sink below it and disappear. Confining our observations to a particular star, we shall see it rise above the horizon at a particular spot, gradually increase in elevation till it reaches its highest point, when it is said to culminate, and then sink by like degrees, and finally fall below the horizon at another spot which may also be ascertained. The same observation may be made with other stars, and extended to any number. It is not even necessary that the observations of different stars should be made at the same time, or that the observations of the rising and setting of any star be made on the same night; for the same star is invariably found to rise and set in the same spots, although at different periods of the night. Now each arch of the horizon intercepted between the points of rising and setting of any star may be bisected, or divided into two equal parts; and the points of bisection will themselves be at the extremities of a diameter of the circle. It is found from observation, that this diameter is the same for every star; and the points of the horizon through which it passes are called the North and South points. The side of the heavens where the stars rise is the East side, that where they set, the West; the East and West points being those equi-distant on each side from the North and South points. If through the North and South points a plane pass perpendicular to the horizon, the intersection of this plane with the celestial hemisphere will be a semi-circle; and this semi-circle is called the meridian of the observer, or

may be best seen in the heavens for the purpose of comparing the original with the representation, about twelve o'clock at night in the middle of December, ten in the middle of January, and eight in the middle of February.