circle at equal diftances from the two poles, and whofe plane is perpendicular to the axis, as a wheel is perpendicular to it's axle-tree. You are therefore to conceive in the heavens a circle exactly between the two poles, and at right angles to the axis of the world. This was indeed the first circle that the ancient aftronomers imagined, and to which the Egyptians and Chaldeans referred all the stars, even as far back as the time of Herodotus, 450 years before Chrift. The equator being at equal distances from the two poles, you may either fay that the fphere, with it's equator, turns about the axis PR, or about the polcs P and R of the equator. As we call the points P and R poles of the equator, because they are every where equally diftant from the equator; fo we also call, in general, POLES of any circle thofe two points of the fphere which are at the greateft diftance from this circle, and which are fituated in a line perpendicular to the plane of the circle, and paffing through it's center. Thus the zenith is the pole of the horizon: it is the fame with every other circle; the pole thereof is always ninety degrees therefrom in every direction. The line which paffes through the two poles of a circle, is called in general the axis of this circle; for inftance, the vertical line is the axis of the horizon. You are not to confound the axis with the diameter of a circle, they are two things altogether different; the diameter is drawn in the plane of the circle, but the axis is elevated on both fides the circle, and at right angles thereto, out of the plane of the circle, and having but one point. common with the axis, that is, the center through which the axis paffes. Let us for a moment now return to the fun, whofe influence extends over every thing round about about us. The rifing and fetting of the fun are two events which form, as it were, every day two remarkable and interefting epochas; they are the first and most obvious phenomena that we notice. He every day feems to defcribe a circle in the heavens, moving from eaft to weft. He rises in the eaft, and all the attendants of night gradually difappear, or fink from his prefence. Nature wakes at his call, and his far-extended beams difcover to our eyes all her variegated beauties. He mounts to the highest point of the circle, in which he moves, and then defcends to the weft, when the lamps of heaven again illumine the divine fcene of night. After having examined each day the points where the fun rifes and fets, you would naturally call the highest point in the fky to which the fun rofe, and from whence he began to defcend again, the mid-day point. By extending this point over your head, you would trace in imagination another circle round the globe, and call it the meridian. If you notice in the fame manner the ftars which rife and fet, you will find that they are at their greatest height in the middle of the interval between their rifing and fetting (though their altitudes may be different); they are then alfo faid to be on the meridian. A circle, as PZRH, fig. 5, pl. 3, paffing through the zenith, the nadir, and the poles, is the meridian. It is thus named, as I have obferved, because when the fun is upon this circle, it is mid-day. Every point of this circle is equally diftant from the horizon; that is, as far from the east fide as from the weft fide. The ftars are in the meridian twice in the course of their diurnal motion; once above the horizon, and once when they arrive at the lower half thereof, under the horizon. Their diurnal motion may therefore be divided into into four parts; one from the time of their rifing to their arrival on the meridian; from this to their fetting; thence to their reaching the lower meridian; and, laftly, from thence to their rifing again the next day. The meridian of a country fituated eaft or weft of London, is a different one from that of London. If you travel caft or weft, you change your meridian by a quantity equal to that which you have advanced towards the eaft or the weft; for your meridian, at every change of fituation, paffes through a new zenith, and the poles of the world. Thus Rome is about 12° 34' eaft of London, and confequently the meridian of Rome differs 12° 34' from that of London. There is but one method of changing your fituation without changing your meridian; which is, to go directly north or fouth, that is, towards either of the poles. Every place is fuppofed to have a meridian. paffing over it's zenith, and going through the poles of the world. All the meridians therefore meet, and interfect each other, at the poles. They are all at right angles to the equator; and the equator, because it is every where at an equal dif tance from the poles, divides every meridian into two equal parts. You have now established three circles in the celeftial fphere, to which you may refer all the ftars you obferve. Thefe circles, though in themfelves imaginary, will become, as it were, fixed points for your obfervations. The horizon is the firft circle which you muft ufe; not only as it diftinguithes night from day, and the rifing and fetting of all the heavenly bodies, but as the higher and farther they are clevated above the horizon, the longer they stay with us; their elevation above it became one of the first objects of an aftronomer's aftronomer's attention: this was one of the means by which he could refer them to the horizon. To this end, fuppofe a circle rifing perpendicularly out of the horizon, paffing through the ftar, and going up to a point directly over your head, or to your zenith. Upon this circle you may, by the help of your quadrant, reckon how many degrees it is from the horizon; and this is called it's altitude, or height. The circle upon which I count the degrees of altitude is called a vertical circle, because it ftands perpendicular to the horizon, and paffes through the zenith. Thus B D, fig, 3. pl. 14, is a quadrant whofe circumference is divided into ninety degrees. Place one of the fides vertically by the means of the plumb-line; put the eye at the center o; observe what point, c, on the circumference of the quadrant, correfponds with the ftar, and the number of degrees between D and C will be the altitude of the ftar above the horizon. For instance, if the arc DC is the half of B D on the fmall inftrument, the celeftial arc AR will be alfo the half of Z R, both one and the other will be forty-five degrees; but as the MEASURE OF ANGLES, by a quadrant, or fome other inftrument, is the basis of aftronomy, it will be neceffary to enter here fomewhat fully into the nature thereof, before we proceed further in our investigation of the heavens. OF THE ASTRONOMICAL QUADRANT. The fmall quadrant before you, fig. 1, pl. 14, is a very fimple and ufeful inftrument. With it you may not only perform a great number of interefting and entertaining problems, but may alfa attain a good idea of practical aftronomy. * * See my Essays on Aftronomy, &c. Every Every circle is fuppofed, by geometricians and aftronomers, to be divided into 360 parts or degrees; ninety degrees, therefore, or one-fourth part of a circle, will be fufficient to meafure all angles formed between a line perpendicular to the horizon, and other lines which are not directed to points below the horizon. An angle is the opening between two lines, which touch one another in a point. In defcribing the extent of an angle, regard is not to be had to the length of the lines, but to the width of their opening. This is eafily illuftrated by a pair of compaffes; the legs of this inftrument will reprefent the fides of the angle, and the joint the vertex of the angle. With the fame pair of compaffes it is poffible to form a great variety of angles, by opening them to different widths; for the angle that is formed by the legs differs in proportion to that opening, and it's quantity is greater in proportion as they are placed farther afunder, and fmaller as they are brought nearer together. Suppose an are of a circle to be placed in fuch a manner as to be paffed over by these points, then the opening or angle will be in proportion to the part of the arc that is paffed over; and if the whole circle be divided into any number of equal parts, as, for example, 360, the number of thefe will denote the magnitude of the angle. But here you are carefully to obferve, that the angle is neither enlarged nor diminished by any change in the length of the legs, provided their pofition remains unaltered; because it is the inclination of their legs, or the space between them, not their length, which conftitutes the angle; for with the fame opening, the imagination may extend the length into indefinite space. So that if a pair of compaffes, with very long legs, were opened to the fame angle as another fmaller |