Fig. V.
An Angle is the inclination of two right lines, as IH and KH, meeting in a point at H; and in describing an Angle by three letters, the middle letter always denotes the angular point: thus, the above lines IH and KH meeting each other at H, make the Angle IHK. And the point H is supposed to be the center of a Circle, the circumference of which contains 360 equal parts called degrees. A fourth part of a Circle, called a Quadrant, as GE, contains 90 degrees; and every Angle is measured by the number of degrees in the arc it cuts off; as the angle EHP is 45 degrees, the Angle EHF 33, &c: and so the Angle EHF is the same with the angle CHN, and also with the Angle AHM, because they all cut off the same arc or portion of the Quadrant EG; and so likewise the Angle EHF is greater than the Angle CHD or AHL, because it cuts off a greater arc.
The nearer an object is to the eye the bigger it appears, and under the greater Angle is it seen. To illustrate this a little, suppose an Arrow in the position IK, perpendicular to the right line HA drawn from the eye at H through the middle of the Arrow at O. It is plain that the Arrow is seen under the Angle IHK, and that HO, which is it’s distance from the eye, divides into halves both the Arrow and the Angle under which it is seen: viz. the Arrow into IO, OK, and the Angle into IHO and KHO: and this will be the case whatever distance the Arrow is placed at. Let now three Arrows, all of the same length with IK, be placed at the distances HA, HC, HE, still perpendicular to, and bisected by the right line HA; then will AB, CD, EF, be each equal to, and represent IO; and AB (the same as IO) will be seen from H under the Angle AHB; but CD (the same as IO) will be seen under the Angle CHD or AHL; and EF (the same as IO) will be seen under the Angle EHF, or CHN, or AHM. Also, EF or IO at the distance HE will appear as long as CN would at the distance HC, or as AM would at the distance HA: and CD or IO at the distance HC will appear as long as AL would at the distance HA. So that as an object approaches the eye, both it’s magnitude and the Angle under which it is seen increase; and as the object recedes, the contrary.
[45]. The fields which are beyond the gate rise gradually till they are just seen over it; and the arms, being red, are often mistaken for a house at a considerable distance in those fields.
I once met with a curious deception in a gentleman’s garden at Hackney, occasioned by a large pane of glass in the garden-wall at some distance from his house. The glass (through which the fields and sky were distinctly seen) reflected a very faint image of the house; but the image seemed to be in the Clouds near the Horizon, and at that distance looked as if it were a huge castle in the Air. Yet, the Angle under which the image appeared, was equal to that under which the house was seen: but the image being mentally referred a much greater distance than the house, appeared much bigger to the imagination.
[46]. The Sun and Moon subtend a greater Angle on the Meridian than in the Horizon, being nearer the Earth in the former case than the latter.
[47]. The Altitude of any celestial Phenomenon is an arc of the Sky intercepted between the Horizon and the Phenomenon. In Fig. VI. of Plate II. let HOX be a horizontal line, supposed to be extended from the eye at A to X, where the Sky and Earth seem to meet at the end of a long and level plain; and let S be the Sun. The arc XY will be the Sun’s height above the Horizon at X, and is found by the instrument EDC, which is a quadrantal board, or plate of metal, divided into 90 equal parts or degrees on its limb DPC; and has a couple of little brass plates, as a and b, with a small hole in each of them, called Sight-Holes, for looking through, parallel to the edge of the Quadrant whereon they stand. To the center E is fixed one end of a thread F, called the Plumb-Line, which has a small weight or plummet P fixed to it’s other end. Now, if an observer holds the Quadrant upright, without inclining it to either side, and so that the Horizon at X is seen through the sight-holes a and b, the plumb-line will cut or hang over the beginning of the degrees at o, in the edge EC; but if he elevates the Quadrant so as to look through the sight-holes at any part of the Heavens, suppose to the Sun at S; just so many degrees as he elevates the sight-hole b above the horizontal line HOX, so many degrees will the plumb-line cut in the limb CP of the Quadrant. For, let the observer’s eye at A be in the center of the celestial arc XYV (and he may be said to be in the center of the Sun’s apparent diurnal Orbit, let him be on what part of the Earth he will) in which arc the Sun is at that time, suppose 25 degrees high, and let the observer hold the Quadrant so that he may see the Sun through the sight-holes; the plumb-line freely playing on the quadrant will cut the 25th degree in the limb CP equal to the number of degrees of the Sun’s Altitude at the time of observation. N. B. Whoever looks at the Sun, must have a smoaked glass before his eyes to save them from hurt. The better way is not to look at the Sun through the sight-holes, but to hold the Quadrant facing the eye, at a little distance, and so that the Sun shining through one hole, the ray may be seen to fall on the other.
[48]. See the Note on § [185].
[49]. Here proper allowance must be made for the Refraction, which being about 34 minutes of a degree in the Horizon, will cause the Moon’s center to appear 34 minutes above the Horizon when her center is really in it.
[50]. By this is meant, that if a line be supposed to be drawn parallel to the Earth’s Axis in any part of it’s Orbit, the Axis keeps parallel to that line in every other part of it’s Orbit: as in Fig. I. of Plate V; where abcdefgh represents the Earth’s Orbit in an oblique view, and Ns the Earth’s Axis keeping always parallel to the line MN.