time measured by the motion of this imaginary sun is called MEAN SOLAR TIME, and the time measured by the motion of the true sun is called APPARENT SOLAR TIME.

The difference between the apparent and mean solar time is called the "EQUATION OF TIME."

The variation of the increase of the sun's right ascension being confined within narrow limits, the true and imaginary suns can never be far asunder, and consequently the difference between mean and apparent time is never considerable.

The time indicated by a sun-dial is apparent time, that indicated by an exactly regulated clock or watch is mean time.

The correction to be applied to apparent time, to reduce it to mean time is often engraved on sun-dials, where it is stated how much"the sun is too fast or too slow."

145. Distance of the sun. —Although the problem to determine with the greatest practicable precision the distance of the sun from the earth is attended with great difficulties, many phenomena of easy observation supply the means of ascertaining that this distance must bear a very great proportion to the earth's diameter, or must be such that, by comparison with it, a line 8000 miles in length is almost a point. If, for example, the apparent distance of the centre of the sun from any fixed star be observed simultaneously from two places upon the earth, no matter how far they are apart, no difference will be discovered between them, unless means of observation susceptible of extraordinary precision be resorted to. However, it may be stated here that the apparent diameter of the earth as viewed from the sun amounts to no more than 17"9, or about the 108th part of the apparent diameter of the sun as seen from the earth. The distance of the sun is equal to about 11,535 diameters of the earth, and amounts therefore to nearly NINETY

ONE AND A HALF MILLIONS OF MILES.

146. Orbit of the earth elliptical.-In what precedes, we have considered the path of the earth around the sun, called by astronomers its ORBIT, to be a circle, in the centre of which the centre of the sun is placed. This is nearly true, but not exactly so, as will appear from the following observed phenomena. Let a telescope supplied with micrometric wires be directed to

the sun, and the wires so adjusted that they shall exactly touch the upper and lower limbs, as in fig. 40. Let the observer then

watch from day to day the appearance of the sun and the position of the wires; he will find that, after a certain time, the wires will no longer touch the sun, but will perhaps fall a little within it, as represented in fig. 41. And after a further lapse of time he will find, on the other hand, that they fall a little without it, as in fig. 42.

Now, as the wires throughout such a series of observations are maintained always in the same position, it follows that the disk of the sun must appear smaller at one time, and larger at anotherthat, in fact, the apparent magnitude of the sun must be variable. It is true that this variation is confined within very small limits, but still it is distinctly perceptible. What, then, it may be asked, must be its cause? Is it possible to imagine that the sun really undergoes a change in its size? This idea would, under any circumstances, be absurd; but when we have ascertained, as we may do, that the change of apparent magnitude of the sun is regular and periodical—that for one half of the year it continually diminishes until it attains a minimum, and then for the next half year it increases until it attains a maximum-such a supposition as that of a real periodical change in the globe of the sun becomes altogether incredible.

If, then, an actual change in the magnitude of the sun be impossible, there is but one other conceivable cause for the change in its apparent magnitude—which is, a corresponding change in the earth's distance from it. If the earth at one time be more remote than at another, the sun will appear proportionally smaller. This is an easy and obvious explanation of the changes of appearance that are observed, and it has been demonstrated accordingly to be the true one.

On examining the change of the apparent diameter of the sun, it is found that it is least on the 1st of July, and greatest on the 31st of December; that from December to July, it regularly decreases; and from July to December, it regularly increases.

Since the distance of the earth from the sun must increase in the same ratio as the apparent diameter of the sun decreases, and vice versá (0.351), the variation of the distance of the earth from the sun in every position which it assumes in its orbit can be exactly ascertained. A plan of the form of the orbit may therefore be laid down, having the point occupied by the centre of the sun marked in it. Such a plan proves on geometric examination to be an ellipse, the place of the sun being one of the foci.

147. Method of describing an ellipse-its foci, axis, and excentricity.—If the ends of a thread be attached to two points less distant from each other than its entire length, and a pencil be looped in the thread, and moved round the points, so as to keep the thread tight, it will trace an ellipse, of which the two points are the

FOCI.

The line drawn joining the foci, continued in both directions to the ellipse, is called its TRANSVERSE, OF MAJOR AXIS.

Another line, passing through the middle point of this at right angles to it is called its MINOR AXIS.

Fig. 43.

The middle point of the major axis is called the CENTRE of the ellipse.

The fractional or decimal number which expresses the distance B of the focus from the centre, the semiaxis major being taken as the unit, is called the excentricity of the ellipse.

In fig. 43, c is the centre, s and s' the foci, A B the transverse axis.

The less the ratio of s s' to A B, or what is the same, the less the excentricity is, the more nearly the form of the ellipse approaches to that of a circle, and when the foci actually coalesce, the ellipse becomes an exact circle.

The

148. Excentricity of the earth's orbit. The excentricity of the elliptic orbit of the earth is so small, that if an ellipse, representing truly that orbit, were drawn upon paper, it would be distinguishable from a circle only by submitting it to exact measurement. excentricity of the orbit has been ascertained to be only 001677. The semi axis major, or mean distance, being 10000, the greatest and least distances of the earth from the sun will be

The difference between these extreme distances is, therefore, only 003354. So that the difference between the greatest and least distances does not amount to so much as four hundredths of the mean distance.

149. Perihelion and aphelion of the earth.-The positions A and B, where the earth is nearest to, and most distant from, the sun are called PERIHELION and APHELION.

The positions of these points are ascertained by observing the places of the sun when its apparent diameter is greatest and least.

It is evident from what has been stated that the earth is in aphelion on the 1st of July, and in perihelion on the 1st of January. Contrary to what might be expected, therefore, the earth is more distant from the sun in summer than in winter.

150. Variations of temperature through the year. — The succession of spring, summer, autumn, and winter, and the variations of temperature of the seasons—so far as these variations depend on the position of the sun-will now require to be explained.

The influence of the sun in heating a portion of the earth's surface, will depend partly on its altitude above the horizon. The greater that altitude is, the more perpendicularly the rays will fall, and the greater will be their calorific effect.

The calorific effect of the sun's rays on a surface more oblique to their direction than another will then be proportionably less.

If the sun be in the zenith, its rays will strike the surface perpendicularly, and the heating effect will therefore be greater than when the sun is in any other position.

The greater the altitude to which the sun rises, the less obliquely will be the direction in which its rays will strike the surface at noon, and the more effective will be their heating power. So far, then, as the heating power depends on the altitude of the sun, it will be increased with every increase of its meridian altitude.

Hence it is that the heat of summer increases as we approach the equator. The lower the latitude is, the greater will be the height to which the sun will rise. The meridian altitude of the sun at the summer solstice being everywhere outside the tropics forty-six degrees and fifty-six minutes more than at the winter solstice, the heating effect will be proportionately greater.

But this is not the only cause which produces the greatly superior heat of summer as compared with winter, especially in the higher latitudes. The heating effect of the sun depends not alone on its altitude at midday; it also depends on the length of time which it is above the horizon and below it. While the sun is above the horizon, it is continually imparting heat to the air and to the surface of the earth; and while it is below the horizon, the heat is continually being dissipated. The longer, therefore, other things being the same, -the sun is above the horizon, and the shorter time it is below it, the greater will be the amount of heat imparted to the earth every twenty-four hours. Let us suppose that between sunrise and sunset, the sun, by its calorific effect, imparts a certain amount of heat to the atmosphere and the surface of the earth, and that from sunset to sunrise a certain amount of this heat is lost : the result of the action of the sun will be found by deducting the latter from the former.

Thus, then, it appears that the influence of the sun upon the seasons depends as much upon the length of the days and nights as upon its altitude; but it so happens that one of these circumstances depends upon the other. The greater the sun's meridional altitude is, the longer will be the days, and the shorter the nights; and the

less it is, the longer will be the nights, and the shorter the days. Thus both circumstances always conspire in producing the increased temperature of summer, and the diminished temperature of winter.

151. Why the longest day is not also the hottest.— The dog-days.—A difficulty is sometimes felt when the operation of these causes is considered, in understanding how it happens that, notwithstanding what has been stated, the 21st of June-when the sun rises the highest, when the days are longest and the nights shortest is not the hottest day, but that, on the contrary, the dogdays, as they are called, which comprise the hottest weather of the year, occur in July and August; and in the same manner, the 21st of December-when the height to which the sun rises is least, the days shortest, aud the nights longest-is not usually the coldest day, but that, on the other hand, the most inclement weather occurs at a later period.

To explain this, so far as it depends on the position of the sun and the length of the days and nights, we are to consider the following circumstances:—

As midsummer approaches, the gradual increase of the temperature of the weather has been explained thus: The days being considerably longer than the nights, the quantity of heat imparted by the sun during the day is greater than the quantity lost during the night; and the entire result during the twenty-four hours gives an increase of heat. As this augmentation takes place after each successive day and night, the general temperature continues to increase. On the 21st of June, when the day is longest, and the night is shortest, and the sun rises highest, this augmentation reaches its maximum; but the temperature of the weather does not therefore cease to increase. After the 21st of June, there continues to be still a daily augmentation of heat, for the sun still continues to impart more heat during the day than is lost during the night. The temperature of the weather will therefore only cease to increase when by the diminished length of the day, the increased length of the night, and the diminished meridional altitude of the sun, the heat imparted during the day is just balanced by the heat lost during the night. There will be, then, no further increase of temperature, and the heat of the weather will have attained its maxi

mum.

But it might occur to a superficial observer, that this reasoning would lead to the conclusion that the weather would continue to increase in its temperature, until the length of the days would become equal to the length of the nights; and such would be the case, if the loss of heat per hour during the night were equal to the gain of heat per hour during the day. But such is not the case; the loss is more rapid than the gain, and the consequence is