that the hottest day usually comes within the month of July, but always long before the day of the autumnal equinox.

The same reasoning will explain why the coldest weather does not usually occur on the 21st of December, when the day is shortest and the night longest, and when the sun attains the lowest meridional altitude. The decrease of the temperature of the weather depends upon the loss of heat during the night being greater than the gain during the day; and until, by the increased length of the day, and the diminished length of the night, these effects are balanced, the coldest weather will not be attained.

These observations must be understood as applying only so far as the temperature of the weather is affected by the sun, and by the length of the days and nights. There are a variety of other local and geographical causes which interfere with these effects, and vary them at different times and places.

On referring to the annual motion of the earth round the sun, it appears that the position of the sun within the elliptic orbit of the earth is such that the earth is nearest to the sun about the 1st of January, and most distant from it about the 1st of July. As the calorific power of the sun's rays increases as the distance from the earth diminishes, in even a higher proportion than the change of distances, it might be expected that the effect of the sun in heating the earth on the 1st of January would be considerably greater than on the 1st of July. If this were admitted, it would follow that the annual motion of the earth in its elliptic orbit would have a tendency to diminish the cold of the winter in the northern hemisphere, and mitigate the heat of summer, so as to a certain extent to equalise the seasons; and, on the contrary, in the southern hemisphere, where the 1st of January is in the middle of summer and the Ist of July the middle of winter, its effects would be to aggravate the cold in winter and the heat in summer. The investigations, however, which had been made in the physics of heat, have shown that that principle is governed by laws which counteract such effects. Like the operation of all other physical agencies, the sun's calorific power requires a definite time to produce a given effect, and the heat received by the earth at any part of its orbit will depend conjointly on its distance from the sun and the length of time it takes to traverse that portion of its orbit. In fact, it has been ascertained that the heating power depends as much on the rate at which the sun changes its longitude as upon the earth's distance from it. Now it happens that, in consequence of the laws of the planetary motions, discovered by Kepler, and explained by Newton, when the earth is most remote from the sun its velocity is least, and consequently the hourly changes of longitude of the sun will be proportionally less. Thus it appears that what the heating power loses by augmented

distance, it gains by diminished velocity; and again, when the earth is nearest to the sun, what it gains by diminished distance, it loses by increased speed. There is thus a complete compensation produced in the heating effect of the sun, by the diminished velocity of the earth which accompanies its increased distance.

This period of the year, during which the heat of the weather is usually most intense, was called the CANICULAR DAYS, or DOG DAYS. These days were generally reckoned as forty, commencing about the 3rd of July, and received their name from the fact, that in ancient times the bright star Sirius, in the constellation of Canis major, or the great dog, at that time rose a little before the sun, and it was to the sinister influence of this star that were ascribed the bad effects of the inclement heat, and especially the prevalence of madness among the canine race. Owing to a cause which will be explained hereafter (the precession of the equinoxes), this star no longer rises with the sun during the hot season.

CHAPTER VIII.

ATMOSPHERIC REFRACTION, AND PARALLAX.

152. Apparent position of celestial objects affected by refraction. The ocean of air which surrounds, rests upon, and extends

Fig. 44.

positions of celestial objects.

S

to a certain limited height above the surface of the solid and liquid matter composing the globe, decreases gradually in density in rising from the surface (H. 223); that when a ray of light passes from a rarer into a denser transparent medium, it is deflected towards the perpendicular to their common surface; and that the amount of such deflection increases with the difference of densities and the angle of incidence (0.92). These properties, which air has in common with all transparent media, produce important effects on the apparent

Let s a, fig. 44, be a ray of light coming from any distant ob

ject, s, and falling on the surface of a series of layers of transparent matter, increasing in density downwards. The ray s a, pass

S

P

Fig. 45.

ing into the first layer, will be deflected in the direction a a' towards the perpendicular, and passing through the lowest layer, it will be still more deflected, and will enter the eye at e, in the direction a" e; and since every object is seen in the direction from which the visual ray enters the eye, the object s will be seen in the direction es', instead of its true direction a s. The effect, therefore, is to make the object appear to be nearer to the zenithal direction than it really is.

And this is what actually occurs with respect to all celestial objects seen, as such objects always must be, through the atmosphere. The visual ray s D, fig. 45, passing through a succession of strata of air, gradually and continually increasing in density, its path will be a curve bending from D towards A, and convex towards the zenithal line A z. The direction in which the object will be seen, being that in which the visual ray enters the eye, will be the tangent as to the curve at ▲. The object will therefore be

seen in the direction a 8 instead of D S.

It has been said that the deflection produced by refraction is increased with the increase of the angle of incidence. Now, in the present case, the angle of incidence is the angle under the true

-H

direction of the object and the zenithal line, or, what is the same, the zenith distance of the object. The extent, therefore, to which any celestial object is disturbed from its true place by the refraction of the atmosphere, increases with its zenith distance. The refraction is, therefore, nothing in the zenith, and greatest in the horizon.

153. Law of atmospheric refraction.-The extent to which a celestial object is displaced by refraction, therefore, depends upon and increases with its distance from the zenith; and it can be shown to be a consequence of the general principles of optics, that when other things are the same, the actual quantity of this displacement (except at very low altitudes) varies in the proportion of the tangent of the zenith distance.

This law prevails with considerable exactitude, except at very low altitudes, where the refractions depart from it, and become uncertain.

154. Quantity of refraction.-When the latitude of the observatory is known, the actual quantity of refraction at a given altitude may be ascertained by observing the altitudes of a circumpolar star, when it passes the meridian above and below the pole. The sum of these altitudes would be exactly equal to twice the latitude (114) if the refraction did not exist, but since by its effects the star is seen at greater than its true altitudes, the sum of the altitudes will be greater than twice the latitude by the sum of the two refractions. This sum will therefore be known, and being divided between the two altitudes in the ratio of the tangents of the zenith distances the quantity of refraction due to each altitude will be known.

The pole star answers best for this observation, especially in these and higher latitudes, where it passes the meridian within the limits of the more regular influence of refraction; and the difference of its altitudes being only 3°, no considerable error can arise in apportioning the total refraction between the two altitudes.

155. Tables of refraction. - To determine with great exactitude the average quantity of refraction due to different altitudes, and the various physical conditions under which the actual refraction departs from such average, is an extremely difficult physical problem. These conditions are connected with phenomena subject to uncertain and imperfectly known laws. Thus, the quantity of refraction at a given altitude depends, not only on the density, but also on the temperature of the successive strata of air through which the visual ray has passed. Although as a general fact, it is apparent that the temperature of the air falls as we rise in the atmosphere, yet the exact law according to which it decreases is not fully ascertained. But even though it were, the refraction is also

influenced by other agencies, among which the hygrometric condition of the air holds an important place.

From these causes, some uncertainty necessarily attends astronomical observations of objects near the horizon, and some embarrassment arises in cases where the quantities to be detected by the observations are extremely minute. Nevertheless, it must be remembered that, since the total amount of refraction is never considerable, and in most cases it is extremely minute, and since, small as it is, it can be very nearly estimated and allowed for, and in some cases wholly effaced, no serious obstacle is offered by it to the general progress of astronomy.

Tables of refraction have been constructed and calculated, partly from observation and partly from theory, by which the observer may at once obtain the average quantity of refraction at each altitude; and rules are given by which this average refraction may be corrected according to the peculiar state of the barometer, thermometer, and other indicators of the physical state of the air.

156. Average quantity at mean altitudes. While the refraction is nothing in the zenith, and somewhat greater than the apparent diameter of the sun or moon in the horizon, it does not amount to so much as 1', or the thirtieth part of this diameter, at the mean altitude of 45°.

157. Effect on rising and setting. Its mean quantity in the horizon is 33', which being a little more than the mean apparent diameters of the sun and moon, it follows that these objects, at the moment of rising and setting, are visible above the horizon, the lower edge of their disks just touching it, when in reality they are below it, the upper edge of the disk just touching it.

The moments of rising of all objects are therefore accelerated, and those of setting retarded, by refraction. The sun and moon appear to rise before they have really risen, and to set after they have really set; and the same is true of all other objects.

158. General effect of the barometer on refraction. — Since the barometer rises with the increased weight and density of the air, its rise is attended by an augmentation, and its fall by a decrease, of refraction. It may be assumed that the refraction at any proposed altitude is increased or diminished by the 300th part of its mean quantity for every tenth of an inch by which the barometer exceeds or falls short of the height of 30 inches.

159. Effect of thermometer. As the increase of temperature causes a decrease of density, the effect of refraction is diminished by the elevation of the thermometer, the state of the barometer being the same. It may be assumed, that the refraction at any proposed altitude is diminished or increased by the 420th part of its

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