Epitome Astronomiae Copernicanae: Liber I, part 4
Principles of the spherical doctrine. Part III.
Of the nature and height of the air poured around the lands and ocean, and its distinction from the breeze diffused through the whole heavens.
Since the globe of the Earth is distant by a very great interval from the uppermost heaven, I ask what fills that interval? The lands, and the seas poured between them, are immediately enclosed and surrounded by the air, whose greatest height scarcely exceeds the topmost ridges of the mountains; above the air, next in order, follows the aethereal breeze, poured through the whole universe, so that through it the planets and comets are borne and the remaining fixed celestial bodies are scattered, each bounded in its own region.
By what difference are aether and air distinguished from each other? Both are fluid, both transparent, both variable in purity according to the diversity of places and times; they differ, however, by manifest and sensible degrees of transparency.
Explain this difference of transparency by its causes. The science of optics delivers three causes of transparency: first, internal unity; second, thinness; and third, purity from the stain of colours.
In the first cause, then, air and aether are nearly equal in degree; for the fluidity common to both causes internal unity, if nothing heterogeneous is mixed in. To the air, however, dry exhalations and smokes are more frequently and copiously admixed, dividing the internal unity of the moist air; the aether, diffused through most ample spaces, is stained by heterogeneous materials more rarely and in fewer of its parts, those by which it touches the globes most nearly.
In the second cause the degrees run in a continuous series, so that the density of waters is greater, that of air middling, that of aether none, but a thinness inestimable and pure.
In the third cause the difference is this, that the air, by reason of its own matter, according to the measure of its density, also has a blue colour, whereas the aether, when considered in its own matter, has no more colour than density.
How do you know that the aether has so great a thinness and purity? First, things transparent that have something of density take in the light of the Sun and shine; but the aethereal region, since, except for the narrowest space which is in the shadow of the Earth, it is always wholly in the rays of the Sun, so far from shining that at night, when the shining of the air is extinguished, it cannot be perceived at all: it is therefore most thin.
Second, the interval between us and the fixed stars is inestimable, and yet the aethereal breeze, poured through so great a depth, transmits to us the tiny gleams of the smallest stars unimpaired, with the difference of colours. This could not happen if the aether had the least density or colour. For the rays of the Sun, when they shine through a red liquid, gather a red colour in passing.
And so, if physics permitted, the astronomer could suppose the whole space of the aether plainly void, and not without reason did Tycho Brahe doubt whether he should recognise an aether and materiate it.
The colour of the heavens seems to be blue by the testimony of the eyes, which languages follow, deriving the word blue from the heavens, as the Germans say Himmelblau.
That colour which strikes our eyes in a clear sky in the morning hours is not the colour of the aether but of the air, illuminated crosswise by the Sun’s rays.
Whence do you prove this? Because, if it were in the heavens, it would also be seen at night; for the heavens, being far higher than the shadow of the Earth, are also at night in the rays of the Sun.
Have you another argument by which you prove that the air rather than the heavens is blue? Because distant mountains, shining through even the purest air, paint themselves on paper in a blue colour, the more saturated and dark the longer the interval.
The ancients, in the elementary region, gave the highest place to the sphere of fire, and subdivided the aethereal region into many solid spheres contiguous to one another and enclosing one another. Have you arguments to the contrary? First, Tycho Brahe observed that some of the comets pass this way and that through those places in which the orbs were believed to be solid.
Second, if besides the single surface of the air other surfaces of orbs touching one another occurred above, various reflections would exist, as in mirrors set against each other. But this does not appear.
Third, the sphere of fire would be thinner than the sphere of air, the celestial spheres again thinner than the sphere of fire, some more, some less, for the heaven is thinner than the elements. If, therefore, there were a passage for the rays of the stars through so many media differing in density, falling obliquely (as must happen in eccentric orbs and epicycles), they would be refracted more often before they came to the surface of the air; the stars, therefore, viewed by refracted rays, would for many reasons appear outside their true places. But the places of the stars agree with the rule, no refraction of the rays being admitted up to the surface of the air; there are, therefore, no orbs distinguished from one another by degrees of density up to the sphere of the air.
By what arguments do you prove that even the celestial breeze, which has in itself so great purity, has sometimes something heterogeneous and impure mixed into it? First, from the cause. From the globe of the Earth smoky exhalations are sent forth, and from things burnt smokes also ascend, which, after they have passed the surface of the air, wander in the amplitude of the aether in uncertain seats; and it is likely that the same happens about the other globes, especially about the globe of the Sun, which is never without dark spots, which appear to be like black clouds or soots, exhaling from the inmost bowels of the globe. But the matter of comets also seems manifestly to be dissipated by the Sun’s rays passing through the bodies of the comets, and scattered through the aether in the form of a tail, which flows from the comet in the direction opposite to the Sun, by which means the aether is stained. Other causes also may be added.
Second, from the effect, which appears chiefly about the body of the Sun. For this impurity mingled with the aether brings night upon day, and day upon night.
For sometimes a sooty matter besets the Sun, dulling the Sun’s rays, as in nearly the whole year of Caesar’s murder, and so in the year of Christ 1547, when for four whole days the face of the Sun appeared bloody, not in one place only, but through the whole of Europe (compare II. 292). If this matter had been low and, like a veil, drawn over the Sun in the air, it would not have hindered the Sun’s rays so widely, nor only in one place; if you say that it was low, but spread very widely over the lands, so that here it covered the Sun with one part of itself, there with another, then it ought also to have covered the stars far distant from the Sun: but this was not done, for we read that the stars shone out by day. The matter, therefore, was close about the Sun, and so adhering to him that this darkening could last through a year, so that it surrounded the Sun on every side, and he could not from any quarter of the heavens which the Earth occupied at any time of the year be seen without hindrance.
Again, this matter drinks in the Sun’s rays and is made by them so bright that in total eclipses of the Sun, when the whole Sun is hidden behind the Moon and there ought therefore to be mere night, this matter performs the office of the Sun, illuminating the lands, so that mere darkness does not follow, as at other times when this matter is absent.
This matter, like a border about the Sun or a shining hair, strikes the eyes before they are directed to the Sun, warning that the rays of the Sun himself are near.
This matter enlarges the image of the Sun admitted through a very small hole, surrounding it with a dusky border.
Finally, this matter rises before the Sun and sets after, as surrounding the Sun; by which it supplies not the least cause of the daylight before the Sun’s rising and after his setting.
Third, from the consequence. For it is credible that from this matter, as the aethereal breeze is as it were cleansed, wiped clean and restored to its transparency, comets at length grow together, since most of them, as soon as they begin to be seen, emerge from the Sun’s rays, as if setting out from the neighbourhood of the Sun, the native place of this matter. Moreover, from the matter remaining after the dissipation of comets it can happen that new globes are at length gathered together among the fixed stars themselves.
What do you think comets are? Comets are aethereal rectilinear passages, consisting of a bright matter capable of condensing and dissipating, which appears most clearly from their tails, which are a certain outflow from the body toward the quarter opposite to the Sun, drawn forth by the Sun’s rays passing through the bodies, like in motion to those flashes which here in the neighbourhood of our air present the appearance of a burning sky and of chasms.
Enough of the aethereal breeze; I now ask of the air, by what figure is its surface bounded? It is bounded by a spherical surface much more perfectly than the ocean, for the same reasons; because, namely, as in density so also in weight it is next in place after the waters, and deserves to be called light only in comparison with water; otherwise, if it were absolutely light, tending by its own nature upward from the centre of the Earth, it would altogether desert the Earth. It comes about, therefore, as in the waves, by the equilibrium of its parts, that it turns out perfectly round. This is to be understood of calm air.
By what arguments do you prove that air is denser than aether? By two chiefly. First, because what experience in astronomy denies happens in the aether above the air, this the curved surface of the air itself altogether testifies happens: namely that the rays of the Sun, which are otherwise straight lines, when they fall obliquely upon the surface of the air, are altogether refracted downward and inward, which optics teaches happens in a denser medium.
Second, because the air, lit by the Sun’s rays, surrounds us with such splendours that we have day before the Sun has risen, and cannot see the stars; and when the Sun has risen there is no chamber so dark, provided it admit the air by even the smallest hole, that does not shine within with the light of the air, although it lies by no means open to the Sun’s rays. But this borrowed shining is, for the opticians who teach it, an argument of density and of the turbidity of colours.
Review some occasions from which it was understood that the rays of the stars and Sun are refracted at the surface of the air and come refracted to the eye. First, in certain eclipses of the Moon, when the centre of the Earth and the centres of the luminaries are in one straight line, it happens that both luminaries are seen at once above the horizon, just as if they were not opposite, but both together in the upper hemisphere.
Here A, B, C are the centres of the Sun, Earth and Moon in one straight line, and so the Moon is in the shadow of the Earth, O is the eye on the surface of the Earth, BD is the air about the Earth. The ray AB is broken at B downward and becomes BO, so from CD comes DO. The eye, therefore, seeing by the refracted rays OB, OD, and not knowing that they are broken at B and D, continues them in imagination straight on without breaking, and supposes A to be at E, and C at F, both above the horizon. But if EO, FO were mere lines, not even so would that line touch both luminaries A and C at once, because O is outside the line AC, but it would touch either neither luminary or only one of them.
Second, in the same eclipses of the Moon it appears most clearly that the shadow which the sphere of the Earth and of the air together casts is diluted at the margins by some ruddy light unequally, so that the Moon, especially when she grazes the sides of the shadow, though wholly in the shadow, yet often reddens so much that she seems still to shine in some part of her body and to be placed in the Sun’s light, until, when she begins to come out, this tint is detected by the coming of the pure sunlight.
But this light, so unequally diffused, cannot come from anywhere else than from rays which have suffered a double refraction, namely at the entrance into the air and at its exit.
For if BOD be one straight line, and several others pass through the air above O, then by the same ways by which the light of the Sun and Moon is carried to the eye O, namely by ABO and CDO, the light of the Sun is carried also to the Moon, namely by ABDC, illuminating her somewhat, though she is in the shadow of the whole globe.
Third, the Hollanders, wintering beyond Tartary, after a night three months long began to see the Sun at midday, when in that part of the year the Sun could not yet attain the horizon by the space of some degrees. It follows, therefore, that the rays of the Sun, still lying under the Earth, when they had fallen upon the air, about to pass far above the heads of the Hollanders, were refracted and bent downward, so as to fall into the eyes of the Hollanders. (Compare II. 44, 214.)
Fourth, when the Sun is sufficiently elevated his body is round, and all his diameters are equal to one another, as is easy to ascertain with fit instruments. But when the Sun first rises, his erect diameter appears by delicate instruments shorter than the transverse diameter, and to one who contemplates it accurately the image of the Sun seems compressed, in a measure imitating the form of an egg. This, then, the refraction of the rays causes. For optics teaches that refractions are not sensible at a great altitude of the Sun, but become sensible only when the Sun is near the horizon. Therefore the lower any point is, the more is its ray refracted, and the more elevated than is just does it appear. Since, then, the upper margin of the Sun appears a little more elevated than is just, the lowest much more elevated than is just, the lowest will seem to approach the upper by refraction, and so the distance of the upper from the lower, that is the erect diameter, seems contracted, the transverse not likewise, because the ends of the transverse are raised equally.
Fifth, Tycho Brahe opened a way of observing refractions every day, especially in the fixed stars. For example, the tail of Leo and the Spike of Virgo are always distant from each other by the same arc of a great circle, which is 35° 2′. This we find by instruments as often as they culminate, and as often as they set, because they set nearly together. But when in the eastern part of the heavens the tail of Leo has gained an altitude of 34 and a half degrees, the Spike of Virgo begins already to be seen in nearly the same perpendicular, as if it were rising, though in truth it is still below, being distant from the tail of Leo by 35° 2′. The cause again is this, that the ray of the tail of Leo is hardly refracted at all, on account of the altitude of the star, sufficiently great above the horizon, but the ray of the Spike is much refracted, because, rising, it shines into the sphere of the air most obliquely; it therefore seems much elevated above its just place and so to approach the tail standing above it.
Let A be the sight on the Earth, AEC the line of the horizon; let the tail of Leo be seen by the ray AH, refracted indeed at the point I of the air, but little, and be supposed to be at H. Let G be the Spike, which ought to have been seen by the ray AG, but is not seen, since it has not yet risen above the horizon AC, and so AG is hindered by the swelling of the Earth AN. Nevertheless it is seen by AE and is supposed to be at C, because GE is refracted at E, and the refracted ray EA reaches the eye A, which eye supposes AE, EG to be one straight line AEC. Thus in place of the angle HAG the smaller angle HAC is found.
Whence did the height of the air first become known to astronomers? From the comparison of the quantity of refractions both when a star rises and when it is raised to some altitude.
What things are to be foreknown from the optics, that this method may be delivered? First, the more a ray of the Sun or of a star is inclined upon the surface of the air, as of a denser medium, the more it is refracted; and so the ray which touches the sphere of the air is refracted most at the contact. Yet all rays at the point of refraction cut one another, and those of the upper rays which are refracted in the rare medium are lower in the dense. Second, the proportion of the two angles of refraction is compounded of two other proportions, of which one is between the angles of inclination, of which the refractions are constituted within the dense medium, the other between the secants of those angles. Therefore, the refraction of one certain inclination being given, the refractions of the other inclinations are also given. Third, since the sphere of the air surrounds the globe of the Earth, one and the same ray in the air is inclined differently upon the Earth and differently upon the hollow surface of the air, and the ray which touches the Earth, namely the ray of a rising star, cuts the surface of the air. Fourth, when we observe the refractions of rays, we take their inclinations not upon the air, whose surface is neither seen nor within reach, being far above us, but upon the Earth on which we stand; the inclination of the refracted ray upon the hollow surface of the air must therefore afterward be found out.
Teach the manner of computing the height of the air from the given inclination of the same ray both upon the Earth and upon the hollow surface of the air, and conversely the inclination from the height. A triangle is formed from the known semidiameter of the Earth, the semidiameter of the sphere of the air, and the ray; in which triangle the angles at the ends of the ray, or inclinations of the ray, are known. Wherefore, as the sine of the inclination upon the hollow surface of the air is to the semidiameter of the Earth, so is the sine of the inclination upon the Earth to the semidiameter of the sphere composed of the Earth and the air; the excess over the semidiameter of the Earth is therefore the height of the air sought.
Example. Let the inclination upon the Earth be the angle DAO, 90°.
AO, the semidiameter, 860 miles.
Let ADO, the inclination of the same upon the hollow surface of the air, be 88° 1′; the sine The excess DM of the air above the surface of the Earth comes out a little greater than half a mile.
But if the height of the air be given and the inclination upon the hollow of the air be sought, conversely the product made from the semidiameter of the Earth and the sine of the inclination upon the Earth is to be divided by the semidiameter of the sphere of the air; the quotient will be the sine of the inclination upon the hollow of the air.
How can the refractions of the other inclinations be computed from the refraction made at one certain inclination of the ray upon the hollow of the air, and conversely the inclinations from the other refractions? The rule of five, or of proportions, is to be used, each inclination being multiplied into its secant.
Example. Let the inclination of the ray in the rare medium upon the surface of the dense be 89° 20′, whose secant is 8594561. Let the refraction of this inclination be 40′. For the refraction is never greater than the complement of the inclination upon the dense, and almost always less. The refraction is now sought for another inclination, 60°, of the ray AI, whose secant is 200000.
Therefore the inclination of AE itself, 89° 20′, gives 40; what does the inclination of AI itself, 60°, give?
The quotient shows 48 parts of one minute, which are 37 seconds, a little more. So great a refraction follows at the inclination of 60° at I.
But if from the second refraction the second inclination is sought, the second refraction is multiplied into the product of the first inclination and its secant, and the product is divided by the first refraction; the result will be the product of the inclination sought and its secant.
Teach now how to compute the inclination of the refracted rays upon the hollow surface of the air, of unknown height. For this work there are needed at least three refractions, observed at three inclinations of the ray upon the Earth. For example, Tycho Brahe denies that the refractions of the fixed stars at an altitude of 20°, that is at an inclination upon the Earth of 70°, are any longer sensible, and so the refraction of this inclination ought not to be much greater than 1′; at an inclination upon the Earth of 89° he makes the refraction 21½′, and at the horizon, or at the full inclination upon the Earth of 90°, Brahe gives the quantity of refraction as 30′. Then, by the rule of positions, there is to be assumed the refraction of the ray touching the sphere of the air, which cannot be less than 30′, the amount a star has when it is seen to rise; but it may be greater. If 30′ is posited, that is, if the refracted ray of a rising star touches the air outside at the point of refraction, then along with the quantity of this refraction the inclination upon the hollow of the air has also been taken, namely 89° 30′.
This inclination being posited, there is posited at the same time (or computed under the condition of this position) the very height of the air sought, by the method already delivered; and from the given height of the air there is fitted to each inclination upon the Earth its inclination upon the air, and from the inclination upon the air its refraction also, by the other method delivered.
All the operations being performed, the refractions which come out are compared with those which Tycho Brahe observed; if they differ very much, the position was false, and the refraction of the ray touching the sphere of the air must be posited greater than the greatest of those observed by Brahe.
Example. Let the refraction FDP of the tangent PD be posited equal to Tycho’s horizontal refraction, 30′. The ray touching the Earth (namely at the horizon, upon which the star is seen to rise) is therefore posited to be inclined to the surface of the air at the angle APO, 89° 30′. Hence IA or DM, the height of the air, by computation intervening, is found to be 38 parts of 1000000 of the semidiameter of the Earth MO or AO, which, since it has 860 miles, each of 32 stadia, makes these 38 parts a very little more than one stadium.
Since the height of the air DM is thus posited, it is now asked how much the ray KA, inclined at 89° upon the Earth, is inclined upon this air. As if KAO is 91°, how great will AKO be?
The sine of the angle AKO, 88° 53′, the inclination upon the air.
The inclination of the second ray upon the air being thus posited as 88° 53′, let its refraction be computed from the refraction of the first.
The products of both, 456086160; refraction posited, 30.
The refraction comes out at K about 13′ 41″ at an inclination upon the Earth of 89°. But Tycho here gave a greater, namely 21½′.
We understand, therefore, that our position is false; the height of the air false, and the inclinations upon the air which were drawn from it false. But since our position cannot be diminished, as was said, let it be increased.
But if the ray which touches the air is posited to suffer a greater refraction than Tycho’s horizontal one, then by a longer way it must first be sought which of the inclinations upon the air, according to our position, yields Tycho’s horizontal refraction of 30′.
Example. Let the refraction of the tangent PD be posited 1°. Therefore, when the ray PD in the rare medium touches the sphere of the air at D, it will be refracted by one degree, and the refracted ray DQ will not touch the Earth and will be inclined inward upon the hollow surface of the air at D by the remaining 89 degrees, namely by the angle QDO, which arc, multiplied into its secant 5729869, makes 509958341, and this multiplied into EDL, the given refraction of the rays LD, DA, namely 30′, makes 15298750230, which divide by the refraction posited, 60′; the quotient 254979170 is the product of the arc of the inclination upon the air sought and its secant.