by Aristotle
That the colours of the rainbow are those we described and how the other colours come to appear in it will be clear from the following considerations. We must recognize, as we have said, and lay down first, that white colour on a black [10] surface or seen through a black medium gives red; second, that sight when strained to a distance becomes weaker and less; third, that black is in a sort the negation of sight: an object appears black because sight fails; so everything at a distance looks blacker, because sight does not reach it. The theory of these matters belongs to the [15] account of the senses, which are the proper subjects of such an inquiry; here we need only state about them what is necessary for us. At all events, that is the reason why distant objects and objects seen in a mirror look darker and smaller and smoother, and why the reflection of clouds in water is darker than the clouds themselves. This [20] latter is clearly the case: the reflection diminishes the sight that reaches them. It makes no difference whether the change is in the object seen or in the sight, the result being in either case the same. The following fact further is worth noticing. When there is a cloud near the sun and we look at it it does not look coloured at all [25] but white, but when we look at the same cloud in water it shows a trace of rainbow colouring. Clearly, then, when sight is reflected it is weakened and, as it makes dark look darker, so it makes white look less white, changing it and bringing it nearer to [30] black. When the sight is relatively strong the change is to red; the next stage is green, and a further degree of weakness gives violet. No further change is visible, but three completes the series of colours (as we find three does in most other things), and the change into the rest is imperceptible. Hence also the rainbow appears with three colours; this is true of each of the two, but in a contrary way. The outer band [375a1] of the primary rainbow is red; for the largest band reflects most sight to the sun, and the outer band is largest. The middle band and the third go on the same principle. So if the principles we laid down about the appearance of colours are true the [5] rainbow necessarily has three colours, and these three and no others. The appearance of yellow is due to contrast; for the red is whitened by its juxtaposition with green. We can see this from the fact that the rainbow is purest when the cloud is blackest; and then the red shows more yellow. (Yellow in the rainbow comes [10] between red and green.) So the whole of the red shows white by contrast with the blackness of the cloud around; for it is white compared to them. Again, when the rainbow is fading away39 and the red is dissolving, the white cloud is brought into [15] contact with the green and becomes yellow. But the moon rainbow affords the best instance of this: it looks quite white—this is because it appears on the dark cloud [20] and at night. So, just as fire is intensified by added fire, black beside black makes that which is in some degree white look quite white; and red is like that. Bright dyes too show the effect of contrast. In woven and embroidered stuffs the appearance of colours is profoundly affected by their juxtaposition with one another (purple, for [25] instance, appears different on white and on black wool), and also by differences of illumination. Thus embroiderers say that they often make mistakes in their colours when they work by lamplight, and use the wrong ones. We have now shown why the rainbow has three colours and that these are its only colours.
[30] The same cause explains the double rainbow and the faintness of the colours in the outer one and their inverted order. When sight is strained to a greater distance the appearance of the distant object is affected in a certain way; and the same thing [375b1] holds good here. So the reflection from the outer rainbow is weaker because it takes place from a greater distance and less of it reaches the sun, and so the colours seen are fainter. Their order is reversed because more reflection reaches the sun from the [5] smaller, inner band. For that reflection is nearer to our sight which is reflected from the band which is nearest to the primary rainbow. Now the smallest band in the outer rainbow is that which is nearest, and so it will be red; and the second and the third will follow the same principle. Let B be the outer rainbow, A the inner and [10] primary one; let C stand for the red colour, D for green, E for violet; yellow appears at the point F. Three rainbows or more are not found because even the second is fainter, so that the third reflection can have no strength whatever and cannot reach [15] the sun.
5 · The rainbow can never be a circle nor a segment of a circle greater than a semicircle. The consideration of the diagram will show this and the other properties of the rainbow.
[20] Let A be a hemisphere resting on the circle of the horizon, let its centre be K and let G be another point appearing on the horizon. Then, if the lines that fall in a cone from K have GK as their axis, and, K and M being joined, the lines KM are [25] reflected from the hemisphere to G over the greater angle, the lines from K will fall on the circumference of a circle. If the reflection takes place when the luminous body is rising or setting the segment of the circle above the earth which is cut off by the horizon will be a semicircle; if the luminous body is above the horizon it will always be less than a semicircle, and it will be smallest when the luminous body reaches its meridian.
[30] First let the luminous body be rising at the point G, and let KM be reflected to G, and let the plane40 determined by the triangle GKM be produced. Then the section of the sphere will be a great circle. Let it be A (for it makes no difference which of the planes passing through the line GK and determined by the triangle [376a1] KMG is produced). Now the lines drawn for G and K to any other point on the semicircle A will not stand in this ratio to one another. For since both the points G and K and the line KG are given, the line MG will be given too; consequently the ratio of the line MG to the line MK will be given too. So M will touch a given [5] circumference. Let this be NM. Then the intersection of the circumferences is given, and the same ratio cannot hold between lines in the same plane drawn from the same points to any other circumference but MN.
Draw a line DB outside of the figure and divide it so that D is to B as MG is to [10] MK. But MG is greater than MK since the reflection of the cone is over the greater angle (for it subtends the greater angle of the triangle KMG). [Therefore D is greater than B.]41 Then add to B a line F such that BF is to D as D is to B. Then [15] make another line KP having the same ratio as to B as KG has to F, and join MP.
Then P is the pole of the circle on which the lines from K fall. For the ratio of D to PM is the same as that of F to KG and of B to KP. If not, let D be in the same [20] ratio to a line lesser or greater than PM—it will not matter—and let this line be PR. Then GK and KP and PR will have the same ratios to one another as F, B, and D. But the ratios between F, B, and D were such that FB is to D as D is to B. Therefore [25] PG is to PR as PR is to PK. Now, if the points K, G be joined with the point R by the lines GR, KR these lines will be to one another as PG is to PR; for the sides of the triangles GPR, KPR about the angle P are homologous. Therefore, GR too will be [30] to KR as GP is to PR. But this is also the ratio of MG to MK; for the ratio of both is the same as that of D to B. Therefore, from the points G, K there will have been [376b1] drawn lines with the same ratio to one another, not only to the circumference MN but to another point as well, which is impossible. Since then D cannot bear that ratio to any line either lesser or greater than PM (the proof being in either case the same), it follows that it must stand in that ratio to MP itself. Therefore as MP is to [5] PK so PG will be to MP [and finally MG to MK].42
If, then, a circle be described with P as pole at the distance MP it will touch all the angles which the lines from H and K43 make by their reflection. If not, it can be [10] shown, as before, that lines drawn to different points in the semicircle will have the same ratio to one another, which was impossible. If, then, the semicircle A be revolved about the diameter GKP, the lines reflected from the points G, K at the point M will have the same ratio, and will make the angle KMG equal, in every [15] plane. Further, the angle which GM44 and MP make with GP will always be the same. So there are a number of triangles on GP and KP equal to the triangles GMP and KMP. Their
perpendiculars will fall on GP at the same point and will be equal. Let O be the point on which they fall. Then O is the centre of the circle, half of [20] which, MN, is cut off by45 the horizon.
For the sun does not master the parts above, but does master those near the earth and dissolve the air. And that is why the rainbow does not make a complete circle. A rainbow at night from the moon occurs rarely: for the moon is not always [25] full and is too weak in its nature to master the air. Rainbows stand most firmly when the sun is most mastered; for then most moisture remains in them.46
Again, let the horizon be AKC, and let G have risen above it; and let the axis now be GP. The proof will be the same for the rest as before, but the pole P of the [377a1] circle will be below the horizon AC since the point G has risen above the horizon. But the pole, and the centre of the circle, and the centre of that circle (namely GP) which now determines the rising of the sun are on the same line. But since KG lies [5] above the diameter AC, the centre will be at O47 on the line KP below the plane of the circle AC which determined the position of the sun before. So the segment XY which is above the horizon will be less than a semicircle. For XYZ48 was a semicircle and it has now been cut off by49 the horizon AC. So part of it, YZ,50 will be invisible when the sun has risen above the horizon, and the segment visible will be [10] smallest when the sun is on the meridian; for the higher G is the lower the pole and the centre of the circle will be.
In the shorter days after the autumn equinox there may be a rainbow at any time of the day, but in the longer days from the spring to the autumn equinox there [15] cannot be a rainbow about midday. The reason for this is that the northerly segments are all greater than a semicircle, and go on increasing, while the invisible segment is small; but as to the segments south of the equator, the upper one is small and the one below the earth large—and the further away they get, the larger it [20] becomes. Consequently, in the days near the summer solstice, the size of the segment is such that before the point A reaches the middle of the segment—its meridian—the point P is well below the horizon; the reason for this being the great size of the segment, and the consequent distance of the meridian from the earth. But [25] in the days near the winter solstice the segments of the circles are small, and the contrary is necessarily the case: for the sun is on the meridian before the point G has risen far.
[30] 6 · Mock suns, and rods too, are due to the causes we have described. A mock sun is caused by the reflection of sight to the sun. Rods are seen when sight reaches the sun under circumstances like those which we described, when there are clouds near the sun and sight is reflected from some liquid surface to the cloud. Here the [377b1] clouds themselves are colourless when you look at them directly, but in the water they are full of rods. The only difference is that in this latter case the colour of the cloud seems to reside in the water, but in the case of rods on the cloud itself. Rods [5] appear when the composition of the cloud is uneven, dense in part and in part rare, and more and less watery in different parts. For when the sight is reflected to the sun its shape is not seen but its colour is; and bright white light of the sun, to which [10] the sight is reflected, being seen on the uneven mirror, appears partly red, partly green or yellow. It makes no difference whether sight passes through or is reflected from a medium of that kind; the colour is the same in both cases; if it is red in the first case it must be red in the other.
Rods then are occasioned by the unevenness of the mirror—as regards colour, not shape. The mock sun, on the contrary, appears when the air is very uniform, and [15] of the same density throughout. This is why it appears white: the uniform character of the mirror gives the reflection in it a single colour, while the fact that the sight is reflected in a body and is thrown on the sun all together by the mist, which is dense and watery though not yet quite water, causes the sun’s true colour to appear just as [20] it does when the reflection is from the dense, smooth surface of copper. So the sun’s colour being white, the mock sun appears white too. This too, is the reason why the mock sun is a surer sign of rain than the rods; for the air is in a more favourable [25] condition for the production of water. Further a mock sun to the south is a surer sign of rain than one to the north; for the air in the south is readier to turn into water than that in the north.
Mock suns and rods are found, as we stated, about sunset and sunrise, not above the sun nor below it, but beside it. They are not found very close to the sun, [30] nor very far from it; for the sun dissolves the condensation if it is near, but if it is far off the reflection cannot take place, since sight weakens when it is reflected from a small mirror to a very distant object. (This is why a halo is never found opposite to the sun.) If the condensation is above the sun and close to it the sun will dissolve it; if [378a1] it is at a distance the sight is too weak for the reflection to take place, and so it will not reach the sun. But at the side of the sun, it is possible for the mirror to be at such an interval that the sun does not dissolve it, and yet sight reaches it in a body because it moves close to the earth51 and is not as it were dissipated in its journey [5] through space. It cannot occur below the sun because close to the earth the sun’s rays would dissolve it, but if it were high up in the heavens sight would be dissipated. Indeed, even by the side of the sun, it is not found in the middle of the sky; for then the line of vision is not close to the earth,52 and so but little sight reaches the mirror [10] and the reflection from it is altogether feeble.
Some account has now been given of the effects of the exhalation above the surface of the earth; we must go on to describe its operations below, when it is shut [15] up in the parts of the earth.
Its own twofold nature gives rise here to two varieties of bodies, just as it does in the upper region. We maintain that there are two exhalations, one vaporous the other smoky, and there correspond two kinds of bodies that originate in the earth, [20] things quarried and things mined. The heat of the dry exhalation is the cause of all things quarried. Such are the kinds of stones that cannot be melted, and realgar, and ochre, and ruddle, and sulphur, and the other things of that kind, most things quarried being either coloured lye or, like cinnabar, a stone compounded of it. The [25] vaporous exhalation is the cause of all things mined—things which are either fusible or malleable such as iron, copper, gold. All these originate from the imprisonment of the vaporous exhalation in the earth, and especially in stones. [30] Their dryness compresses it, and it congeals just as dew or hoar-frost does when it has been separated off, though in the present case the metals are generated before that separation occurs. Hence, they are water in a sense, and in a sense not. Their matter was that which might have become water, but it can no longer do so; nor are [378b1] they, like savours, due to a qualitative change in actual water. Copper and gold are not formed like that, but in every case the evaporation congealed before water was formed. Hence, they all (except gold) are affected by fire, and they possess an admixture of earth; for they still contain the dry exhalation.
[5] This is the general theory of all these bodies, but we must take up each kind of them and discuss it separately.
BOOK IV
[10] 1 · We have explained that the causes of the elements are four, and that their combinations determine the number of the elements to be four.
Two of the causes, the hot and the cold, are active; two, the dry and the moist, passive. We can satisfy ourselves of this by looking at instances. In every case heat [15] and cold determine, conjoin, and change things of the same kind and things of different kinds, moistening, drying, hardening, and softening them. Things dry and moist, on the other hand, both in isolation and when present together in the same body are the subjects of that determination and of the other affections enumerated. [20] The account we give when we define their natures shows this too. Hot and cold we describe as active, for combining is a sort of activity; moist and dry are passive, for it is in virtue of its being acted upon in a certain way that a thing is said to be easy to [25] determine or difficult to determine. So it is
clear that some are active and some passive.
Next we must describe the operations of the active qualities and the forms taken by the passive. First of all, unqualified becoming and natural change are the [30] work of these powers and so is the corresponding natural destruction; and these are found in plants and animals and their parts. Unqualified natural becoming is a change introduced by these powers into the matter underlying a given natural thing when they are in a certain ratio; and matter is the passive qualities we have [379a1] mentioned. When the hot and the cold are masters of the matter they generate a thing; if they are not, the object is imperfectly boiled or otherwise unconcocted. But the strictest general opposite of unqualified becoming is putrefaction. All natural destruction is on the way to it, as are, for instance, growing old or growing dry. [5] Putrescence is the end of all these things,53 that is of all natural objects, except such as are destroyed by violence:54 you can burn, for instance, flesh, bone, or anything else, but the natural course of their destruction ends in putrefaction. Hence things that putrefy begin by being moist and end by being dry. For the moist and the dry were their matter, and the operation of the active qualities caused the dry to be [10] determined by the moist.
Destruction supervenes when the determined gets the better of the determining by the help of the environment (though in a special sense the word putrefaction is applied to partial destruction, when a thing’s nature is perverted). Hence everything, except fire, is liable to putrefy; for earth, water, and air putrefy, [15] being all of them matter relatively to fire. Putrefaction is the destruction of the peculiar and natural heat in any moist subject by external heat, that is, by the heat of the environment. So since lack of heat is the ground of this affection and everything which lacks heat is cold, both heat and cold will be the causes of [20] putrefaction, which will be due indifferently to cold in the putrefying subject or to heat in the environment.