§ 2. Huygens
In Huygens' paper, "Treatise on Light" (1690), Huygens describes Roemer's observation of the period of Io that produces a 10 minute time delay.
"But that which I employed only as a hypothesis, has recently received great seemingness as an established truth by the ingenious proof of Mr. Römer which I am going here to relate, expecting him himself to give all that is needed for its confirmation. It is founded as is the preceding argument upon celestial observations, and proves not only that Light takes time for its passage, but also demonstrates how much time it takes, and that its velocity is even at least six times greater than that which I have just stated. For this he makes use of the Eclipses suffered by the little planets which revolve around Jupiter, and which often enter his shadow: and see what is his reasoning." (Huygens, p. 8-9).
"Hence, if light would travel the diameter of the Earth in one second, it would travel each interval FG and KL in 3 1/2 minutes. This should lead to a deviation of about half an hour between two revolutions of this satellite observed in FG and KL respectively. On the other hand, nothing of such a substantial difference has been found." (Roemer, p. 276).
"For instance, 40 revolutions observed from the side F should be substantially shorter that 40 other revolutions, observed from the opposite side (this effect is independent of any position in the Zodiac where Jupiter would be located), and this is in a ratio of 22 to the interval HE, which is twice the distance from us to the Sun.The necessity of the new equation of delayed light was established by all the observations obtained at the Royal Academy and the Observatory during the past 8 years. This was verified later, by the appearance of the first satellite from the shadow of Jupiter, observed in the evening 5h35m45s on November 9 of this year, in Paris, that occurred 10 minutes later than it was expected on the basis of the observations produced in August, when the Earth was much closer to Jupiter; this was predicted by monsieur Rømer, at the Academy in the beginning of September ." (Roemer, p. 277-8).
Roemer did not measure or calculate the velocity of light in his three page paper. Roemer describes the time delay of the period of Io, a moon of Jupiter, and the earth's orbital diameter HE. Roemer states that after a ten month time interval between November 9 and the beginning of September a 10 minute time delay of Io's period was recorded that Roemer attributed to the velocity of light.
Huygens calculates the velocity of light using the earth's orbital diameter KL and a 22 minute time delay of the period of Io (fig 2).
"If one considers the vast size of the diameter KL, which according to me is some 24 thousand diameters of the Earth, one will acknowledge the extreme velocity of Light. For, supposing that KL is no more than 22 thousand of these diameters, it appears that being traversed in 22 minutes this makes the speed a thousand diameters in one minute, that is 16-2/3 diameters in one second or in one beat of the pulse, which makes more than 11 hundred times a hundred thousand toises; since the diameter of the Earth contains 2,865 leagues, reckoned at 25 to the degree, and each each league is 2,282 Toises, according to the exact measurement which Mr. Picard made by order of the King in 1669. But Sound, as I have said above, only travels 180 toises in the same time of one second: hence the velocity of Light is more than six hundred thousand times greater than that of Sound. This, however, is quite another thing from being instantaneous, since there is all the difference between a finite thing and an infinite. Now the successive movement of Light being confirmed in this way, it follows, as I have said, that it spreads by spherical waves, like the movement of Sound." (Huygens, p. 10-11).
Huygens uses the earth's orbital diameter KL and a 22 minute time delay of the period of Io to calculate the velocity of light; Huygens' calculation is based on a 22 minute time delay of Io's period that is produce by the finite magnitude of the velocity of light and the earth's orbital diameter KL but after the earth propagates to the position L, Huygens cannot view Io since at position L, the dark side of the earth (night) is not facing Jupiter. Example, Jupiter is in opposition on May 9, 2018 and on November 9, 2018 after the earth propagates the distance of the earth's orbital diameter in a six month time period Jupiter does not appear in the night sky (http://www.seasky.org/astronomy/astronomy-calendar-2018.html.).
Huygens' describes light using spherical waves based on a sound wave analogy.
"We know that by means of the air, which is an invisible and impalpable body, Sound spreads around the spot where it has been produced, by a movement which is passed on successively from one part of the air to another; and that the spreading of this movement, taking place equally rapidly on all sides, ought to form spherical surfaces ever enlarging and which strike our ears. Now there is no doubt at all that light also comes from the luminous body to our eyes by some movement impressed on the matter which is between the two; since, as we have already seen, it cannot be by the transport of a body which passes from one to the other. If, in addition, light takes time for its passage—which we are now going to examine—it will follow that this movement, impressed on the intervening matter, is successive; and consequently it spreads, as Sound does, by spherical surfaces and waves" (Huygens, p. 5).
"It is true that we are here supposing a strange velocity that would be a hundred thousand times greater than that of Sound. For Sound, according to what I have observed, travels about 180 Toises in the time of one Second, or in about one beat of the pulse. But this supposition ought not to seem to be an impossibility; since it is not a question of the transport of a body with so great a speed, but of a successive movement which is passed on from some bodies to others. I have then made no difficulty, in meditating on these things, in supposing that the emanation of light is accomplished with time, seeing that in this way all its phenomena can be explained, and that in following the contrary opinion everything is incomprehensible. For it has always seemed tome that even Mr. Des Cartes, whose aim has been to treat all the subjects of Physics intelligibly, and who assuredly has succeeded in this better than any one before him, has said nothing that is not full of difficulties, or even inconceivable, in dealing with Light and its properties." (Huygens, p. 7).
"the velocity of Light is more than six hundred thousand times greater than that of Sound. This, however, is quite another thing from being instantaneous, since there is all the difference between a finite thing and an infinite. Now the successive movement of Light being confirmed in this way, it follows, as I have said, that it spreads by spherical waves, like the movement of Sound." (Huygens, p. 10).
Huygens' optical spherical waves are formed by the motion of an ether composed of matter yet light propagates in vacuum that is void of matter which contradicts the existence of Huygens' ether and spherical waves. A wave is a mechanical entity that is formed by the motion of a medium, composed of matter (solid, liquid or gas). Example, air is the medium that forms sound waves which are produced by the exchange of the kinetic energies of interacting air molecules but sound cannot propagate in vacuum since vacuum is void of air molecules required in forming sound waves yet Huygens is using an acoustical analogy to represent the propagation of light. One of the most important physical characteristic of sound is not applicable to light since light propagates in vacuum that is void of air that is required in forming sound yet Huygens is using an acoustical analogy to describe the propagation of light.
Huygens is describing the formation of light waves produced by the motion of an ether, composed of matter.
"Now if one examines what this matter may be in which the movement coming from the luminous body is propagated, which I call Ethereal matter" (Huygens, p. 11).
"But the extreme velocity of Light, and other properties which it has, cannot admit of such a propagation of motion, and I am about to show here the way in which I conceive it must occur. For this, it is needful to explain the property which hard bodies must possess to transmit movement from one to another." (Huygens, p. 13).
"But it is still certain that this progression of motion is not instantaneous, but successive, and therefore must take time. For if the movement, or the disposition to movement, if you will have it so, did not pass successively through all these spheres, they would all acquire the movement at the same time, and hence would all advance together; which does not happen. For the last one leaves the whole row and acquires the speed of the one which was pushed. Moreover there are experiments which demonstrate that all the bodies which we reckon of the hardest kind, such as quenched steel, glass, and agate, act as springs and bend somehow, not only when extended as rods but also when they are in the form of spheres or of other shapes." (Huygens, p. 13).
"Now in applying this kind of movement to that which produces Light there is nothing to hinder us from estimating the particles of the ether to be of a substance as nearly approaching to perfect hardness and possessing a springiness as prompt as we choose. It is not necessary to examine here the causes of this hardness, or of that springiness, the consideration of which would lead us too far from our subject. I will say, however, in passing that we may conceive that the particles of the ether" (Huygens, p. 14).
"But though we shall ignore the true cause of springiness we still see that there are many bodies which possess this property; and thus there is nothing strange in supposing that it exists also in little invisible bodies like the particles of the Ether. Also if one wishes to seek for any other way in which the movement of Light is successively communicated, one will find none which agrees better, with uniform progression, as seems to be necessary, than the property of springiness; because if this movement should grow slower in proportion as it is shared over a greater quantity of matter, in moving away from the source of the light, it could not conserve this great velocity over great distances. But by supposing springiness in the ethereal matter, its particles will have the property of equally rapid restitution whether they are pushed strongly or feebly; and thus the propagation of Light will always go on with an equal velocity." (Huygens, p. 15).
Huygens' light waves are formed by the motion of an ether that hardness forms a springiness which transfers the energy of the luminous source through a stationary ether in the formation of propagating light waves similar to the propagation of sound waves in air yet light propagates in vacuum that is void of matter which proves the propagation of light does not involve an ether. Furthermore, sound waves are formed by the interaction of air molecules that are propagating in random directions. The collective motion of interacting air molecules that exchange kinetic energies form sound waves yet a light ray is composed of massless optic particles that are not interacting and are propagating in a single direction at a constant velocity which conflicts with Huygens' sound wave analogy.
Huygens states the ether propagates through glass, water or mercury and exists within the glass vacuum tube.
"This may be proved by shutting up a sounding body in a glass vessel from which the air is withdrawn by the machine which Mr. Boyle has given us, and with which he has performed so many beautiful experiments. But in doing this of which I speak, care must be taken to place the sounding body on cotton or on feathers, in such a way that it cannot communicate its tremors either to the glass vessel which encloses it, or to the machine; a precaution which has hitherto been neglected. For then after having exhausted all the air one hears no Sound from the metal, though it is struck. One sees here not only that our air, which does not penetrate through glass, is the matter by which Sound spreads; but also that it is not the same air but another kind of matter in which Light spreads; since if the air is removed from the vessel the Light does not cease to traverse it as before. And this last point is demonstrated even more clearly by the celebrated experiment of Torricelli, in which the tube of glass from which the quicksilver has withdrawn itself, remaining void of air, transmits Light just the same as when air is in it. For this proves that a matter different from air exists in this tube, and that this matter must have penetrated the glass or the quicksilver, either one or the other, though they are both impenetrable to the air. And when, in the same experiment, one makes the vacuum after putting a little water above the quicksilver, one concludes equally that the said matter passes through glass or water, or through both." (Huygens, p. 11 & 12).
Huygens' wave theory of light is based on light waves formed by the motion of an ether, composed of matter yet light propagates in vacuum that is void of matter which contradicts Huygens' wave theory of light; consequently, Huygens states that the ether, composed of matter, propagates through glass, water or mercury that is producing the vacuum of Torricelli's glass vacuum tube but the ether propagating through glass would produce a hole in the glass or shatter the glass and the ether propagating through mercury or water would be detectable; henceforth, light propagating through the glass vacuum tube proves the propagation of light does not involve Huygens' ether.
Huygens describes spherical waves that originate from a candle flame (fig 3).
"I have then shown in what manner one may conceive Light to spread successively, by spherical waves, and how it is possible that this spreading is accomplished with as great a velocity as that which experiments and celestial observations demand. Whence it may be further remarked that although the particles are supposed to be in continual movement (for there are many reasons for this) the successive propagation of the waves cannot be hindered by this; because the propagation consists nowise in the transport of those particles but merely in a small agitation which they cannot help communicating to those surrounding, notwithstanding any movement which may act on them causing them to be changing positions amongst themselves.
But we must consider still more particularly the origin of these waves, and the manner in which they spread. And, first, it follows from what has been said on the production of Light, that each little region of a luminous body, such as the Sun, a candle, or a burning coal, generates its own waves of which that region is the centre. Thus in the flame of a candle, having distinguished the points A, B, C, concentric circles described about each of these points represent the waves which come from them. And one must imagine the same about every point of the surface and of the part within the flame." (Huygens, p. 17).
Huygens' candle flame produces optical spherical waves, from points A, B and C, by the motion of an ether that does not exist (vacuum). Huygens dismisses the fact that light propagates in vacuum that is void of matter and describes the "agitation" of the ether particles that form Huygens' optical spherical waves but the existence of Huygens' candle flame spherical waves is contingent on the existence of an ether, composed of matter, that does not exist.
Huygens represents the propagation of light using spherical waves represented with partial waves that points C, C, C are used to construct the wave DCF (fig 4).
"There is the further consideration in the emanation of these waves, that each particle of matter in which a wave spreads, ought not to communicate its motion only to the next particle which is in the straight line drawn from the luminous point, but that it also imparts some of it necessarily to all the others which touch it and which oppose themselves to its movement. So it arises that around each particle there is made a wave of which that particle is the centre. Thus if DCF is a wave emanating from the luminous point A, which is its centre, the particle B, one of those comprised within the sphere DCF, will have made its particular or partial wave KCL, which will touch the wave DCF at C at the same moment that the principal wave emanating from the point A has arrived at DCF." (Huygens, p. 19).
Huygens' expanding spherical waves originate from points b, b, b, along the wave HI. The far points C, C, C, of the spherical waves are used to construct the wave DCF which represents Huygens' propagation mechanism of light but Huygens' wave HI is arbitrarily creating energy (spherical waves) which violates energy conservation.
Huygens describes a light beam using expanding spherical waves that structures are arbitrarily eliminated at the boundaries of a light beam.
"To come to the properties of Light. We remark first that each portion of a wave ought to spread in such a way that its extremities lie always between the same straight lines drawn from the luminous point. Thus the portion BG of the wave, having the luminous point A as its centre, will spread into the arc CE bounded by the straight lines ABC, AGE. For although the particular waves produced by the particles comprised within the space CAE spread also outside this space, they yet do not concur at the same instant to compose a wave which terminates the movement, as they do precisely at the circumference CE, which is their common tangent.
And hence one sees the reason why light, at least if its rays are not reflected or broken, spreads only by straight lines, so that it illuminates no object except when the path from its source to that object is open along such lines." (Huygens, p. 21).
A light beam has distinct borders represented with boundaries (fig 2). Huygens' expanding spherical waves would propagate outside the boundary lines and produce an intensity outside the light beam; consequently, Huygens arbitrarily eliminates the expanding spherical waves structures at the boundary lines ABC and AGE.
Huygens describes the transmission and reflection effects of light (fig 5 & 6) using spherical waves generated by the transmission and reflection surface AB.
"If one considers further the other pieces H of the wave AC, it appears that they will not only have reached the surface AB by straight lines HK parallel to CB, but that in addition they will have generated in the transparent air, from the centres K, K, K, particular spherical waves, represented here by circumferences the semi-diameters of which are equal to KM, that is to say to the continuations of HK as far as the line BG parallel to AC." (Huygens, p. 24).
Huygens' expanding spherical waves originate from points K, K, K, along the glass surface AB (fig 23) which represents the arbitrary creation of energy by the glass surface which violates energy conservation. In addition, Huygens' spherical waves that are used to construct the reflection wave NB (fig 4) have varying circumferences that would form an inconsistent amplitude along the constructed reflection wave. Furthermore, the points of the spherical waves that are used to construct the reflection wave, propagate different distances from the glass surface to the reflection wave which cannot form the reflection wave that requires all of the spherical wave points to arrive at the reflection wave NB simultaneously. The same problems occur in the construction of the transmission light wave NB (fig 5).