The Story of the Heavens

by Robert S. Ball

One of the most celebrated attempts to ascertain the distance of the sun is derived from a combination of experiments on the velocity of light with astronomical measurements. This is a method of considerable refinement and interest, and although it does not so fulfil all the necessary conditions as to make it perfectly satisfactory, yet it is impossible to avoid some reference to it here. Notwithstanding that the velocity of light is so stupendous, it has been found possible to measure that velocity by actual trial. This is one of the most delicate experimental researches that have ever been undertaken. If it be difficult to measure the speed of a rifle bullet, what shall we say of the speed of a ray of light, which is nearly a million times as great? How shall we devise an apparatus subtle enough to determine the velocity which would girdle the earth at the equator no less than seven times in a single second of time? Ordinary contrivances for measurement are here futile; we have to devise an instrument of a wholly different character.

In the attempt to discover the speed of a moving body we first mark out a certain distance, and then measure the time which the body requires to traverse that distance. We determine the velocity of a railway train by the time it takes to pass from one mile-post to the next. We learn the speed of a rifle bullet by an ingenious contrivance really founded on the same principle. The greater the velocity, the more desirable is it that the distance traversed during the experiment shall be as large as possible. In dealing with the measurement of the velocity of light, we therefore choose for our measured distance the greatest length that may be convenient. It is, however, necessary that the two ends of the line shall be visible from each other. A hill a mile or two away will form a suitable site for the distant station, and the distance of the selected point on the hill from the observer must be carefully measured.

The problem is now easily stated. A ray of light is to be sent from the observer to the distant station, and the time occupied by that ray in the journey is to be measured. We may suppose that the observer, by a suitable contrivance, has arranged a lantern from which a thin ray of light issues. Let us assume that this travels all the way to the distant station, and there falls upon the surface of a reflecting mirror. Instantly it will be diverted by reflection into a new direction depending upon the inclination of the mirror. By suitable adjustment the latter can be so placed that the light shall fall perpendicularly upon it, in which case the ray will of course return along the direction in which it came. Let the mirror be fixed in this position throughout the course of the experiments. It follows that a ray of light starting from the lantern will be returned to the lantern after it has made the journey to the distant station and back again. Imagine, then, a little shutter placed in front of the lantern. We open the shutter, the ray streams forth to the remote reflector, and back again through the opening. But now, after having allowed the ray to pass through the shutter, suppose we try and close it before the ray has had time to get back again. What fingers could be nimble enough to do this? Even if the distant station were ten miles away, so that the light had a journey of ten miles in going to the mirror and ten miles in coming back, yet the whole course would be accomplished in about the nine-thousandth part of a second—a period so short that even were it a thousand times as long it would hardly enable manual dexterity to close the aperture. Yet a shutter can be constructed which shall be sufficiently delicate for the purpose.

Fig. 63.—Mode of Measuring the Velocity of Light.

The principle of this beautiful method will be sufficiently obvious from the diagram on this page (Fig. 63), which has been taken from Newcomb's "Popular Astronomy." The figure exhibits the lantern and the observer, and a large wheel with projecting teeth. Each tooth as it passes round eclipses the beam of light emerging from the lantern, and also the eye, which is of course directed to the mirror at the distant station. In the position of the wheel here shown the ray from the lantern will pass to the mirror and back so as to be visible to the eye; but if the wheel be rotating, it may so happen that the beam after leaving the lantern will not have time to return before the next tooth of the wheel comes in front of the eye and screens it. If the wheel be urged still faster, the next tooth may have passed the eye, so that the ray again becomes visible. The speed at which the wheel is rotating can be measured. We can thus determine the time taken by one of the teeth to pass in front of the eye; we have accordingly a measure of the time occupied by the ray of light in the double journey, and hence we have a measurement of the velocity of light.

It thus appears that we can tell the velocity of light either by the observations of Jupiter's satellites or by experimental enquiry. If we take the latter method, then we are entitled to deduce remarkable astronomical consequences. We can, in fact, employ this method for solving that great problem so often referred to—the distance from the earth to the sun—though it cannot compete in accuracy with some of the other methods.

The dimensions of the solar system are so considerable that a sunbeam requires an appreciable interval of time to span the abyss which separates the earth from the sun. Eight minutes is approximately the duration of the journey, so that at any moment we see the sun as it appeared eight minutes earlier to an observer in its immediate neighbourhood. In fact, if the sun were to be suddenly blotted out it would still be seen shining brilliantly for eight minutes after it had really disappeared. We can determine this period from the eclipses of Jupiter's satellites.

So long as the satellite is shining it radiates a stream of light across the vast space between Jupiter and the earth. When the eclipse has commenced, the little orb is no longer luminous, but there is, nevertheless, a long stream of light on its way, and until all this has poured into our telescopes we still see the satellite shining as before. If we could calculate the moment when the eclipse really took place, and if we could observe the moment at which the eclipse is seen, the difference between the two gives the time which the light occupies on the journey. This can be found with some accuracy; and, as we already know the velocity of light, we can ascertain the distance of Jupiter from the earth; and hence deduce the scale of the solar system. It must, however, be remarked that at both extremities of the process there are characteristic sources of uncertainty. The occurrence of the eclipse is not an instantaneous phenomenon. The satellite is large enough to require an appreciable time in crossing the boundary which defines the shadow, so that the observation of an eclipse cannot be sufficiently precise to form the basis of an important and accurate measurement.[23] Still greater difficulties accompany the attempt to define the true moment of the occurrence of the eclipse as it would be seen by an observer in the vicinity of the satellite. For this we should require a far more perfect theory of the movements of Jupiter's satellites than is at present attainable. This method of finding the sun's distance holds out no prospect of a result accurate to the one-thousandth part of its amount, and we may discard it, inasmuch as the other methods available seem to admit of much higher accuracy.