# On a method for making the wave length of sodium light the actual and practical standard of length

Journal of the Association of Engineering Societies, Volume 7, No. 5 (May 1888), pp. 153-160; read December 1887
ON A METHOD FOR MAKING THE WAVE LENGTH OF SODIUM LIGHT THE ACTUAL AND PRACTICAL STANDARD OF LENGTH.
By Profs. Albert A. Michelson and Edward W. Morley, Members of the Civil Engineers' Club of Cleveland.
[Read December 27, 1887.]
Abridged.
The first actual attempt to make the wave length of sodium light the standard of length was made by Pierce. This method involves two distinct measurements. First, of the angular displacement of the image of a slit by a, diffraction grating; second, of the distance between the lines of the grating. Both of these are subject to errors due to temperature changes and instrumental errors. The results of this work have not as yet been published, but it is probable that the degree of accuracy attained is not much greater than one part in 50 or 100 thousand.
More recently Mr. Bell, of the Johns Hopkins University, using Rowland's gratings, has made a determination of the length of the wave of sodium light which is claimed to be accurate to one two-hundred thousandth. If this claim is justified, it is probably very near to the limit of accuracy of which the method admits.
A short time before this another method was proposed by Macé de Lepinay. This consists in the calculation of the number of wave lengths between two surfaces of a cube of quartz. Besides the spectroscopic observations of "Talbot's fringes," the method involves the measurement of the index of refraction and of the density of the quartz, and it is not surprising that the degree of accuracy attained was only one in fifty thousand.
Several years ago a method suggested itself which seemed likely to furnish results much more accurate than either of the foregoing, and ​some preliminary experiments made in June last have confirmed the anticipation.
The apparatus for observing the interference phenomena is the same as that used in our experiments "on the relative motion of the earth and the ether."
Light from the source at s, a sodium flame, falls on the plane glass a, and is divided, part going to the plane mirror c, the rest to plane mirror b. These two pencils are returned along c a e and b a e, and the interference of the two pencils is observed in the telescope at e.
The distances a c and a b being made equal by moving the mirror b, and the plane of c being made parallel with the image of b in a, and the compensating glass d interposed, the interference is at once visible.
If the adjustment is exact, the whole field will be dark (since one pencil experiences internal reflection at a and the other external).
If now b be moved parallel with itself a measured distance by the micrometer screw, the number of alternations of light and darkness is exactly twice the number of wave lengths in the measured distance.
Thus the determination consists absolutely of a measurement of length and the counting of a number.
The degree of accuracy attainable depends on the number of wave lengths which it is possible thus to count. Fizeau was able to observe interference when the difference of path amounted to 50,000 wave lengths.
It seemed probable that with a smaller density of sodium vapor this number might be increased, and the experiment was tried with sodium in an exhausted tube provided with aluminium electrodes, and it was found possible to increase this number to over 200,000. But it is very easy to estimate tenths or even twentieths of a wave length, which means that it is possible to find the number of waves in a given fixed ​distance between two planes, with an error less than one in two millions, and probably one in ten millions.
But the distance corresponding to 400,000 wave lengths is roughly a decimeter, and this cannot be determined or reproduced more accurately than, say ${\tfrac {1}{500000}}$, so that it would be necessary to increase this distance. This can be done by using the same instrument, together with a comparator.
The intermediate standard decimeter a b is put in place of the mirror b; a b is a piece of cast iron, c and d are plane glass mirrors, c rests on the points of three studs, d rests on the points of three screws, c and d are made exactly parallel and the distance c d is made conveniently near to some aliquot part of the meter.
The end c is now adjusted till colored fringes appear in white light. These can be measured to within one twentieth of a wave length (probably within one-fiftieth).
The piece a b is then moved forward till the fringes appear again at d; then the refractometer is moved in the same direction till the fringes appear again at c, and so on till the whole meter has been stepped off.
Supposing that in this operation the error in the setting of the fringes is always in the same direction, the whole error in stepping of the meter would be one in two million.
By repetition, this would of course be reduced.
A microscope attached to the carriage holding the piece a b would serve to compare, and a diamond attached to the same piece would be used to produce copies.
All measurements would be made with the apparatus surrounded by melting ice, so that no temperature corrections will be needed.
Probably there would be considerable difficulty in counting 400.000 wave lengths, but this can be avoided by first counting the number of waves and fractions in a length of one millimeter and using this to 'step off' a centimeter. This will give the nearest whole number of waves, and the fractions may be observed directly. The centimeter is then used in the same way to 'step off' the decimeter, which again determines the nearest whole number, the fractions being determined directly as before.
These fractions are determined as follows:
The fringes observed in the refractometer under the conditions above mentioned can readily be shown to be concentric circles. The center has the minimum intensity when the difference in the distances a b, a c is an exact number of wave lengths. The diameters of the consecutive circles vary as the square roots of the corresponding number of waves. Therefore, if x is the fraction of a wave to be determined, and y the diameter of the first dark ring, d being the diameter of the ring corresponding to one wave length, then $x={\tfrac {y^{2}}{d^{2}}}$.
There is a slight difficulty to be noted in consequence of there being two series of waves in sodium light. The result of the superposition of ​these is that, as the difference in path increases, the interference becomes less distinct, and sometimes finally disappears, reappears and becomes most distinct again when the distance is an exact multiple of both wave lengths.
Thus there is an alternation of clear interference fringes with uniform illumination or less clear interference fringes, and if the length to be measured, the centimeter for instance, is such that the interference does not fail exactly in the middle of the series but say a tenth of the distance to one side, there will be an error of one-twentieth of a wave length, which is of the same order as the error of observation.
Among other substances tried in these preliminary experiments were thallium, lithium and hydrogen, all of which gave interference up to 50 or 100 thousand wave lengths, and could therefore all be used as checks on the determinations with sodium.
It may be noted that in the case of the red hydrogen light, the interference phenomena disappeared at about 15,000 wave lengths and again at about 45,000 wave lengths. So that the red hydrogen line must be composed of two lines about one-sixtieth as distant as the sodium lines.
DISCUSSION.
Mr. C. G. Force: Is the change from the black spot to the white instantaneous?
Prof. Morley: No, it is gradual.
Mr. Force: Then the coincidence of the two planes is a matter of judgment.
Prof. Morley: It is; but the limits of possible error of judgment are very narrow. A motion of one plane by the hundred thousandth of an inch produces all the gradations from blackness to maximum light and blackness again. It is hardly possible to err in judgment by one tenth of this quantity, or the millionth of an inch. But if so much dependence on the judgment of the observer be deprecated, we can use micrometric measurement, and then we can trust the mean of repeated measurements even to the hundredth of a wave length, or the fifty millionth of an inch. In some observations made by use of interference phenomena (though for a very different purpose), we made the mean of our measurements 42 per cent, of a wave length, and found that the true value was 43, so that our measurements were within one per cent, of a wave length.
Prof. A. Michelson: Permit me to state that Professor Morley has given me more than my due in attributing so large a share of this work to me. Without his assistance, our present results would never have been attained.
You will observe that if we are to make our measurements, say to within one part in 10 or 20 millions, it would be an absurdity to allow the surfaces to be in error by more than the same quantity. That would mean that the surfaces must not be anywhere different from a plane more than one five hundred thousandth of an inch. So far such surfaces have not been made, no mechanician had been found who could do that work; but there is now one who will be enabled to do it, and he is Professor Morley.
Mr. Whitelaw: Do these fringes enable you to see the summit or depression of the waves of light?
​Prof. Morley: The condition in which they appear when we count them may be described. Suppose our standard is adjusted so that its front mirror rigorously coincides with the image of the opaque mirror of the refractometer. This image becomes an immaterial plane of reference which we can move slowly till it coincides with the rear mirror of the standard, being throughout parallel to both. During this motion, interference fringes appear as alternate light and black circles, the one at the centre being a light or black spot of considerable size; the black or light circle outside the central spot moves inwards, taking its place, and the central spot vanishes; the other circles all move inwards at the same time. While the central black or white spot has become white or black, the immaterial reference plane has moved one quarter of a wave length; when it has again become black or white, the motion has been one half wave length. So if we count the returns of the blackness, we count the half wave lengths in the motion of our reference plane. The phenomenon is one very easy to count. I counted 4,500 wave lengths the first time I tried counting at all. If it were necessary a machine could be made to count them automatically, only needing the observer to verify the continuance of restoration of its adjustment during the process. It is as easy to count them as to count the black posts of a fence with a white background.
Mr. Warner: Can Professor Morley give us some familiar illustration of the magnitude of a wave length? He spoke the other day of a piece of split glass which would show all the colors of the rainbow.
Prof. Morley: Mr. Warner, I think, showed me a piece of glass cracked, but not broken apart. Looking at it in a proper light, a part of the light was reflected to the eye from the upper surface and a part from the lower surface of the fracture, and these two rays again united. We then got the colors of the rainbow due to interference. If you press the two parts enough to make one band of color take the place of the adjacent band of the same color, you have compressed the glass by one half wave length.
Mr. Force: You said that the temperature did not affect the measurements by this method; was that on account of your using a vacuum in counting wave lengths?
Prof. Morley: The wave length in a vacuum is the same at any temperature. It is necessary to have a good vacuum; but that is easy to obtain.
Mr. Warner: You said that the waves first issuing from the source of light have the greater amplitude. Have they any greater length?
Prof. Morley: No increase in length has been detected. The first of a series of luminous vibrations emanating from a disturbed atom have a greater amplitude, just as the first vibrations from a musical instrument of percussion have the greater amplitude.
As spherical waves pass out from their source, they have work to do on a larger scale, therefore their amplitude decreases. Imagine that an atom of sodium in a flame suffers a collision which sets it in motion. It continues to vibrate, and like a piano string, with lessening amplitude; these vibrations are propagated outwards in all directions. As they pass outwards their amplitude decreases. Now a sodium atom may ​send out, according to our experiments, as many as 200,000 vibrations before it receives a new impulse, and begins to send out a new set of waves, with perhaps the original amplitude. These 200,000 waves make a length of four inches. Suppose we could see the disturbance in a straight line of ether particles made when the set of 200,000 waves was included between the distances 30 feet, and 30 feet 4 inches from the source. The waves at the head of this line would have an amplitude one per cent, less than they had when 30 feet from the source. But the waves at the rear end of this 4 inches might have an amplitude only one-half or one third of those at the head.
We can get interference only between waves of the same set; that is, waves sent out by a sodium particle, after receiving one impulse and before receiving another. And, further, we can observe interferences only while the amplitude of the waves of this set remains sufficient. So far we have been able to observe interferences up to 200,000 wave lengths, which enables us to count wave lengths up to 4 inches.
Prof. Michelson: An article received a week ago recorded experiments made in Germany. The intensity of the light was varied from 1 to 250. There was no variation perceived in wave length. If there was any variation, it must have been less than one part in 20 or 30 millions.
Mr. Eisenmann: Is it more easy to count long waves than short?
Prof. Michelson: The shorter they are, the more easily they can be used for our purpose; the error is less.
Prof. Morley: Practically we are limited by the fact that we must take light in which we can obtain a sufficient amount of monochromatic light. Sodium light is perhaps the most convenient.
I may add that the method promises to be fruitful. It will enable us to measure expansions with an accuracy and convenience not yet attained. For instance, we can compare the length of a bar before and after heating. We can compare bars at the freezing and boiling points by an immaterial scale, an immaterial standard of length which cannot alter. I will show you how we can measure the expansion of a bar.
We will surround the bar a with a tube enclosed in a jacket in which we can have either ice or steam, so that the bar can be heated or cooled to the desired temperature. Let b be a similar bar in a tube surrounded by ice, and so kept of constant length. The tubes c and d are exhausted of air. Between them at e we put the mirror of our refractometer. The air around it is so far from the hot or cold masses that it can be kept at a uniform temperature. Now our ray of light going from e to a and b is our immaterial scale, the two rays can be made exactly equal in length and are not affected by any amount of heat or cold.
​First, when a and b are both at the freezing point, we make the distances e f and e h equal, and measure the difference between distances e g and e k. Second, when a is at any desired temperature and b still at the freezing point, we make distances e f and e h again equal and again measure the difference between distances e g and e k. So we measure the expansion of bar a by a scale absolutely unaffected by temperature.
Another instance: The question how much a cubic inch of water weighs is one on which scientific men of different countries are not agreed. Different determinations of the weight of a cubic decimeter of water differed by 480 milligrammes or about one-twentieth of one per cent. The reason was not inaccuracy in weighing, but the fact that the dimensions of the body weighed in water cannot be accurately determined, but by our method we can now measure the dimensions of the body to be weighed in water, and may hope to better the determination of the relation between standards of length and of weight.
Mr. Eisenmann; How are the differences of the temperatures of the bars and their supports overcome? Are they assumed to be of the same temperature.
Prof. Morley: We assume nothing. When our two cold bars have remained motionless for some time, we measure their difference in length. If we change the temperature we wait till they become motionless again, and again measure the difference. We do not even assume equilibrium. We verify the fact that the bars are motionless on their supports by examination.
Mr. Eisenmann: When I was engaged upon the old method, defining some standards, we had sweat boxes in which the temperature differed several degrees. We were not allowed to remain in the chamber more than 15 minutes.
Prof. Michelson: In the case of all comparisons made heretofore, the difference between what the thing rested upon and the thing itself had to be taken into consideration. In our experiments we do not have to consider that.
Mr. Eisenmann: After you have measured the distance from c to d in Fig. 2, and determined the number of wave lengths, is that affected by the temperature? How long must it have been submitted to a constant temperature?
Prof. Morley: We like to have our standard in ice for 24 hours. But we assume nothing. We prove the length c lo d consists of a counted whole number of wave lengths and a fraction. The fraction can be measured in a very simple way by measuring with a micrometer the diameter of the interference fringe produced in sodium light. When this fraction remains constant, the length of the bar is constant. The observation required is as simple as the reading of a thermometer.
Mr. Eisenmann: I have observed that where the changes of temperature were sudden, a difference of 20 or 30 degrees, there was a set which was not overcome in 24 hours.
Prof. Morley: In our work our standard is first placed in an ice-box, in front of which is a refractometer. There we measure the fraction and count the whole number. When we have had it in there as long as may be required, we transfer it to our comparer, which is already in an icebox; ​so there are no changes of temperature suffered by our standard between the time when we measure its length in wave lengths and the time when we stop off its length for comparison with, or verification of some other standards.
Mr. Eisenmann: In measuring the base of the Lake Survey, of course we worked in all seasons, so that we were subject to great changes of temperature. When we brought our work into the operating room we found that even the thermometers had a set in the glass.
Mr. Whitelaw: Would not glass be better than metal for your standards?
Prof. Morley: We tried glass first, but the artists did not succeed in making the surface plane, and we tried metal.
* ↑ Nature, xx , p. 99 (1879); Amer. Journ. Sci. [3], p. 51 (1879).
* ↑ On the Absolute Wave-Lengths of Light," Amer. Journ. Sci. [3], xxxiii., p. 167 (1887); Phil. Mag. [5], xxiii., p. 365.
* ↑ Comptes Rendus, cii., p. 1,153 (1886): Journ. de Phys. [2], v., p. 411 (1886).
* ↑ [April, 1888.] With the light from Plücker tubes, containing vapor of mercury and thallium chloride, we have obtained interference with a difference of path of 540,000 and 340,000 wave-lengths respectively.
* ↑ [April, 1888.] The green thallium line has also been found to be composed of two lines about as close as in the red hydrogen line.
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