Faraday’s words.
There is a splendid ring of resolution about these words. Let us compare them with a notable utterance of Faraday:—
“The philosopher should be a man willing to listen to every suggestion, but determined to judge for himself. He should not be biassed by appearances; have no favourite hypothesis; be of no school; and in doctrine have no master. He should not be a respecter of persons, but of things. Truth should be his primary object. If to these qualities be added industry, he may indeed hope to walk within the veil of the temple of Nature.”
Tested by this severe standard, Mr. Chandler fails in no particular, least of all in that of industry.Chandler’s other work at this time. The amount of work he got through about this time was enormous, for besides the main line of investigation, of which we have only had after all a mere glimpse, he had been able to turn aside to discuss a subsidiary question with Professor Comstock; he had examined with great care some puzzling characteristics in the variability of stars; he computed some comet ephemerides; and he was preparing a new catalogue of variable stars—a piece of work involving the collection and arrangement of great masses of miscellaneous material. Yet within a few months after replying as above to Professor Newcomb’s criticism,His ultimate satisfactory solution. he was able to announce that he had found the key to the new puzzle, and that “theory and observation were again brought into complete accord.” We will as before listen to the account of this new step in his own words, but a slight preliminary explanation may help those unaccustomed to the terminology. The polar motion was found to be compounded of two independent motions, both periodic, but having different periods. Now, the general results of such a composition are well known in several different branches of physics, especially in the theory of sound.Interference of two waves. If two notes of nearly the same pitch be struck at the same time, we hear the resultant sound alternately swell and die away, because the vibrations caused by the two notes are sometimes going in the same direction, and after an interval are going exactly in opposite directions. Diagrammatically we should represent the vibrations by two waves, as below; the upper wave goes through its period seven and a half times between A and D, the lower only six times; and it is easily seen that at A and C the waves are sympathetic, at B and D antipathetic. At A and C the compound vibration would be doubled; at B and D reduced to insensibility. The point is so important that perhaps a numerical illustration of it will not be superfluous. The waves are now represented by rows of figures as below. The first series recurs after every 6, the second after every 7.
Fig. 8.
| First Wave | 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 |
| Second Wave | 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 |
| Combined Effect | 2 4 6 8 7 5 3 3 5 7 7 6 4 4 4 6 6 6 5 5 5 5 5 5 5 6 6 6 4 4 4 |
| Great disturbance. Calm. | |
| First Wave | 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 |
| Second Wave | 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 |
| Combined Effect | 6 7 7 5 3 3 5 7 8 6 4 2 4 6 8 7 5 3 3 5 7 7 6 4 4 4 6 6 6 5 5 |
| Great disturbance. |
Adding the two rows together, the oscillations at first reinforce one another and we get numbers ranging from 2 to 8 instead of from 1 to 4; but one wave gains on the other, until it is rising when the other is falling, and the numbers add up to a steady series of 5’s. It will be seen that there are no less than seven consecutive 5’s, and all the variation seems to have disappeared. But presently the waves separate again, and the period of great disturbance recurs; it will be seen that in the “combined effect” the numbers repeat exactly after the 42nd term. Now those unfamiliar with the subject may not be prepared for the addition of one physical wave to another, as though they were numbers, but the analogy is perfect.Illustration from ocean travel. Travellers by some of the fast twin-screw steamers have had unpleasant occasion to notice this phenomenon, when the engineer does not run the two screws precisely at the same speed; there come times when the ship vibrates violently, separated by periods of comparative stillness. Instances from other walks of life may recur to the memory when once attention is called to the general facts; but enough has been said to explain the point numbered (2) in the subjoined statement. To understand the rest, we must remember that if the two waves are not equal in “amplitude,” i.e. if the backward and forward motion is not the same in both, they cannot annul one another, but the greater will always predominate. Those interested in following the matter further should have no difficulty in constructing simple examples to illustrate such points. We will proceed to give Mr. Chandler’s statements:—
Chandler’s final formulæ.
“We now come upon a new line of investigation. Heretofore, as has been seen, the method has been to condense the results of each series of observations into the interval comprised by a single period, then to determine the mean epoch of minimum and the mean range for each series, and, finally, by a discussion of these quantities, to establish the general character of the law of the rotation of the pole. It is now requisite to analyse the observations in a different way, and discover whether the deviations from the general provisional law, in the last column of Table II., are real, and also in what manner the variation of the period is brought about. The outcome of this discussion, which is to be presented in the present paper, is extremely satisfactory. The real nature of the phenomenon is most distinctly revealed, and may be described as follows:—