The Physics
Opus in profectus

The sixth place of decimals

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Some of the Objects and Methods of Physical Science

Convocation Address Delivered by
Head Professor Albert A. Michelson
The University of Chicago

The Proceedings of the Seventh University Convocation
July 2, 1894

It is never safe to affirm that the future of physical science has no marvels in store which may be even more astonishing than those of the past; but it seems probable that most of the grand underlying principles have now been firmly established and that further advances are to be sought chiefly in the rigorous application of these principles to all the phenomena which come under our notice. It is here that the science of measurement shows its importance — where quantitative work is more to be desired than merely qualitative results. It is an almost daily task of the scientific student and investigator to reply to queries concerning the practical use of such an extraordinary degree of refinement as is shown in almost every modern scientifically conducted experiment. It is frequently admitted that these uses are not practical — but I would not concede even this much. Two thousand years ago there was no occasion for divisions smaller than an inch. Two hundred years ago measurements smaller than one-sixteenth of an inch were required of only the most careful workmen. Twenty years ago — outside of scientific measurements — a thousandth of an inch was nil. Today an error of this magnitude in one of our modern engines would mean all the difference between success and failure. If now it be granted that for scientific work, upon which every important practical advance depends, the order of accuracy is from ten to one hundred times us great as this, who can say what will be required two hundred years — nay, twenty years hence? These are undoubtedly sufficiently weighty reasons for the time and care which are indispensable in properly conducted scientific work — but unquestionably, the most important reason of all is, that by such work, and such work alone, must we look for the steady onward march of science, by which alone truth is to be dug from its well and placed upon a foundation more solid and enduring than the pyramids.

An eminent physicist has remarked that the future truths of physical science are to be looked for in the sixth place of decimals. In order to make such results possible the student and investigator must have at his disposal the methods and results of his predecessors, must know how to gauge their value, and to apply them to his own work; and especially must he have at his command all the modern appliances and instruments of precision which constitute a well-equipped physical laboratory — without which results of real value can be obtained only at immense sacrifice of time and labor.

Some of the Objects and Methods of Physical Science. Albert A. Michelson. The Quarterly Calendar. Vol. III., No. 2. Whole No. 10 (August 1894): 12–15.

Light Waves and Their Uses

By A. A. Michelson
of the Department of Physics

The University of Chicago Press

Before entering into these details, however, it may be well to reply to the very natural question: What would be the use of such extreme refinement in the science of measurement? Very briefly and in general terms the answer would be that in this direction the greater part of all future discovery must lie. The more important fundamental laws and facts of physical science have all been discovered, and these are so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. Nevertheless, it has been found that there are apparent exceptions to most of these laws, and this is particularly true when the observations are pushed to a limit, i.e., whenever the circumstances of experiment are such that extreme cases can be examined. Such examination almost surely leads, not to the overthrow of the law, but to the discovery of other facts and laws whose action produces the apparent exceptions.

As instances of such discoveries, which are in most cases due to the increasing order of accuracy made possible by improvements in measuring instruments, may be mentioned: first, the departure of actual gases from the simple laws of the so-called perfect gas, one of the practical results being the liquefaction of air and all known gases; second, the discovery of the velocity of light by astronomical means, depending on the accuracy of telescopes and of astronomical clocks; third, the determination of distances of stars and the orbits of double stars, which depend on measurements of the order of accuracy of one-tenth of a second — an angle which may be represented as that which a pin's head subtends at a distance of a mile. But perhaps the most striking of such instances are the discovery of a new planet by observations of the small irregularities noticed by Leverier in the motions of the planet Uranus, and the more recent brilliant discovery by Lord Rayleigh of a new element in the atmosphere through the minute but unexplained anomalies found in weighing a given volume of nitrogen. Many other instances might be cited, but these will suffice to justify the statement that "our future discoveries must be looked for in the sixth place of decimals." It follows that every means which facilitates accuracy in measurement is a possible factor in a future discovery, and this will, I trust, be a sufficient excuse for bringing to your notice the various methods and results which form the subject matter of these lectures.

Light Waves and Their Uses. A. A. Michelson. Chicago: The University of Chicago Press (1903): 23–24.