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ESSENCE OF PHYSICAL
RELATIVITY. -In an
important investigation recently reported, Mr. Leigh Page has determined an expression for the translatory force required to sustain an assigned varying velocity in an electrostatic system of a certain type, that namely which it has been usual to investigate as a model of an electron in analytical discussions. The expression contains terms involving the acceleration of the system and its time gradients, but no term involving its velocity except in combination with these other quantities. The application of his formula to which Mr. Page restricts himself is to challenge a result that an isolated radiating system is subject to retarding force from the reaction of its own radiation of amount equal to its velocity multiplied by rate of radiation divided by c2. The necessity for such refutation is based on the idea that on principles of relativity the velocity of an isolated body could have no meaning. But the formula obtained seems to leave this question as it was: for equally the acceleration of the isolated body could have no meaning; and moreover, though the thrust of the radiation is, in this case compensated, the velocity appears to be actually involved in the formula in the same manner as the impugned result would require for this partieular problem of a convected electrostatic system, for which the radiation is extremely transient and very slight in the absence of extraneous force.
It has always seemed to me that this subject, which may be
described as that of interaction of the æther with uniform motion, though of slight account phenomenally, is theoretically of high significance, in that it is destined perhaps to throw light on the nature of the forward momentum that is convected by radiation, and thence on the intimate dynamical nature of radiation itself and the physical function of the æther. I therefore propose briefly to indicate what I hold, provisionally of course, to be their present trend of knowledge.
The true essence of the relativity of external knowledge is that we can investigate a system only in relation to some other system, and the most convenient perhaps the only feasible other system has been hitherto the ideal Newtonian frame of reference of space and time; for that is the canonical system, so to speak, with regard to which dynamical principles take on an ideal simple form, and it is a system which is being determined with continually expanding precision by the progress of astronomical science.
The special question now in evidence is Is it now expedient to exchange this frame of reference, corresponding to c infinite, for another far more complex but very slightly different continuum having a finite space-time modulus ? The more fundamental question is Are we to assign to either frame dynamical properties, typified by propagation of physical effect in space in terms of undulations sustained by stress and inertia, or are we to assign to it properties solely geometrical and regard all physical effect as merely projected in duration across space? The forms of special unrestricted relativity which have been recently current ultimately demand and perhaps prefer the latter course; and such modes of expression can apparently be elaborated so as to include most of optics, though perhaps in an artificial and unfruitful manner, if we replace the Newtonian scalar corpuscles of light by projected vector elements of fields of potential (not however conserved in value) from which forces would be analytically derivable. Mr. Page's work has improved very remarkably such a scheme of projected influence by showing that, provided c-relativity is postulated for space and time, it is ele
ments of longitudinal electric force that may be regarded as projected from the sources, and are moreover conserved after the manner of quanta as they travel onward.
There is no absolute criterion to decide between the two ideals. The first order of ideas has proved itself as the foundation on which the interlaced fabric of electric and optical science has been actually constructed: the other seems to offer as yet only somewhat ingenuous and disjointed though significant expression for certain striking features of recent discovery which the former has not yet succeeded in assimilating, and seems to require us to obliterate the course of evolution of the science or perhaps to retain it as a mere historical survival.
All these modes of restatement of departments of physical science in more expressly relative terms may be comprehended as partial analytic developments of the far wider principle of the purely relational character of our external knowledge, which was advanced and systematically fortified with great abstract force in the general metaphysical domain by Bishop Berkeley; a principle by means of which he passed on to examine the criterion of real objective existence, and one which was well understood in its present aspect by his friends in Yale College nearly two centuries ago.
Thus in these matters we are hardly concerned with refuting any theory, for all are relative; it is fruitless to traverse any proposition, unless we take into account the definitions and context in which it subsists. The question is, as to which scheme of formulation gives as a whole the closest and most expressive representation of the complex of natural knowledge, and affords. the most promising clue to its future elaboration and extension. But a choice does not by any means preclude development along other promising but provisional lines for which an interpretation has yet to be found.-SIR JOSEPH LARMOR, Cambridge, England, Proceedings of the National Academy of Sciences,' U.S.A., November, 1918.
J. R. C.
NOTES AND QUERIES
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APPARENT SIZE, STELLAR MAGNITUDE
1. How are the "apparent" sizes of the heavenly bodies measured? Example, Jupiter 40" diameter.
2. What is the "star magnitude" of Jupiter's sixth and seventh satellites? - F. KERR, Alexandria.
1. The apparent distance between two points in the sky (such as two stars, or the opposite ends of the diameter of a planet) is the angle between the rays of light which come from those two points and meet in the eye. It is measured by means of a micrometer in the eyepiece of a telescope, a description of which will be found in any work on astronomy.
However the method can be illustrated in a simple way. Suppose we wish to determine the apparent diameter of the full moon. Stick a 5-cent silver coin on a wire and then move back from it until the coin just covers the moon's disc; then get some one to measure the distance of the coin from the eye. It will be about 70 inches; and the diameter of the coin is about 5g inch. Now draw a circle on a sheet of paper and suppose its radius to be 70 inches, and inragine the eye at the centre of it. If now we take a portion of the circumference 58-inch in length and draw straight lines from its two ends to the centre, the angle between these radii will be the "angular diameter" of the moon, and we can calculate it in this way. The diameter of the circle is 140