Joseph Larmor

“ When a beam of radiation travels without suffering absorption, its temperature thus continues to be that of its source multiplied by the coefficient of emission of the source for that kind of radiation, this coefficient being less than unity except in the case of a perfect radiator; but when its intensity I falls by δI in any part of its path owing to absorption or other irreversible process, this involves a further fall of temperature of the energy of the beam and a rise of entropy which can be completely determined when the relation connecting μ−3Eλ with T and λ is known. ”

“ If we imagine a field of radiation to be enclosed within perfectly reflecting walls, then, provided there is no material substance in the field which can radiate and absorb, the constitution of the radiation in it may be any whatever, and it will remain permanent. ”

“ It is only the presence of material bodies that by their continued emission and absorption can transform the surrounding radiation towards the unique constitution which corresponds to their temperature. We can define the temperature of an isolated field of radiation, of this definite ultimate constitution, to be the same as that of the material bodies with which it would thus be in equilibrium. ”

“ According to the latter, for an indefinitely numerous system of molecules, with known properties and in given circumstances, there is a definite probability of the occurrence of each statistical distribution of velocities, or' say each “complexion” of the system, that is formally possible when all velocities consistent with given total energy are considered to be equally likely as regards each molecule; the distribution of greatest possible probability is the state of thermal equilibrium of the system, and the probability of any other state is a function of the entropy of that state. ”

“ The question of the temperature of a directed wave-train travelling through space, such as a beam of light, will come up later. The temperature of each constituent in a region of undirected radiation is thus a function of its wave-length and its intensity alone. It is the fundamental principle of thermodynamics, that temperatures tend to become uniform. ”

“ Experimental Knowledge.—Under the stimulus of Wien’s investigation and of improvements in the construction of linear thermophiles and bolometers for the refined measurement of the distribution of energy along a spectrum, the general character of the curve connecting energy and wave-length in the complete radiation at a given temperature has been experimentally ascertained over a wide range. At each temperature there is a wave-length hm of maximum radiation, which is displaced towards the ultra-violet as the temperature rises, and Wien's law of homology (§ 6) shows that λmT should be constant. ”

“ The point of Lord Rayleigh's argument was that, at any rate at low frequencies, the law of distribution would suggest an equable partition of the energy between temperature heat and radiant vibrations, and that therefore the energy of the latter should ultimately vary as T; and this prediction, which has thus been verified, may be grafted on to any formula that is in other respects appropriate. ”

“ The elasticity that transmits it may be assumed to be mathematically perfect: any slight loss in transit of the light from the most distant stars, which recent statistical comparisons of brightness with distance may possibly indicate, is to be explained far more suitably by the presence of nebulous matter than by any imperfection of the aether. The latter would thus be the one perfect frictionless medium known to us: it could not be such if it were constituted, like matter, of independent molecules. ”

“ The abstract statistical theory of entropy, which is here invoked, admits of generalization in a way which is a modification of that of Planck, itself essentially different from the earlier idea of Boltzmann. The molecules of matter, whose interactions control physical phenomena, including radiation, are too numerous to be attended to separately in our knowledge. ”

“ Elements of energy of specified types might at first sight constitute such classes: but the identity of a portion of energy cannot be traced during its transformations, while an element of physical disturbance can be definitely followed, though its energy changes by interaction with other elements as it proceeds. ”

“ A molecule of matter is a kinetic system compounded of simpler elements; its energy may be classified into constitutive energy essential to its continued existence, and vibratory energy which it can receive from or radiate away into aether. A piece of matter isolated in free aether would in time lose ag energy of the latter type by radiation ”

“ When it is a case of transverse waves in an elastic medium, reflected by an advancing obstacle, the origin of the working pressure is not so obvious, because we cannot easily formulate a mechanism for the advancing reflector like that of the lamina above employed. In the case of light-waves we can, however, imagine an ideal material body, constituted of very small molecules, that would sweep them in front of .it with the same perfection as a metallic mirror actually reflects the longer Hertzian waves. ”

“ Any directed quality in radiant energy increases its effective temperature. Splitting a beam into two at s reflecting and refracting surface diminishes the temperature of each part; it is true that if the reflecting surface were non molecular the operation could be reversed, but actually the reversed rays would encounter the reflecting molecules in different collocations, and could not (§ 11) recombine into the same detailed phase-relations as before. The direct solar radiation falling on the Earth is almost completely convertible into mechanical effect on account of its very high temperature ”

“ It has been remarked by Planck and by Thiesen that the coefficient of T4 in Stefan's law, and the value of λmT, are two absolute physical constants independent of any particular kind of matter, which in conjunction with the constant of gravitation would determine an entirely absolute system of physical units. ”

“ The frequencies of the series of very close lines which constitute a single band in a banded spectrum are connected by a law of quite different type, namely, in the simpler cases n2= A−Bm2. It may be remarked that this is the kind of relation that would apply to a row of independent similar vibrators in which the neighbours exert slight mutual influence of elastic type. If ξ denote displacement and x distance along the row, the equation d 2ξ/dt2+k2ξ=−gd 2ξ/dx2 would represent the general features of their vibration, the right-hand side arising from the mutual elastic influences. ”

“ Considering electric radiation incident at angle L, the tangential electric force is annulled at the reflector; hence the amplitude of the electric vibration is conserved on reflexion, though its phase is reversed. As already seen, the wave-length is shortened approximately by the fraction 2U cos L/c in each reflexion; thus, just as in § 2, the energy transmitted per unit time per unit area is increased in the same ratio ”

“ But in a material medium under the influence of a strong magnetic field these equations are altered by the addition of extraneous terms involving differential coefficients of the third order, and the dynamical consistency of the cardinal principle of the theory of exchanges is no longer thus directly verified. A system of this kind has, in fact, been imagined by Wien in which the principle is imperfectly fulfilled. ”

“ When the radiation in a spectrum is constituted of wide bands it may on these principles be expected to be in equilibrium with a lower temperature than when it is constituted of narrow lines, if the total intensity is the same, in the cases compared ”

“ When we are dealing with the natural radiation in an enclosure, which is distributed equally in all directions, this factor .COSZL must be averaged; and we thus attain Boltzmann's result that the radiant pressure is then one-third of the density of radiant energy in front of the reflector, this statement holding good as regards each constituent of the natural radiation taken separately. ”

“ If we consider a finite train of waves thus sent back from a moving reflector, the time integral of the pressure must represent force transmitted along the cord, or a gain of longitudinal momentum in the reflected waves, or both together. ”

“ Now suppose that the constitution of the enclosed radiation corresponded initially to a definite temperature. During the shrinkage thermal equilibrium must be maintained among its constituents; otherwise there would be a running down of their energies towards uniformity'of temperature, if material radiating bodies are present, which would be superposed on the mechanical operations belonging to the shrinkage, and the process could not be reversible. Such a state of affairs is not possible, for it would land us in processes of the following type. ”

“ There is thus ground for the view that the impacts of the colliding molecules in a gas, or rather their mutual actions as they swing sharply round each other in their orbits during an encounter, may not be sufficiently violent to excite sensibly the free vibrations of the definite periods belonging to the molecules. ”

“ He found that in the group of alkaline metals three series of lines exist, the so-called principal and two subordinate series. whose frequencies fit approximately into this formula, and that similar statements apply to other natural groups of elements; that the constant N is sensibly the same for all series and all substances, while no, and μ have different values for each; and that other approximate numerical relations exist. In each series the lines of high frequency crowd together towards a definite limit on the more refrangible side ”

“ But a closer examination removes this discrepancy. In order to make the system self-contained, reflectors must be added to' it, so as to send back into the sources the polarized constituents that are turned aside out of the direct line by the nicols. ”