262 



NA TURE 



[July 13, 1905 



inside the enclosure is no longer a conservative system. 

 This definite ratio between matter and ether, however, 

 lends a meaning to the expression " radiation at a given 

 temperature," at any rate so long as we are concerned 

 with the same enclosure and the same enclosed matter. 



Stefan's empirical law states that the radiation is pro- 

 portional to the fourth power of the absolute temperature, 

 and Bartoli and Boltzmann have attempted to raise the 

 law to the level of a theoretical law. 



Their argument rests fundamentally upon the application 

 of Carnot's principle to the working of a heat engine, in 

 w-hich the working substance is the ether. 



Carnot's principle is, in effect, identical with the second 

 law of thermodynamics, and this in turn is a special case 

 of a special proposition in statistical mechanics. In the 

 present investigation the most general methods of statistical 

 mechanics are used, and the conclusion arrived at is 

 different from that of the second law. The general in- 

 vestigation ought, of course, to take precedence over the 

 attempted extension of the special case. It is, moreover, 

 easy to find the exact point at which the general argument 

 parts company with that used in the special case. In the 

 special case, we are dealing only with forms of material 

 energy such that there is an easy and rapid transfer of 

 energv to the final state. The increase of entropy in- 

 dicates simply the tendency to move towards this final 

 state, and Carnot's principle is seen to be a special case 

 of this general tendency in which it is supposed that the 

 working substance is at every instant in the final state 

 appropriate to its energy at that instant. When the ether 

 is in question, it is found that the transfer of energy 

 to vibrations of short wave-length, instead of being in- 

 finitely rapid, is, in point of fact, extremely slow, so that 

 we never have to deal with a final state at all. 



Moreover, it has to be assumed for Bartoli's argument 

 Ihat the energy of the working substance is a function of 

 only two independent variables, e.g. the temperature and 

 the density. This is not true in the case of an engine 

 in which ether is the working substance; the ether energy 

 is the sum of a number of vibrations of different wave- 

 lengths, and the number of vibrations which have to be 

 included in this sum \\'ill depend on the nature as well 

 as on the temperature of the matter with which the ether 

 is in communication. 



Again, in the proposed argument for Stefan's law, the 

 piston of the pump forms a moving boundary for the 

 ether. The action of such a pump w'ould change the 

 frequency of vibrations in the ether, and energy which at 

 one instant belonged to a vibration of one period would, 

 after passing through the pump, belong to a vibration of 

 some entirely different frequency. The energy of the 

 vibrations of high frequency no longer remains unaltered 

 and very small, for there is a transfer of energy to thee 

 vibrations at every stroke of the pump. The svstem will 

 rapidly assume the final state appropriate to the value of 

 this total energy, and this is a state in which the energy 

 of matter vanishes in comparison with that of ether. 

 Thus Bartoli's proof might be applicable to a universe in 

 which pumps of the kind assumed had an actual existence, 

 but has no application to our own universe in which the 

 vibrations of highest frequency do not come into plav at 

 all. 



It now appears that in attempting to obtain a law of 

 radiation in conformity with the analysis of the present 

 paper, we shall not be able to use anv method so general 

 as that of the second law of thermodynamics. The whole 

 question is not one of partition of energy, but of transfer 

 of energy. 



" The Microsporangia of Lvginodendron." Bv R. 

 Kidston, F.R.S. 



In a preliminary note a description was given of the 

 microsporangia of Sphenopteris (Lvginodendron) Honing- 

 hansi. Brongt. It had been thought by some that the 

 Telangium Scotti, Benson, might be the microsporangia 

 of Lyginodendron, but the discovery of sporangia possess- 

 ing all the characters of Crossotheca, ZeiUer, in organic 

 connection WMth the sterile foliage of Lyginodendron 

 [Sphenopteris Honinghausi) shows that Telangium Scotti 

 must belong to another plant. 



The members of the genus Crossotheca (of which several 

 NO. 1863, VOL. 72] 



species are known) had previously been regarded as true 

 ferns, but now they must be classed with the Pterido- 

 spermeae. The barren foliage of the species included in 

 Crossotheca is very varied, and though the majority of 

 the species possess sphenopteroid pinnules, one at least 

 bears pinnules of the pecopteroid type. 



In Sphenopteris (Crossotheca) Honinghausi each " fertile 

 lobe bore six to eight broadly lanceolate sharply-pointed 

 microsporangia. In the early condition the sporangia are 

 bent inwards, and form a small hemispherical bunch with 

 their apices meeting in the centre. At maturity the 

 sporangia spread outwards, when they appear as a fringe 

 hanging from the margin of the fertile pinnule, but are 

 in reality connected for some distance to its lower surface. 

 The microsporangia are bilocular, the parallel loculi being 

 only separated bv a narrow band of tissue. Dehiscence 

 took place by a longitudinal cleft which passes down the 

 inner surface of the sporangium in the line of the dividing 

 wall of the two loculi." 



The figure shows a penultimate pinna enlarged two 



times. The ultimate pinnx c and d bear sterile pinnules 

 at their base, above which are some fertile pinnules. These 

 latter, however, are better seen at e. 



It has previously been shown by Prof. Oliver and' Dr. 

 Scott that the " seed " of Sphenopteris Honinghausi is 

 the Lagenostoma Lomuxi of Williamson. Sphenopteris 

 Honinghausi is thus the first pteridosperm of which the 

 male and female organs are known. 



The specimens described were derived from the lo-foot 

 Ironstone-measures, Coseley, Dudley, which belong to the 

 Westphalian series of the Coal-measures, and were com- 

 municated to the author by Mr. H. W. Hughes. 



Royal Microscopical Society, June 21.— Mr. G. C. 

 Karop, vice-president, in the chair. — Dr. Lazarus-Barlow 

 exhibited and described a new form of warm stage, devised 

 by him, that could be heated by oil or gas. — Mr. Cecil 

 R. C. Lyster exhibited an improved form of warm stage, 

 heated by electricity.— Mr. C. L. Curties exhibited an 

 arrangement for obtaining dark ground illumination with 

 high powers, which had been suggested to him by a con- 

 trivance made by Leitz for attaining this object. He 

 showed Pleurosignni angulatum on a dark ground under a 

 I /12-inch oil immersion objective. — Mr. Rheinber^ 

 directed attention to an experiment showing that the ap- 



