July 13, 1905] 



NA TURE 



26r 



in ihree divisions : — The graduate department, in which 

 arrangements are made ior the instruction of advanced 

 students in the higher branches of science and literature ; 

 the medical department, in which students (men and 

 women) who have already received a liberal education 

 are received as candidates for the degree of M.D., and 

 in which doctors of medicine may attend special courses ; 

 the collegiate department, in which students receive a 

 liberal education leading to a degree. The Armour In- 

 stitute of Technology was founded in 1892, and the work 

 of instruction was begun in September, 1893. Courses are 

 now offered in mechanical engineering, electrical engineer- 

 ing, civil engineering, chemical engineering, fire protection 

 engineering, general science, and architecture, and all lead 

 to the degree of Bachelor of Science. 



In the course of an address on degree day, July 8, at 

 the University of Liverpool, Lord Derby, the chancellor, 

 said that since they last met they had several new 

 laboratories, some complete and some in progress. Another 

 building, to be opened in November, will be for the study 

 of natural history. They had also an extension to record 

 of the chemical laboratories, to provide accommodation 

 for the department of physical chemistry, and an addition 

 to the existing department. This had been provided at an 

 estimated cost of 10,500?., which the president of the 

 council, Mr. E. K. Muspratt, had promised to contribute. 

 Since they last met 10,000/. had been given by Mrs. 

 Barrow, the borough of BirUenhead had given an annual 

 grant of 500/., and a grant of 10,000!. had been received 

 from the Liverpool City Council, looo/. from the county 

 of Lancaster, from Cheshire 300/., and from, the borough of 

 Bootle 5ooi. The sum of 1500/. had been given to endow 

 a lectureship in memory of Sir William Mitchell Banks. 

 Mr. E. Whitley had promised 1000!., and under the will 

 of the late Mr. J. L. Bowes the LIniversity would receive 

 a legacy of Soooi. for the benefit of the department of 

 chemistry and other purposes. The company subsequently 

 proceeded to the new electrotechnical laboratory, and Sir 

 Joseph Swan formally opened the building, which he 

 described as eminently suited for the purpose for which 

 it was intended. The cost of the laboratory has been 

 defrayed by a sum of 12,000/., drawn from the university 

 fund, and the Lancashire County Council has contributed 

 1000/. towards meeting the more pressing demands for 

 equipment. 



SOCIETIES AND ACADEMIES. 



LoNnoN. 



Royal Society, May 18. — " On the Chemical Mechanism 

 of Gastric Secretion." By J. S. Edkins. 



June 8. — " On the Application of Statistical Mechanics 

 to the General Dynamics of Matter and Ether." By 

 J. H. Jeans. Communicated by Prof. J. Larmor, Sec.R.S. 



The object of the paper is to apply the methods of 

 statistical mechanics to questions connected with radiation 

 and the energy of the ether. An attempt is made to 

 examine whether or not the modern theory of thermo- 

 dynamics of radiation can be regarded as resting on sound 

 dynamical principles. The result arrived at is that the 

 use made of the second law of thermodynamics in this 

 theory, in particular in the proof of Stefan's law, is one 

 which cannot be justified, and hence that those parts of 

 the theory of thermodynamics of radiation which are based 

 upon the use of the second law must be regarded as 

 unsound. 



The problem is obtained in its simplest form by con- 

 sidering either a finite universe, or else a finite portion 

 of an infinite universe, enclosed within a perfectly reflect- 

 ing boundary. Let the number of degrees of freedom of 

 the matter inside this boundary, neglecting the interaction 

 with the ether, be N, so that there are 2N coordinates of 

 the aggregate system which very nearly represent motion 

 of matter only. The number N is known to be actually 

 finite, although it may be supposed to be so large that the 

 error involved in treating it as infinite will be negligible. 

 Let the number of degrees of the ether be M, giving 2M 

 coordinates to the aggregate system. If we suppose the 



NO. 1863, VOL. 72] 



ether to have an absolutely continuous structure, the 

 number M will be absolutely infinite. 



The energy of the 2M coordinates of the ether is ex- 

 pressible as a sum of 2M squares. The energy of the 

 2N material coordinates may, again neglecting small 

 terms, be divided into kinetic and potential energy. The 

 kinetic energy is expressible as a sum of N squares, namely, 

 the sum of the three components of energy of each electron 

 of which the matter is composed. Thus the total energy 

 is expressible as the sum of 2M-(-N squares, plus an 

 unknown potential energy of electrons. It now follows, 

 as in the proof of the well known theorem of equi- 

 partition of energy, that after an infinite time the sum 

 of any p of these squares stands to the sum of the remain- 

 ing q squares in a ratio which is equal to p/q, subject 

 only to the condition that p and q are large enough to 

 be treated as infinite without appreciable error. Since 

 2M and N satisfy these conditions, it follows that the 

 system tends towards a state in which the energy of the 

 ether is infinite in comparison with the kinetic energy 

 of the matter. In other words, there is a general tendency 

 for the ether to gain energy at the expense of matter. 



It is, however, obvious that our own universe is at 

 present far removed from its final state, so that the study 

 of this final state is of less interest than the study of the 

 stages through which the final state is being reached. 



In discussing the transition to the final state, a principle 

 proved elsewhere ("The Dynamical Theory of Gases," 

 chapter ix.) is of service. Suppose that a vibration of any 

 dynamical system is influenced by an external agency. 

 Then the principle in question asserts that the ultimate 

 effect of this influence is infinitesimal, except when the 

 external agency changes to a considerable extent in a time 

 comparable with the period of the vibration. If the time 

 of change in the external agency is n times the period 

 of the vibration, where n is large, then the ultimate change 

 in the energy of the vibration vanishes to the same order 

 as e-n, a quantity which soon becomes negligible as n 

 increases. 



Thus, if $ is some small interval of time, so small that 

 the material system may be regarded as perceptibly un- 

 altered through a time $, then the change produced in 

 the energy of ether vibrations of which the period is less 

 than will be very slight. The energy of such vibrations 

 may therefore be treated as though it were incapable of 

 change, so long as our consideration of the system does 

 not extend over a very long period. 



The total number of modes of vibration of any enclosed 

 or unenclosed piece of ether is, as has been said, either 

 very great or infinite, but the number of vibrations of an 

 enclosed piece of ether of which the frequencies are below 

 an assigned value is finite. Thus, we can now suppose M 

 replaced by some small number M', and the value of M' 

 will be finite. So long as we limit our consideration of 

 the system to a finite time, say a million years, we may 

 regard the energies of the remaining modes of vibration 

 as constant and very small. The ratio of ethereal to 

 material kinetic energy is now 2M'/N, a quantity which 

 cannot be infinite and may be very small. 



If 9 is a small time satisfying the conditions specified, 

 then the rate at which an ether vibration of high frequency 

 p gains energy will involve a factor e-''', so that the 

 time required for the vibration to acquire a perceptible 

 amount of energy will involve a factor ef". This is, of 

 course, only true when pO is large. The energy of those 

 vibrations for which pe is not large is rapidly adjusted, 

 and a state will soon be reached in which these vibrations 

 have the share of energy allotted to them by the theorem 

 of equipartition of energy. With the progress of time the 

 energy of the remaining vibrations gradually becomes per- 

 ceptible, until ultimately the final state is reached. 



We cannot, however, realise in nature the boundary 

 impervious to all forms of energy, so that it is important 

 to consider whether these predictions have to be modified 

 if the boundary, instead of being perfect, is simply as 

 perfect as we can make it. 



It is found that there is no longer any tendency for the 

 energy of the matter, even after infinite time, to vanish 

 in comparison with that of the ether inside the enclosure ; 

 the two tend to assume a finite ratio, although neither 

 of the actual energies can be permanent, as the system 



