190 SCIENCE PROGRESS 



Relativity has now to cover change of gauge as well as change 

 of co-ordinates, i.e. laws of nature in the form of our differential 

 equations of physics have to be invariant not only for arbitrary 

 transformation of co-ordinates but also for arbitrary variation 

 of gauges. The geometry of the world will now involve the 

 four gauge-coefficients ^a, as well as the ten frame-coefficients 

 gap. It is a much more complicated geometry, as anyone read- 

 ing Weyl's work discovers to his cost. But, parallel to 

 Einstein's physical assumption regarding the geometrical 

 quantities gap, Weyl has a physical assumption for his ^^ ; 

 they determine the electro-magnetic field ; they are, in fact, the 

 three vector-potential components and the scalar potential of 

 the field in Maxwell's theory. This assumption serves to bring 

 Weyl's generalised Riemann geometry into relation with 

 physical occurrences, in a fashion similar to that by which 

 Einstein brought Riemann's geometry into such relation. The 

 whole attractiveness of the theory rests at present on its 

 mathematical elegance and the feeling of pushing a particu- 

 lar method of investigation to still further bounds. No experi- 

 mental tests, such as those which contributed so signally to 

 the success of Einstein's own theory, seem available at the 

 moment ; although it is not impossible that the theory may one 

 day have some statements to make concerning the size of our 

 universe on the one hand, and the atomic nature of electricity 

 on the other, which might conceivably be investigated experi- 

 mentally. There is a possibility also that it may help to clear 

 up the vexed question of the Einstein displacement of the solar 

 spectral lines. 



PHYSICAL CHEMISTRY. By W. E. Garner, M.Sc, University College, 

 London. 



Monomolecular Reactions. — Daniels and Johnston {J.A.C.S., 

 1 92 1, 43, 53 and 72) have shown that the decomposition of 

 nitrogen pentoxide is a monomolecular reaction, which takes 

 place at room temperatures. It differs from the much discussed 

 gaseous monomolecular reaction, the decomposition of phos- 

 phine, in that it is not catalysed by the walls of the reaction 

 vessel. It is thus of considerable importance for the theory 

 of chemical kinetics. The " critical increment," or heat of 

 activation, is practically constant over the temperature range 

 of 12-5 to 65° C, and this is in agreement with the Arrhenius' 

 relation. The wave-length of the activating energy, calculated 

 in accordance with the theories of W. C. McC. Lewis and 

 Perrin, gives the value i-i6 fj,. Light of this wave-length is, 

 however, without action on N2O5 ; a result which is contrary 

 to the Lewis-Perrin theory but not in disagreement with the 

 treatment proposed by Tolman (J.A.C.S., 1920, 42, 2506). 



