172 Proceedings of the British Association. 



the rings being alternately dark and bright centered. This af- 

 forded a further field for the application of theory, and Mr. Airy 

 investigated a formula for the rings under these varying condi- 

 tions, with which the phenomena are in perfect accordance. 



Mr. Nasmyth presented a paper on the application of the law 

 of Definite Proportions to the Stratification of clouds, — prefacing 

 it with the remark, that he was first led to speculate on this sub- 

 ject, by observing the arrangement of clouds in fine weather ; 

 when, towards the horizon particularly, they may be seen ex- 

 tended in parallel bands or stripes. He conceived that the ex- 

 cess of vapor floating in the atmosphere beyond what the air 

 could combine with, formed clouds ; and that the air in each 

 electrical state, was capable of sustaining a definite proportion of 

 vapor, and consequently that the clouds of one class or descrip- 

 tion floated, (in what might be called a plane of equal electricity,) 

 at a uniform distance from the earth. 



Sir William Hamilton made a brief communication on a mode 

 of expressing fluctuating or arbitrary functions by mathematical 

 formula. The subject was illustrated by diagrams, and excited 

 great attention among the eminent men present. Prof. Jacobi 

 said that Lagrange stated it as his opinion that it was not possible 

 to express these functions by any mathematical formula. It ap- 

 peared however to him, that Sir W. Hamilton had shown that it 

 was possible. 



The following communications were also made to the section. 



On recurring Decimal Fractions, and a new species of Logarithms; by Mr. An- 

 thony Peacock. 



Observations on Oceanic Waves ; by Mr. W. Walker. 



General Considerations on the Analytic Theory of Equilibrium and Movement; 

 by Prof. Braschman, of Moscow. 



Report of the Commissioners for the restoration of lost standards of Weights 

 and Measures, and upon their proposal for the introduction of a Decimal System ; 

 by the Dean of Ely. 



On the meteorology of the Northern Atlantic and on the Southwest Monsoon of 

 India ; by Mr. Hopkins. 



On improved Permanent Magnets, and the modes of determining their powers, 

 with certain undescribed Phenomena in permanent magnets ; by Rev. Dr. Scoresby. 



On the Meteorology of the Province of Coorg in the Western Gats of India ; 

 by Col. Sykes. 



On the Magnetic Action of instantaneous currents of Electricity ; by Prof. Ma- 

 rianini. 



On the causes of the dissimilarity in the Frictional and Voltaic Electricities, 

 with remarks on the Decomposition of Water by the former, and on Magnetism ; 

 by Mr. Goodman. 



{To be continued.) 



