Royal Society. 1S9 



has been done in the matter of determining the relations 

 between the coefficients of an equation corresponding to a 

 given amount and distribution of multiplicity in its roots. 



I ought to add, that my method enables me not merely to 

 determine the conditions of multiplicity, but also to decompose 

 the equations containing multiple roots into others free of mul- 

 tiplicity, z. e. to find, dpriori,\he values of the several quantities 



Moreover, other decompositions, not necessary to be enlarged 

 upon in this place, may be obtained with equal facility. 

 University College, London, or 58 Doughty Street. 

 [To be continued.] 



XXX. Proceedings of Learned Societies. 



ROYAL SOCIETY. 



[Continued from vol. xvii. p. 387] 

 Nov. 19, A PAPER was read, entitled. Supplement to a paper 

 1840. x\. "On the Theoretical Explanation of an apparent 

 new Polarity in Light;" by George B. Airy, Esq., M.A., F.R.S., 

 Astronomer Royal. 



In a paper published in the second part of the Philosophical 

 Transactions for 1840*, the author explained, on the undulatory 

 theory of light, the phsenoraena observed by Sir David Brewster, 

 and apparently indicating a new polarity in light. That explanation 

 was founded on the assumption that the spectrum was viewed out of 

 focus ; an assumption which corresponded with the observation of 

 the author and of other persons. But the author having, since the 

 publication of that memoir, been assured by Sir David Brewster that 

 the phaenomenon was most certainly observed with great distinct- 

 ness when the spectrum was viewed so accurately in focus that 

 many of Frauenhofer's finer lines could be seen, he has continued the 

 theoretical investigation for that case, which had been ornitted in 

 the former memoir, namely, when the spectrum is viewed in focus ; 

 and he has arrived at a result, which appears completely to recon- 

 cile the seemingly conflicting statements, and to dispel the obscurity 

 in which the subject had hitherto been enveloped. 



Nov. 26, 1840. — Description of the Electro-magnetic Clock. By 

 C. Wheatstone, Esq., F.R.S. 



The object of the apparatus forming the subject of this commu- 

 nication, is stated by the author to be that of enabling a single clock 

 to indicate exactly the same time in as many different places, distant 

 from each other, as may be required. Thus, in an astronomical 



• An abstract of which appeared in L, E. & D. Phil. Mag., vol. xvii. 

 p. 381.— Edit. 



