CONTENTS. 



NOTICES AND ABSTRACTS OF MISCELLANEOUS 

 COMMUNICATIONS TO THE SECTIONS. 



MATHEMATICS AND PHYSICS. 



Page 



Professor Young on Diverging Infinite Series 1 



■ on a Principle in the Tlieory of Probabilities • 1 



Mr. Rawson on the Summation of Infinite Series 2 



Mr. J. J. Sylvkster on the Double Square Representation of Prime and Com- 

 posite Numbers •■ "■ 2 



Sir William R. Hamilton on a Theory of Quaternions 2 



The Astronomer Royal's Account of the State of the Reductions of the 



Planetary and Lunar Observations made at Greenwich 2 



Lieut. -Col. Everest on the Geodetical Operations of India 3 



The Astronomer Royal's Account of the Results of the Tide Observations on 



the Coast of Ireland 4 



Mr. J. Scott Russell on the Tides of the East Coast of Scotland 6 



Professor MacCullagh on an attempt lately made by M. Laurent, to explain 



on mechanical principles the Phsenomenon of Circular Polarization of Liquids. 7 

 Rev. Professor Powell on certain points connected with Elliptic Polarization 



of Light 7 



Rev. M. O'Brien on the Propagation of Waves in a Resisted Medium> with a 

 new Explanation of the Dispersion and Absorption of Light, and other Opti- 

 cal Phsenomena ^ 8 



Mr. Oliver Byrne's Account of a new Proportional Compass 8 



Mr. E. J. Dent on the Shape of the Teeth of the Wheels of the Clock in the 



New Royal Exchange 8 



Sir David Brewster's Notice explaining the Cause of an Optical Phsenotnenon 



observed by the Rev. W. Selwyn 8 



• Account of the Cause of the Colours in precious Opal... 9 



Notice respecting the Cause of the beautiful White Rings 



which are seen round a luminous body when looked at through certain speci- 

 mens of Calcareous Spar 9 



on Crystals in the Cavities of Topaz, which are dissolved 



by Heat and re-crystallized on Cooling 9 



Professor Wheatstone on a singular Effect of the Juxtaposition of certain 



Colours under particular circumstances 10 



Sir David Brewster on the same Subject 10 



■ on the Accommodation of the Eye to Various Distances . 10 



■ 's Account of a series of Experiments on the Polarization of 



Light by rough surfaces, and white dispersing surfaces 11 



Mr. J. Scott Russell on the Nature of the Sound Wave 11 



Mr. John Goodman on the Analogy of the Existences or Forces, Light, Heat, 



Voltaic and ordinary Electricities 11 



Rev. William Scoresby on a new Process of Magnetic Manipulation, and its 



Action on Cast Iron and Steel Bars 12 



Mr. E. J. Dent on a new Steering and Azimuth Compass 12 



Sir John F. W. Herschel's Contributions to Actino-Chemistry. On the 

 Amphitype, a new Photographic Process 12 



