CONTENTS. 



NOTICES AND ABSTRACTS OF MISCELLANEOUS 

 COMMUNICATIONS TO THE SECTIONS. 



Page 

 Correction of an error in this part of the Report for 1841 1 



MATHEMATICS AND PHYSICS. 



M. Bessel on the Astronomical Clock 1 



M. Jacobi on a New General Principle of Analytical Mechanics 2 



Professor Braschmann's Extract from a Memoir entitled " Considerations on 



the Principles of Analytical Mechanics" 4 



Dean or Ely on the Report of the Commissioners for the restoration of lost 

 standards of Weights and Measures, and upon their proposal for the intro- 

 duction of a Decimal System 8 



Professor Wheatstone's Letter to Colonel Sabine, on a New Meteorological 



Instrument g 



Mr. Follet Osler on the Application of the Principle of the Vernier to the 



Subdividing of Time 9 



Mr. E. J. Dent on the Longitude of Devonport 9 



on the Rate of Protected Chronometer Springs ^, 9 



on the Rate of a Patent Compensating Pendulum N 10 



on a New Chronometer Compensating Balance 10 



Sir W. Hamilton on a Mode of expressing Fluctuating or Arbitrary Func- 

 tions by Mathematical Formulae 10 



Mr. Moses Holden on a simple Method of arriving at the decimal part of the 

 Sine or Tangent below a second of a degree, to the , ; a th or x u 5 th part 



of it 10 



Mr. Anthony Peacock on Decimal Fractions 10 



Professor Nichol's Extracts from a Letter on the state of the Observatory at 



Glasgow (25th June 1842) 12 



Professor MacCullagh on the Mathematical Expressions which lead to an 



Explanation of all the ordinary Phenomena in Optics 12 



Sir David Brewster on a New Property of the Rays of the Spectrum, with 

 Observations on the Explanation of it given by the Astronomer Royal, on the 



Principles of the Undulatory Theory 12 



• on the Dichroism of the Palladio-chlorides of Potas- 

 sium and Ammonium 13 



on the existence of a New Neutral Point, and two 



Secondary Neutral Points 13 



Professor Powell on certain Cases of Elliptically Polarized Light 13 



Sir David Brewster on Crystalline Reflexion 13 



Professor Bessel on a very curious fact connected with Photography, dis- 

 covered by M. Moser of Kbnigsberg, communicated to Sir D. Brewster 14 



Sir David Brewster on the Dichroism of a Solution of Stramonium in 



.<Ether 14 



— on the Geometric Forms, and Laws of Illumination 



of the Spaces which receive the Solar Rays, transmitted through Quadrangu- 

 lar Apertures 15 



— on Luminous Lines in certain Flames corresponding to 



the defective Lines in the Sun's Light 15 



; — ■ on the Structure of a Part of the Solar Spectrum 



hitherto unexamined 15 



