CONTENTS. 



PART IV. 



PAGE 



N". XXXI. On a Netv Notation for expressing various Conditions and Equations in 

 Geometry, Mechanics, and Astronomy : by the Rev. M. O'Bbien, late 

 Fellotv of Cuius College, Professor of Natural Philosophy and Astronomy 

 in King's College, London 415 



XXXII. On the Principle of Continuity, in reference to certain Results of Analysis : 



by J. R. Young, Professor of Mathematics in Belfast College 429 



XXXIII. On the Theory of Oscillatory Waves ; by G. G. Stokes, M.A., Fellow of Pem- 



broke College 44 1 



XXXIV. On the Internal Pressure to which Rock Masses may be subjected, and its 



possible Influence in the Production of the Laminated Structure: by 



W. Hopkins, Esq., M.A., F.R.S., &c 456 



XXXV. On the Partition of Numbers, and on Combinations and Permutations : by 



Henry Wabbubton, M.A., M.P., F.R.S., F.G.S., formerly of Trinity 

 College 471 



XXXVI. On a Peculiar Defect of Vision : by Henry Goode, M.B., of Pembroke 



College 493 



XXXVII. Contributions towards a System of Symbolical Geometry and Mechanics : by the 



Rev. M. O'Brien, Professor of Natural Philosophy and Astronomy in 

 King's College, London, and late Fellow of Caius College, Cambridge 497 



XXXVIII. On the Symbolical Equation of Vibratory Motion of an Elastic Medium, 



whether Crystallized or Uncrystallized : by ike Rev. M. O'Brien, late 

 Fellow of Caius College, Professor of Natural Philosophy and Astronomy 

 in King's College, London 508 



XXXIX. A Theory of the Transmission of Light through Transparent Media, and 

 of Double Refraction, on the Hypothesis of Undulations : by the Rev. 

 J. CbalI/IS, M. a., Plumian Professor of Astronomy and Experimental 

 Philosophy in the University of Cambridge 524 



