CONTENTS. 



PAGE 



BlOGBAPHIOAL MEMOIR ix 



On the Foundations of the Theory of Probabilities .... I 



On the Method of Least Squares . 12 



Some Remarks on the Theory of Matter 38 



Remarks on the Fundamental Principle of the Theory of Probabilities 49 



Remarks on an Alleged Proof of the Method of Least Sqxtares . . 53 

 Note to a Former Paper on an Alleged Proof of the Method of Least 



Squares 62 



On some Properties of the Parabola 63 



On the Existence of a Relation among the Co-efficients of the Equation 



of the Squares of the Differences of the Roots of an Equation . 68 



On the Achromatism of Eye- Pieces of Telescopes and Microscopes . 71 

 On the Condition of Equilibrium of a System of Mutually Attractive 



Fluid Particles -75 



Mathematical Notes . . . .81, 92, 130, 142, 149, 157, 191, 223 



Variation of Node and Inclination . ...... 82 



Investigation of the Aberration in Right Ascension and Declination . 84 



On the Lines of Curvature on an Ellipsoid ..... 86 



On the Tautochrone in a Resisting Medium 94 



On the Integration of Certain Differential Equations. No. I. . 97 



No. II. . . 108 



Analytical Demonstrations of Dr Matthew Stewart's Theorems 118 



Note on a Definite Integral 124 



Remark on the Distinction between Algebraical and Functional Equa- 

 tions 126 



On the Solution of Functional Differential Equations . . . 132 



Evaluation of Certain Definite Integrals 14 3 



On the Evaluation of Definite Multiple Integrals .... 150 



Note on a Definite Multiple Integral 160 



Notes on Magnetism. No. 1 163 



No. II . 186 



On a Multiple Definite Integral 169 



On a Question in the Theory of Probabilities *73 



On the Balance of the Chronometer . . . . 180 



