Scientific Papers - Vi

I. MATHEMATICS
PAGE
ri
On the Values of the Integral QnQn'dp, Qn, Qn' being
• o
Laplace's Coefficients of the orders n, ri, with an application to the Theory of Radiation. Art. 3. 1870 . . Vol.1 21 On a Correction sometimes required in Curves professing to
represent the connexion between two Physical Magnitudes.
Art. 12. 1871......... ,,135
Notes on Bessel'a Functions. Art. 15. 1872 .... „ 140
Note on the Numerical Calculation of the Roots of Fluctuating
Functions. Art. 28. 1874......„ 190
A History of the Mathematical Theories of Attraction and the
Figure of the Earth from the time of -Newton to that of
Laplace. By I. Todhunter, M.A., F.R.S. Two Volumes.
(London, Macmillan & Co., 1873.) Art. 29. 1874 . • . „ 196 •
On the Approximate Solution of Certain Problems relating to
the Potential. I. Art. 39. 1876 ...... 272
Questions from Mathematical Tripos Examination for 1876.
Art. 41. 1876.........„ 280
On the Relation between the Functions of Laplace and Bessel.
Art. 61. 1878.....'. ,,338
A simple Proof of a Theorem relating to the Potential. Art. 54
1878...........,,347
On the Resultant of a large number of Vibrations of the same
Pitch and of arbitrary Phase. Art. 68. 1880 . 491
On Point-, Line-, and Plane-Sources of Sound. Art. 147. 1888 Vol. Ill 44 On James Bernoulli's Theorem in Probabilities. Art. 243.
1899...........Vol. IV 370
On the Acoustic Shadow of a Sphere. Art. 292. 1904. . Vol. V 149
Appendix. [Values of Legendre's Functions from PI to P20 at
intervals of 5 degrees] By Prof. A. Lodge .... „ 162
Note by Lord Rayleigh. [Approximate expression for Pn when
n is large]........... „ 164
The Problem of the Random Walk. Art. 307. 1905 . . „ 256
The Problem of the Whispering Gallery. Art. 348. 1910 . „ 617 Note on Bessel's Functions as applied to the Vibrations of a
Circular Membrane. Art. 350. 1911 .... Vol. VI 1 On a Physical Interpretation of Schlomilch's Theorem, in
Bessel's Functions. Art. 352. 1911.....,,22
Remarks concerning Fourier's Theorem as applied to Physical
Problems. Art. 369. 1912 ...... ,,131
On Conformal Representation from a Mechanical Point of View.
Art. 373. 1913 . ......,,153rs from that calculated, the reflexion is finite, and we may ask what it then becomes. If we denote the value of 8, as calculated from fa, k2, by $0, (24) gives