A Digitally Enlarged Printing To Include All Examples And Tables: Bernoulli's Problem Of The Oscillating Chain - Conduction Of Heat In A Solid Cylinder - Bessel's Astronomical Problem - Bessel's Differential Equation - Solution Of The Differential Equation - Functions Of Integral Order - Expansions In Series Of Bessel Functions - Semi-Convergent Expansions - The Zeroes Of The Bessel Functions - Fourier-Bessel Expansions - Complex Theory - Definite Integrals Involving Besel Functions - The Relation Of The Bessel Functions To Spherical Harmonics - Vibrations Of Membranes - Hydrodynamics - Steady Flow Of Electricity Or Of Heat In Uniform Isotropic Media - Propagation Of Electromagnetic Waves Along Wires - Diffraction Of Light - Miscellaneous Applications - Note On The Second Solution Of Bessel's Equation Which Vanishes At Infinity - Examples - Formulae For Roots Of Bessel And Related Functions - Explanation Of Tables - Bibliography - Graph Of J/0 And J/1

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