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X. On the Application of Fourier's Double Integrals to Optical Problems. 
By Charles Godfrey, B.A., Scholar of Trinity, Isaac Newton Student in the 
University of Cambridge. 
Communicated by Professor J. J. Thomson, F.P.S. 
Received June 12—Read June 15, 1899. 
Contents. 
Introductory : Page 
§§ 1-3. Natural Light. Representation by Circular Functions.331 
§ 4. Only Plane and Plane-polarised Light to be considered.331 
§5. Gouy on “ Luminous Motions ”.331 
§ 6. Fourier’s Double Integral .332 
§§ 7-8 Poincare’s Criticism. 333 
The Fundamental Theorem : 
c 
§§ 9-10. Schuster’s Theorem. 334 
§11. Discussion to be confined to “ Constant” Light.335 
§ 12. Our cognizance of Light is by effects averaged over a length of time which 
depends upon the means by which the Light is being detected .... 335 
§§ 13-17. All observable effects of Constant Light may be estimated by summing 
the effects of the monochromatic elements into which it is resolved 
by Fourier’s Double Integral.335 
Radiations composed of a random Aggregate of Pulses : 
§§ 18-20. Radiation of Incandescent Gas. Lommel’s theory of widening of 
spectrum lines as due to damping of molecular vibrations. Thomson’s 
theory of Rontgen pulses .338 
§21. The effect of a sequence of similar pulses as treated by Lord Rayleigh. . 339 
§ 22. Further questions suggested. Degree of crowding of the pulses .... 339 
§§ 23-27. The sequence of pulses will be equivalent to light of composition 
determined by the Fourier analysis of a single pulse, subject to the 
condition that there are many complete pulses in the smallest observable 
interval of time. Difficulty connected with long waves.339 
§ 28. Effective width of a pulse whose strict mathematical expression gives 
infinite width..342 
§ 29. Crowded pulses whose width is observable.342 
§ 30. Composition of aggregate of unequal pulses connected by a law.343 
VOL. CXCV.—A 271 2 IT 24.12.1900. 
