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cade earlier. It is possible that Strutt first met Maxwell when Maxwell was involved in the composition of the Cambridge Mathematical Tripos Examination in the late 1860s. They began to correspond on scientific and mathematical topics by May 1870 and interacted at the Liverpool BAAS meet- ing in September 1870. In December 1870, Maxwell wrote Strutt about the statistical nature of the second law of ther- modynamics and his idea of a superhuman “doorkeeper.” Figure 3 shows Strutt’s appearance at about that time. By May 1873, their relationship had progressed so that when Maxwell learned that Strutt was planning to write a book on acoustics, he wrote to him suggesting, “Why not call it The- ory of Sound?” (Harman, 1995), advice that Strutt followed (Rayleigh, 1877). To appreciate Maxwell’s early scientific in- fluence on Strutt, notice that Strutt’s first two publications (in 1869 and 1870) concern applications to electromagnetic phenomena of the analysis of field energy in Maxwell’s 1865 dynamical theory (Rayleigh, 1964). In the second edition of his Theory of Sound, Rayleigh added several sections ex- panding on Maxwell’s approach to “Electrical Vibrations.” Another example of Maxwell’s influence concerns Rayleigh’s application in Section 226 of his book of Maxwell’s graphical method of drawing field lines and equipotential curves to the construction of modal curves of vibrating plates. Maxwell, however, was also the beneficiary of early interactions with Rayleigh from his existing replies to Rayleigh’s letters from 1870 to 1872 that included discussions of the construction of streamlines for fluid flow (partially analogous for electrical current flow) and Rayleigh’s remarks on Maxwell’s Lagrang- ian approach to the dynamics of circuits (Harman, 1995).
Other interactions concern Maxwell's reviews of Strutt's manuscripts (Harman, 1995, 2002). The first of these is his review of Strutt (1871) on the improved analysis of the fre- quency of gas-filled acoustic resonators through the approx- imation of (in modern terminology) the radiation reactance. Strutt needed to approximate the kinetic energy of oscillat- ing flows of air close to the openings of air-filled resonators. To do this, he considered incompressible flow lacking fric- tion and extended an analogy with electrical current flow within conductors similar to one explored by Maxwell in the mid-1850s. Strutt was able to place bounds on the analogous electrical conductance problem and hence on the resonance frequency of interest. In his review, Maxwell was favorably impressed by the method, suggesting some improvements and additional applications including the estimation of elec- trical capacitance. It appears that Maxwell retained a copy of his review because the electrical applications of Strutt’s
Figure 3. Rayleigh’s self-portrait from the early 1870s scanned from a copy of Strutt (1924) owned by the present author.
method that he developed in Articles 102 and 306 of his Treatise (with acknowledgments) closely parallel aspects of his review. Neither Maxwell nor Strutt may have noticed at this time some similarities to William Thomson’s 1849 ap- proach to related calculations of hydrodynamic kinetic en- ergy (Harman, 1995). Maxwell also suggested in his review that Strutt consider the lowering of the natural frequency caused by the deficient rigidity of the container holding the oscillating volume of gas. Strutt included such a discussion in the publication (with acknowledgment to Maxwell), al- though he found the lowering to be negligible.
The aforementioned papers by Stokes, Rankine, and Strutt were reprinted in the ASA series Benchmark Papers in Acous- tics in the 1970s and 1980s (Lindsay, 1973, 1974; Beyer, 1984). Maxwell's remaining reviews of Strutt's manuscripts con- cern items for the London Mathematical Society (Rayleigh, 1964; Harman, 1995, 2002). These include the 1873 paper introducing what is now known as the “Rayleigh dissipation function.” Maxwell’s review is important for its recognition of other applications (in modern terminology, the stability of systems with feedback and the nature of wave dispersion); he also suggested Strutt should consider reciprocity relation- ships, something that Strutt eventually pursued. In a lecture during the autumn term of 1873, Maxwell used Rayleigh’s dissipation function, the notes from the lecture having been
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