40 PHYSICS 



solutions have taxed the powers of Poisson (1812, 1829), Cauchy 

 (1829), Kirchhoff (1850), Boussinesq (1871-79), and others. For the 

 circular plate Kirchhoff gave the complete theory. Rayleigh system- 

 atized the results for the quadratic plate, and the general account 

 makes up his ninth and tenth chapters. 



Longitudinal vibrations, which are of particular importance in case 

 of the organ-pipe, were considered in succession by Poisson (1817), 

 Hopkins (1838), Quet (1855); but Helmholtz in his famous paper 

 of 1860 gave the first adequate theory of the open organ -pipe, involv- 

 ing viscosity. Further extension was then added by Kirchhoff (1868), 

 and by Rayleigh (1870, et seq.), including particularly powerful 

 analysis of resonance. The subject in its entirety, including the allied 

 treatment of the resonator, completes the second volume of Ray- 

 leigh's Sound. 



On the other hand, the whole subject of tone-quality, of combin- 

 ation and difference tones, of speech, of harmony, in its physical, 

 physiological, and aesthetic relations, has been reconstructed, using 

 all the work of earlier investigators, by Helmholtz (1862), in his mas- 

 terly Tonempfindungen. With rare skill and devotion Konig contrib- 

 uted a wealth of siren-like experimental appurtenances. 



Acousticians have been fertile in devising ingenious methods and 

 apparatus, among which the tuning-fork with resonator of Marloye, 

 the siren of Cagniard de la Tour (1819), the Lissajous curves (1857), 

 the stroboscope of Plateau (1832), the manometric flames of Konig 

 (1862, 1872), the dust methods of Chladni (1787) and of Kundt 

 (1865-68), Melde's vibrating strings (1860, 1864), the phonograph 

 of Edison and of Bell (1877), are among the more famous. 



Heat: Thermometry 



The invention of the air thermometer dates back at least to Amon- 

 tons (1699), but it was not until Rudberg (1837), and more thor- 

 oughly Regnault (1841, et seq.) and Magnus (1842), had completed 

 their work on the thermal expansion and compressibility of air, 

 that air thermometry became adequately rigorous. On the theoret- 

 ical side Clapeyron (1834), Helmholtz (1847), Joule (1848), had in 

 various ways proposed the use of the Carnot function (1894) for 

 temperature measurement, but the subject was finally disposed of 

 by Kelvin (1849, et seq.) in his series of papers on temperature and 

 temperature measurement. 



Practical thermometry gained much from the measurement of the 

 expansion of mercury by Dulong and Petit (1818), repeated by 

 Regnault. It also profited by the determination of the viscous 

 behavior of glass, due to Pernet (1876) and others, but more from 

 the elimination of these errors by the invention of the Jena glass. 



