Along with the celebrated achievement in the heat conduction research, J. Fourier (1768-1830) carried out extensive studies on thermal radiation in the years of about 1805-1828, the process and accomplishment of which are analysed here on the basis of his MS's (1805-1807), nine papers (1807-1828) and the eminent monograph Theorie Analytique de la Chaleur (1822). Fourier's concern in the early stage was to control the radiative characteristics of the surfaces of the samples for heat conduction experiments, either by blackening or by polishing. These trials enriched his view on the boundary condition for heat conduction equation.
Nextly he developed mathematical means for expressing radiative processes, for example, multiple reflection among surfaces having various configuration. On the physical sides of the radiation phenomena, he discussed repeatedly the significance of Lambert's law of emission, not in line with the corpuscular theory but on a more realistic standpoint of thermal equilibrium. This standpoint made him able to proceed to conceptualize the equivalence of emission and absorption of thermal radiation at every element of the surfaces in thermal equilibrium.
Finally, he clarified the meaning of thermal state in the cavity, the wall of which was kept at a uniform temperature. The last two of the above-mentioned attainments of Fourier seem to be of great importance as interconnections between the Genevan phenomenological approach (by Pictet, Prévost) and the German thermodynamical formulation (by Kirchhoff, W. Wien) of thermal radiation doctrine.
The three physicists, Count Rumford, Biot and Fourier, almost simultaneously made experimental researches on heat conduction in solid This comparative study of their researches sheds light on the significance of Fourier's.
Fourier's theoretical originality is that he first paid attention to heat diffusion in solid and soon comprehended its law by the notion, "mode elementaire" based on Fourier's series. Although Fourier confirmed the law later by the experiment on annulus, his early research had been so mathematical, that he had not been able to grasp its physical aspects sufficientlly. Rumford's and Biot's works must have prompted Fourier not only to pay attention to steady thermal state in bar, but also to set with experimental researches. Although Fourier may have owed his theoretical success to Biot, it is Fourier that thought out hydrodynamical approach to thermal phenomena prior to the accomplishment of the mechanics of continuum and completed the concept of temperature gradient and the differential equation of heat conduction. Noticeable as well is that all these theoretical achievements based on the results of his fine experiments, conducted with both technical skill and refined methodology, which were much superior to those of Rumford and Biot. Also in relation to the partial validity of Newton's cooling law, he had a clear insight into the interaction between "Experiment and Theory".
Therefore I concluded that Fourier was a better experimentalist in his time, compared with Rumford and Biot, in other words it is not proper to consider Fourier's study of heat conduction only as a mathematical and theoretical one.
In this paper, the author attempts to clarify to what extent the coordinate relations theoretically hold among the Copernican, the Tychonian, and the Ptolemaic world systems as they are compared by means of simplified models consisting of combined uniform circular motions. The results are:
(1) Concerning the apparent positions and movements of the planets against the celestial sphere, there can be exact coordinate relationships among the three systems.
(2) Concerning the distance from the observer, the visual size and brightness, and the phase of the planets, any of these systems can give satisfactory accounts of the phenomena observed with the naked eye, although exact coordinate relationships in these respects do not quite hold among the three systems.
From the above, the present author concludes that the naked eye observations before the telescopic ones could not have established the superiority of the Copernican system over the others. The author also presents a new interpretation concerning A. OsianderJs description of the changes in brightness of Venus given in his Foreword to De Revolutionibus, and points out some of the related errors made in the recent historical investigations of the world systems.