Constitution of Matter and Analytical Theories of Heat. 



An Essay in four Parts. 



By 



Ganesh Prasad of Baiia (india). 



Commmiicated by F. Klein, July 11, 1903. 



iPreface. 



„Mathematical analysis has no marks to express confused notions." J. Fourier. 



The following essay was undertaken with the object of utilising the recent 

 advances in mathematical analysis for working out analytical theories of heat, 

 eaeh theory being based on definite suppositions as to the Constitution of matter. 



In carrying on the investigation embodied in this essay I consulted a very 

 large number of authorities. I am chiefly indebted to the writings of Gr. Cantor, 

 Fourier, Du Bois Raymond, Lord Kelvin, Larmor, Maxwell, Poisson, 

 Broden, KarlPearson, Poincare and Wei erstras s. To these I must add 

 Dini-Lüroth's „Grundlagen für eine Theorie der Functionen einer veränder- 

 lichen reellen Grösse", from which my knowledge of continuous analysis is chiefly 

 derived. I am also indebted to Fitzgerald' s scientific papers-^) and Som- 

 merfeld' s dissertation ^). Finally, I must mention that in the early stage of 

 this investigation I received great encouragement from the vie ws of F. Klein 

 as given in his Evanston Colloquium and „Gutachten der Göttinger philoso- 

 phischen Facultät betreifend die Beneke - Preisaufgabe für 1901" (Göttinger 

 Nachrichten 1901, Geschäftliche Mitteilungen; Math. Ann. Bd. 55). 



The essay in its present form was completed in the year 1902 , with the 

 exception of certain purely verbal alterations and a few unimportant corrections. 



1) „The Scientific Writings of George Francis Fitzgerald", Dublin 1902. 



2) „Die willkürlichen Functionen in der Mathematischen Physik", Inaugural - Dissertation, 

 Königsberg 1891. 



