PROFESSOR IN BERLIN 357 



which the kinetic potential contains terms which are linear in 

 the velocities, as cases of concealed motion ; these cases differ 

 essentially from those in which the kinetic potential involves 

 velocities only in the terms of the second degree, inasmuch as 

 the motion cannot under similar conditions be reversed unless 

 the concealed motions be simultaneously reversed. 



He then considers, under the above general assumptions, the 

 reciprocal relations between the forces which the system simul- 

 taneously exerts in different directions, and its accelerations 

 and velocities, which embrace a series of highly interesting 

 associations of physical phenomena, such, e. g., as the law of 

 thermodynamics : if increase of temperature raises the pressure 

 of a material system, then its compression will raise the tempera- 

 ture ; further, if heating of any point in a closed circuit produces 

 an electric current, the same current will produce cold, if the 

 heat due to the resistance be disregarded ; and many others. 

 After deriving the necessary conditions for this extension of 

 kinetic potential from the extended form of Lagrange's equations, 

 he enunciates the theorem that these conditions are moreover 

 adequate for the existence of the kinetic potential, but reserves 

 the proof of this for another occasion. In his posthumous 

 papers we find more about the method of proof which he had 

 chosen for this, but in regard to this point he came to no 

 satisfactory conclusion. On April 25, 1886, he writes from 

 Baden-Baden to Kronecker : 



' I have received your card from Berlin with the address you 

 give for my manuscript, and your letter of the 2ist inst. from 

 Florence finds me here. As a matter of fact most of my MS. 

 already has the pages numbered, but I am still hung up over 

 one point as to which I must consult a paper by Lipschitz, which 

 was sent on to me here by Konigsberger. Pray, however, do 

 not delay the printing for me; that would distress me very 

 much. I can appear just as well in the third or the fourth part. 

 In the attempt to reverse my propositions, I have been led to 

 the theory of polydimensional potential functions, where one has 

 to walk very warily, and I have not decided whether to make 

 this discussion a digression in the main essay, or to treat it 

 separately. Even in the second case, however, I must first get 

 my excursus worked out. . . . Boltzmann's essay opens with 

 some very interesting observations, with which I also occupied 



