206 HERMANN VON HELMHOLTZ 



wife, returning with restored health and rejuvenated mind and 

 body. He was now able to participate cheerfully in all that 

 life offered him in the beautiful city on the Neckar, where for 

 the first time he felt himself at home. In September he 

 brought his children Kathe and Richard (who since April had 

 been at Dahlem with their grandmother) to Heidelberg, where 

 he now had a commodious dwelling on the Anlage which he 

 shared with Frau von Velten. 



Helmholtz took up his book on Acoustics with fresh energy, 

 plunged into arduous optical problems (the solution of which 

 was to form Part III of the Physiological Optics), elaborated 

 the structure and detail of his Theory of Knowledge, and at 

 the same time continued the electrical investigations to which 

 he had been led by du Bois-Reymond and by his own 

 physiological researches. 



In a lecture given to the Nat. Hist. Med. Verein at Heidelberg 

 (December 8, 1861) on 'A Universal Method of the Trans- 

 formation of Problems of Electrical Distribution ' a number of 

 interesting and important propositions were brought forward 

 by Helmholtz, who was not acquainted with the work done by 

 others in this department. 



Immediately after the publication of this paper, he was 

 informed that its essential results were already contained in 

 two letters from W. Thomson to Liouville, and at once acknow- 

 ledged this in the Heidelberg Transactions of May 30, 1862. 

 He also wrote on May 27 to W. Thomson : 



'I have to beg you to answer a scientific question. Last 

 autumn I fell back on potential functions again. I was troubled 

 by the difficulties that remained unsolved in my work on sound 

 vibrations in an open cylindrical tube. The difficulty of attacking 

 the question lay in the fact that the aerial motions are discon- 

 tinuous at the edge of the open end of the tube. This led me 

 to investigate the distribution of electricity at a circular edge. 

 I found that I could derive this in certain cases from the 

 distribution along the straight edge in which two infinite 

 planes intersect one another, and I solved the problem for this 

 case. Afterwards, however, I noticed that you had already 

 stated in the Cambridge Math. Journ. that you had solved this 

 question, and I want to know whether you have published the 

 solution, or intend to publish it, in which case it is not worth 



