3 86 HERMANN VON HELMHOLTZ 



the motions of the air, save at the limits next the earth's 

 surface, and the internal surfaces of discontinuity, where indeed 

 changes of temperature might take place between the warmer 

 and colder layers, by the actual conduction of heat, and dif- 

 fusion of the molecules that are in motion. It was shown on 

 the basis of Maxwell's friction-constants for air, that a motion 

 delayed by friction at o would fall to half its velocity in 42,747 

 years, if the interval between the two layers is 8,026 m., the 

 mean height of an atmosphere of constant density; and the 

 lower temperature of the upper layers still further diminishes 

 the effect of friction. In the same way, the conduction of heat 

 may reduce the difference of temperature in the upper and 

 lower surfaces of an atmosphere of 8,026 m. to one-half in 

 36,164 years. 



'For meteorology,' says von Bezold, 'the researches of 

 Helmholtz into the integrals of hydrodynamic equations will 

 be of enormous importance in time to come.' 



When, at the end of July, Helmholtz communicated Part II 

 of his Meteorological Investigations to the Academy, his 

 colleagues found him markedly depressed. Sorrow and 

 trouble weighed upon his family. It was increasingly certain 

 that the bodily affections of his younger son Fritz must perma- 

 nently hinder his mental development, although the malady of the 

 elder son Robert appeared for the time at least arrested, and 

 his parents hoped that a long life might lie before him. His 

 scientific work had found general recognition, his cheerful 

 disposition made him the life of the house, and he was always 

 surrounded by a set of talented young people, who shed 

 4 the sunshine of their youthful candour' on the Helmholtz 

 household. 



' Even if Robert Helmholtz,' writes the Assyriologist Pro- 

 fessor Lehmann from Berlin, ' at all times represented a some- 

 what unattainable standard to his friends, this was due in 

 part at least to the sincerity of his disposition. What was a 

 striking trait in both parents had descended to their son. He 

 reminded one of the mother, whose features he bore, in his 

 frankly outspoken yet never depreciatory criticisms, and his 

 no less generous appreciations. His father's immense scientific 

 veracity extended to his judgements of all human relations, 

 so that Frau von Helmholtz justly observed, " My husband 



