380 HERMANN VON HELMHOLTZ 



'As regards your problem, I know the astronomers have 

 discussed the question whether time is required in gravitation. 

 I do not know how far its exact determination is possible. 

 They assert that observation goes against this hypothesis. In 

 any case it is useless to attack a problem of this kind until one 

 knows what observations are possible, and how they should be 

 carried out in order to decide it. 



' The thermoelectric currents in the body of the Earth present 

 a complicated problem. An arrangement of different concentric 

 shells in the Earth's crust would only yield currents correspond- 

 ing with closed ring magnets, with no external action. Our 

 present methods of measuring gravity are not exact enough to 

 enable us to measure the gravitation of the Moon. Meantime 

 the geodesists are seeking for better methods, and an Academic 

 prize-question has been set on the influence of the suspension 

 of the pendulum on its vibration-period (elasticity of the sup- 

 port, form of the knife-edge, or, on the other hand, length and 

 elasticity of the spring by which it is suspended). For my 

 own part I have learned whatever I know of mathematics 

 merely from the problems I have tried to solve, and have never 

 been able to grasp anything from purely abstract study unrelated 

 to problems. But you must first choose simpler tasks, either in 

 mechanics, or the theory of potential functions, electrical dis- 

 tribution, or the distribution of electrical currents. The theory 

 of the pendulum, for instance, suspended by an elastic watch- 

 spring would be a good example. This kind of suspension is 

 far less subject to friction than that from a knife-edge/ 



Helmholtz spent his birthday as usual in Pontresina, in the 

 company of his wife, and had the accustomed number of 

 respectful congratulations ; this first birthday in his new post 

 brought him a letter from the mathematician L. Kronecker on 

 August 28, which is interesting both in its style and its con- 

 tents : 



1 In a few more days, on the last of this month, you will 

 complete the 67th year of your prolific life, by which light has 

 been thrown on innumerable fields of activity. I send you my 

 warmest congratulations. ... I am happy in the conviction that 

 your present phase of exclusive devotion to mathematical 

 physics will be succeeded by a phase in which you will turn to 

 pure mathematics, and bring the light of your intellect to bear 



