PROFESSOR AT HEIDELBERG 213 



systematizing concept, whereby it is rendered capable of being 



expressed in words'. He finds in the simpler relations of 



inorganic nature an instrument for the systematic development 



of a train of ideas, comparable with ' no other human invention 



in respect of its congruity, certainty, exactitude, and fecundity '. 



In the Academic Discourse he insists on the incontrovertible 



fact that even if the antithesis between the moral and the 



physical sciences had been unduly emphasized by Hegel and 



Schelling, it had a real basis in the nature of things, and must 



be taken into consideration. In comparing the different 



physical sciences one with another, he points out the great 



advantage which the experimental sciences have over those 



which depend on observation in the investigation of the 



universal laws of nature, since they can arbitrarily modify the 



conditions under which the effect ensues, and may therefore 



limit themselves to quite a small number of characteristic 



observations, in establishing the validity of any law. He 



demands of experimental and mathematical science that it 



shall strive after the attainment of laws, to which there are 



no exceptions, 'since it is under this form alone that our 



knowledge prevails over space and time, and the forces of 



nature/ Thus he regards the Law of Gravitation as the 



greatest logical achievement of the human mind, but finds 



absolute certainty of inference in mathematics alone ; there 



no authority is paramount other than pure reason, and the 



whole of science is constructed from the fewest axioms. 



1 In mathematics we see the conscious, logical activity of our 

 mind in its purest and most complete form; we can here 

 ppreciate its travail as a whole the precaution with which 

 it must advance, the accuracy that is necessary in order to 

 determine the exact import of the acquired general propositions, 

 the difficulty of forming and of understanding abstract con- 

 cepts while at the same time we learn to put confidence in the 

 certainty, the scope, and the profit of such intellectual labour.' 

 At this time Helmholtz was busying himself with difficult 

 questions in physiological optics, and more particularly with 

 the construction of the Horopter, while the issue of the Lehre 

 von den Tonempfindungen (Theory of the Sensations of Tone) 

 was completed by the end of 1862, and on December 14 

 Helmholtz writes to Thomson : ' I am much interested in the 



