PEEFAOB. 



THE FAVOUR with which the first series of Professor 

 Helmholtz's Lectures has been received would justify, 

 if a justifi cation were needed, the publication of the 

 present volume. 



I have to express my acknowledgments to Pro- 

 fessor G. Croome Eobertson, the editor, and to Messrs. 

 Macmillan, the publishers of ' Mind,' for permission to 

 use a translation of the paper on the * Axioms of 

 Modern Geometry ' which appeared in that journal. 



The article on ' Academic Freedom in German 

 Universities ' contains some statements respecting the 

 Universities of Oxford and Cambridge to which ex- 

 ception has been taken. These statements were a fair 

 representation of the impression produced on the mind 

 of a foreigner by a state of things which no longer 

 exists in those Universities, at least to the same 

 extent. The reform in the University system, which 



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