INTRODUCTION. 



of exact reasoning attempts to condense and unify 

 knowledge were discredited. The result especially in 

 Germany was that in many sciences information be- 

 came buried in periodicals and in the memoirs of learned 

 societies: text -books were chiefly written by men of 

 secondary importance, translated from the French and 

 English, and frequently on somewhat antiquated lines. 1 

 The new spirit which began to leaven scientific research in 

 the middle of the century was confined to a few master 

 minds, who frequently almost unknown marched in 

 advance of their age. In the course of the last thirty 

 years this has been entirely changed. The means of 

 intercourse and communication, referred to above, make 

 scientific isolation almost impossible ; the necessity has 

 21. been felt of remodelling the whole of the popular school 



Reform in 



school Htera. literature on more modern lines : some of the first in- 



ture. 



1 The greater part of the higher 

 German school literature in mathe- 

 matics and physics was supplied by 

 the French or modelled on French 

 ideas Legendre and Monge in ele- 

 mentary and descriptive geometry, 

 Lacroix in the higher branches. 

 Francceur's course of mathematics 

 was introduced in England as well 

 as Germany ; Poisson, and later 

 Lagrange and Duhamel, became 

 the models in mechanics, Biot and 

 Pouillet in experimental physics, 

 Regnault in chemistry. The only 

 great popular authorities which 

 did not belong to France were 

 Berzelius and Graham in chem- 

 istry, and Euler in mathematics. 

 As late as 1860 hardly any text- 

 book existed in Germany on the 

 theoretical and mathematical por- 

 tions of physics. The second 

 volume of ' Baumgartner ' was 

 a miserable compilation. Beer's 

 ' Hohere Optik ' was the first im- 



portant work of this kind. Ger- 

 many had indeed not been wanting 

 in original research, but the new 

 ideas of Mobius, Steiner, Staudt, 

 Pliicker, and Grassmann in geom- 

 etry found no adherents till, mainly 

 through the translation of Sal- 

 mon's text-books by Fiedler, a new 

 spirit came over geometrical teach- 

 ing. In the meantime Lejeune 

 Dirichlet, and Neumann the elder, 

 cultivated in their academical lec- 

 tures the higher branches of mathe- 

 matical physics, and educated a 

 whole generation of mathematicians 

 and physicists. Through them the 

 original researches of Gauss and 

 Jacobi became better known, and 

 an independent school of German 

 mathematical thought was estab- 

 lished. In England the influence 

 of French science was much more 

 limited, and to the present day 

 Euclid is preferred to Legendre's 

 more elegant methods. 



