44 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 ami 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 liters- literature on more modern lines : some of the first in- 



tnie. 



1 The greater part of the higher portant work of this kind. Ger- 

 Gennau school literature in mathe- many had indeed not been wanting 

 matics and physics was supplied by in original research, but the new 

 the French or modelled on French ideas of Mubius, Steiner, Staudt, 

 ideas Legendre and Monge in ele- Pliicker, and Grassmann in geom- 

 mentary and descriptive geometry, etry found no adherents till, mainly 

 Lacrois in the higher branches. through the translation of Sal- 

 Francreur's course of mathematics mon's text-books by Fiedler, a new 

 was introduced in England as well spirit came over geometrical teach- 

 as Germany ; Poisson, and later ing. In the meantime Lejeune 

 Lagrange and Dubamel, became Dirichlet. and Neumann the elder, 

 the models in mechanics, Biot and cultivated in their academical lec- 

 Pouillet in experimental physics, tures the higher branches of mathe- 

 Regnault in chemistry. The only matical physics, and educated a 

 great popular authorities which whole generation of mathematicians 

 did not belong to France were and physicists. Through them the 

 Berzelius and Graham in chem- original researches of Gauss and 

 istry. and Euler in mathematics. Jacobi became better known, and 

 As late as 1860 hardly any text- an independent school of German 

 book existed in Germany on the mathematical thought was estab- 

 theoretical and mathematical por- lished. In England the influence 

 tions of physics. The second of French science was much more 

 volume of ' Baumgartner : was limited, and to the present day 

 a miserable compilation. Beer's Euclid is preferred to Legendre ? s 

 ' Hohere Optik ' was the first im- more elegant methods. 



