THE SCIENTIFIC SPIRIT IN ENGLAND. 



243 



Grassmann, in his ' Aiisdehnimgslehre,' published in 1844, i5. 



Grassmann, 



is now generally admitted to have originated quite a novel 

 way of considering geometrical relations,^ It took twenty 

 years, however, before he succeeded in attracting any at- 

 tention, and his great work, of which the first edition had 

 been sold as waste-paper, was later on reprinted in its 

 original form mathematicians having now begun to study 

 and recognise its intrinsic value. Such cases of neglect 

 have undoubtedly been much more frequent in England, 

 where even at the present day no central organisation le. 



^ J o Central or- 



exists which annually collects and arranges the scattered ^^^^ntf^""? 

 labours of individual workmen, and where that historical ^siand. 

 and encyclopa-dic spirit is wanting which does its utmost 

 to guarantee completeness and thoroughness of search 

 and of research. Men of the greatest eminence, pioneers 



^ Hermann Grassmann (1809-77) 

 was born, lived, and died at Stettin. 

 He did not succeed till late in life, 

 and fully thirty years after he had 

 published his original investigations 

 in geometry, in gaining for these the 

 recognition and appreciation which 

 they deserved. Neither he nor even 

 Jacob Steiner at Berlin attained to 

 positions worthy of their ability ; 

 the latter, in spite of his connec- 

 tion with other great mathemati- 

 cians, never filled the chair of an 

 ordinary professorship, whilst the 

 former never entered the sphere of 

 university teaching at all. The 

 * Ausdehnungslehre,' as a new 

 branch of mathematics, appeared 

 in 1844. It is a science of pure 

 extension, the application of which 

 to empirical space is geometry. 

 Similar investigations, in which 

 space of three dimensions is con- 

 sidered to be merely a particular case 

 of pure extension of any number of 

 dimensions, which are not neces- 

 sarily determined by the same pro- 



perties as our empirical sijace, have 

 become familiar since the publica- 

 tion of Riemann's celebrated disser- 

 tation of 1854 (published in 1867), 

 and since Helmholtz was led to 

 similar investigations by consider- 

 ing the different dimensions or 

 manifoldnesses of our sense per- 

 ceptions (see his ' Vortriige und 

 Reden,' in many passages). Grass- 

 mann, who at the end of his life 

 witnessed the growing appreciation 

 of his ideas, had filled up the in- 

 terval with entirely different studies, 

 the translation of the ' Rig-Veda ' 

 (Leipzig, 1876-77), and the compo- 

 sition of a dictionary to the same 

 (1872-75). He seems to have been 

 the only mathematician, besides 

 Thomas Young, who combined the 

 ability for exact mathematico- 

 physical and for philological studies. 

 Both can complain of having been 

 very insufficiently appreciated by 

 their contemporaries. See Victor 

 Schlegel, ' Hermann Grassmann,' 

 Leipzig, 1878. 



