No. 109.] 27 



REMARKS OF PROF. PAVIES. 



To one accustomed to speak only on the abstract quantities of 

 number and space, this is an unusual occasion, and this an unusual 

 audience. How is it possible for me to discuss the abstract foims 

 of geometry, when I see before me, in such profusion, the most 

 beautiful real forms that Providence has vouchsafed to the sight 

 of man ! 



I propose to introduce and develop but a single train of thought, 

 viz. the unchangeable connection between what in common lan- 

 guage is called the theoretical and practical, but, in more technical 

 phraseology, the ideal and actual. 



The actual, or true practical, consists in the uses of the forces 

 of nature according to the laws of nature ; and here we must 

 distinguish between it and the empirical, which uses or attempts 

 to use those forces without a knowledge of the laws. The true 

 practical, therefore, is the result or actual of an antecedent ideal. 

 The ideal, full and complete, must exist in the mind before the 

 actual can be brought forth according to the laws of science. 



Who, then, are the truly practical men of our age? Are they 

 not those who are engaged most laboriously and successfully in 

 investigating the great laws 1 Are they not those who are pressing 

 out the boundaries of knowledge into new and unexplored regions, 

 where, perchance, yet may slumber some great principle of nature, 

 corresponding in the simplicity of its laws, and the magnitude of 

 its results, to that which gave birth to the steam engine or electric 

 telegraph ? Is not the gentleman from Massachusetts ( Professor 

 Agassiz) the most practical man in our country, in the department 

 of natural history ; not because he has collected the greatest num- 

 ber of specimens, but because he has laid open to us all the laws 

 of the animal kingdom 1 



Are the formulas written on the blackboard by the gentleman 



