KVOLUTION OF THK SCIENTIFIC INVESTIGATOR. 225 



plu'iioiiK'ii:! of nature wtTc rudely ()1)s(m-v(mI, and striking occurrences 

 in the eartli or in the' lieavens i-ecorded in tlie annals of the nation. 



A'ast was the pro<>Tf'ss of knowledo-e during the interval Ix'tween 

 these eni})ires and the century in which modern science began. Yet, 

 if I am right in making a distinction hetween the slow and regular 

 stejjs of jirogress, each growing naturally out of that which pre- 

 ceded it, and the entrance of the mind at some fairly definite epoch 

 into an entirely new sphei-e of activity, it would apjx'ai- that there 

 was only one such epoch during the entire interval. This was when 

 abstract geometrical n'asoning connnenced, and astronomical observa- 

 tions aiming at pn'cision were recorded, compared, and discussed. 

 Closely associated with it nuist have been the construction of the 

 forms of logic. The radical ditl'erence between the demonstration 

 of a theorem of geometry and the reasoning of everyday life which 

 the masses of men nnist have practiced from the beginning, and 

 which few even to-day e\'er get l)eyond, is so evident at a glance 

 that I need not dwell upon it. The principal feature of this ad- 

 vance is that, by one of those antinomies of the human intellect of 

 which examples are not wanting even in our time, the develo}> 

 nient of abstract ideas })receded the concret<^ knowledge of 

 natural phenomena. When we reflect that in the geometry of 

 Euclid the science of space was l)rouglit to such logical perfection 

 that even to-day its teachers are not agreed as to the practicability 

 of any great improvement upon it, we can not avoid the feeling that 

 a very slight change in the direction of the intellectual activity of 

 the (ireeks. would have led to the beginning of natural science. But 

 it would seem that the very purity and i)erfection which was aimed 

 at in their system of geometry stood in the way of any extension or 

 application of its methods and spirit t(» the field of natui-e. One 

 exam])le of this is worthy of attention. In modern teaching the 

 idea of magnitude as gcMiei'ated l)y motion is freely introd'.iced. A 

 line is descril)ed l)V a moving point; a plane by a moving line; a 

 solid l)y a moving plane. It may, at first sight, seem singular that 

 this conce])tion finds no place in the Euclidian system. But we may 

 legard the omission as a mark of logical purity and rigor. Had the 

 real or supposed advantages of introducing motion into geometrical 

 conceptions been suggested to P^iiclid, we may suppose him to have 

 replied that the theorems of space are independent of time; that the 

 idea of motion necessarily implies time, and that, in ccMisequence, to 

 avail ourselves of it would be to introduce an extraneous element into 

 geometry. 



It is quite possible that the contem})t of the ancient philosophers 

 for the practical application of their science, which has continued 

 in some form to our own time, and whicli is not altogether unwhole- 

 SM 1904 15 



