582 THE POPULAR SCIENCE MONTHLY. 



to embrace so much of systematic botany as will enable scholars " to 

 analyze plants." 



If a child, twelve or fourteen years of age, is made to observe 

 the characteristic qualities of a few common minerals so as to enable 

 it to recognize them in the rocks, and is likewise led to examine the 

 structure of a few familiar flowers, not only will a new power have 

 been acquired, but a new interest will have been added to life. 



Of course, the faculty of observation thus early exercised in child- 

 hood only attains the highest degree of development after long experi- 

 ence and continued practice. The acuteness which practice gives is 

 frequently very remarkable, and rude men often surprise us by the 

 extent to which their power of observation has been cultivated in cer- 

 tain special directions. The sailor who recognizes the outlines of to 

 him a well-known coast, where the ordinary traveler sees nothing but 

 a bank of clouds, or the miner who recognizes in the rock indications 

 of valuable ores, are illustrations which may give a clearer conception 

 of the nature of the power we have been attempting to describe. 



Naturally following the power of observation in the order of edu- 

 cation is the power of conception with the cognate power of abstrac- 

 tion ; that is, the power of forming in the mind distinct and accurate 

 images of objects, and relations, which have been previously appre- 

 hended either by direct observation, or through description ; and also 

 the power of confining the attention to certain features which these 

 images may present to the exclusion of all others. This is a power 

 which depends very greatly on the imagination and is capable of being 

 cultivated to a very high degree. There is no study which is so well 

 suited to the training both of the powers of conception and of abstrac- 

 tion as the study of geometry. 



To this end the study of geometry should be begun at an early 

 period in school-life, and it should be studied at first not as a series of 

 propositions logically connected, but as a description of the properties 

 and relations of lines, surfaces, and solids — what has sometimes been 

 called " the science of form." A text-book prepared on this idea by 

 Mr. G. A. Hill forms an admirable introduction to the study. 



I esteem very highly the system of geometry of Euclid, either in 

 its original form or as it has been modified by modern writers, as a 

 means of developing the logical faculty. The completeness of the 

 proof of the successive propositions and their mutual dependence by 

 means of which, as on a series of steps, we mount from simple axiomatic 

 truths to the most complex relations, furnish an admirable discipline 

 for the reasoning power ; but too often the whole value of this dis- 

 cipline is lost by the failure of the pupil to form a clear conception of 

 the very relations about which he is reasoning, and the study becomes 

 an exercise of the memory and nothing more. Often have I seen a 

 conscientious and faithful student draw an excellent figure, and write 

 out an accurate demonstration, without noticing that the two were not 



