666 THE POPULAR SCIENCE MONTHLY. 



ceeds ap3.ce when one sees the marvels of curious problems solved, un- 

 likely properties discovered, among numbers and geometrical figures. 

 A certain ease in holding in the memory the abstract symbols, after a 

 moderate application, is enough to prepare us for a positive relish in 

 the pursuit. Such is the case with generalities in all departments. If 

 we can hold on till they bear their fruits in the explanation of thino-s 

 that we have already begun to take notice of, the pursuit is sustained 

 by a genuine and proper scientific interest, whose real groundwork, 

 however deeply hidden, is the stimulus of agreement among differing 

 particulars, and the lightening of the intellectual labor in comprehend- 

 ing the world. These are the feelings that have to be awakened in the 

 minds of pupils when groaning under the burden of abstractions. 



The opposition of the concrete and the abstract, while but another 

 way of expressing the opposition of the particular and the general, 

 brings into greater prominence the highly composite or combined char- 

 acter of individuality. The individual thing is usually a compound of 

 many qualities, each of which has to be abstracted in turn, in rising to 

 general notions ; any individual ball has, in addition to its round form, 

 the properties called weight, hardness, color, and so on. Now, this 

 composite nature, by charming several senses at once, gives a greater 

 interest to individuals, and urges us to resist that process of decompo- 

 sition, and separate attention, to which are given the designations " ab- 

 straction" and "analysis." It is for individuals in all their multiplicity 

 of influence that we contract likings or affections ; and, according as 

 the charm of sense, and especially the color-sense, is strong in us, we 

 are averse to the classing or generalizing operation. A fire is an object 

 of strong individual interest: to rise from this to the general notion of 

 the oxidation of carbon under all varieties of mode, including cases with 

 no intrinsic charm, is to quit with reluctance an agreeable contempla- 

 tion. The emotions now described the pleasure of identity, and the 

 liarhteninjr of labor are of avail to counterwork this reluctance. 



The second of the two motives that we have coupled together the 

 easing of intellectual labor may be viewed in another light. When 

 objects are viewed as operating agents in the economy of the world, as 

 causes or instruments of change, they work by their qualities or powers 

 in separation, and not by their entire individuality or concreteness. An 

 iron bar, or a poker, is an individual concrete thing; but, when we come 

 to use it, we put in action its various qualities separately. We may 

 employ it as a weight, in which case its other properties are of no 

 account ; we use it as a lever, and bring into play simply its length and 

 its tenacity. We can put it in motion as a moving power, wherein its 

 inertia is alone taken into account, with perhaps its form. In all these 

 instances, the magnetical and the chemical and the medicinal properties 

 of iron are unthought of. Now, this consideration opens up an impor- 

 tant aid to the abstracting process, the analytic separation of properties, 

 as opposed to the mind's fondness for clinging to concrete individuality. 



