SCIENTIFIC CULTURE, 583 



mated ; and in a recent meeting of teachers of our best secondary schools 

 it was gravely asserted that solid geometry was the most difficult study 

 with which the teachers had to deal. In solid geometry, however, the 

 reasoning is no more difficult than in plane geometry, but the concep- 

 tions are far more complex, and, if the teacher insisted that the pupil 

 should not take a single step until his conceptions were perfectly clear, 

 all the difficulties would disappear. Of this I am fully persuaded, for 

 I have had to encounter the same difficulties over and over again in 

 teaching crystallography. In beginning the study of geometry, of 

 course the power of conception should be helped in every possible 

 way. Let your pupil find out by actual measurement that the sum of 

 the angles of a triangle is equal to two right angles, and he will easily 

 discover the proof of the proposition himself. So also, if he actually 

 divides with his knife a triangular prism made from a potato or an 

 apple into three triangular pyramids, he will find no difficulty in fol- 

 lowing the reasoning on which the measurement of the solid contents 

 of a sphere depends. Let me assure teachers that the study of geom- 

 etry, taught as I have indicated, is a most valuable introduction to the 

 study of science. But, as it has been usually taught as a preparation 

 for college, it is almost worthless in this respect, however valuable it 

 may be as a logical training, 



I consider practice in free-hand drawing from natural objects a 

 most valuable means of training both the power of observation and 

 the power of conception, besides giving a skill in delineation which 

 is of the greatest importance to the scientific student. Accuracy 

 of drawing requires accuracy in observation, and also the ability to 

 seize upon those features of the object which are the most promi- 

 nent and characteristic. Hence, in a course of scientific training, the 

 importance of practice in drawing can hardly be exaggerated, and it 

 should be made one of the most important objects of school- work from 

 an early period. 



To the scientific student the powers of observation and conception 

 are not sought as ends in themselves, but as means of studying Na- 

 ture. The precise portions of this wide field to which the attention 

 of the student shall be directed will be determined by many circum- 

 stances, and it is not our purpose in this address to lay down a plan 

 of study. To most students the natural history subjects offer the 

 most attractive field ; but all, I think will admit, that the experi- 

 mental sciences should form a considerable portion, at least, of the 

 course of all scientific students, whatever specialty may subsequently 

 be chosen. That on which I desire particularly to dwell is the spirit 

 in which all these studies should be pursued ; and I can best illustrate 

 what I mean by confining my remarks to that subject in which I am 

 most interested, and in regard to which I have the greatest experience. 



In a course of scientific study, chemistry can not be dissociated from 

 physics, and the two sciences ought to be studied to a great extent in 



