202 THE TEACHING BOTANIST 



one another, or when without petiole, the material is more 

 condensed toward the tip, giving the obovate, etc. Leaflets 

 may be told from leaves by absence of axillary buds, and by 

 their not originating in whorls nor spirally. There is much 

 value, it is true, in drawing and naming the different shapes 

 of leaves, but it is of much the same nature as the fitting 

 together of some kinds of puzzles ; and the same time and 

 labor may be spent much more profitably upon doing work 

 which is distinctively botanical and scientific. Still, if the 

 teacher values terminology as a discipline, here is the place 

 for it. 



The teacher should note that the systems of phyllotaxy 

 described in the books and expressed by fractions unques- 

 tionably exist, and may be traced ; and a certain amount of 

 this should be done, enough to give the pupil a clear idea of 

 its principles ; but the teacher should carefully avoid leading 

 the pupils to imagine they find certain fractions which theo- 

 retically ought to be present, for the systems are very easily 

 thrown out by twisting of the stem in growth or by injuries. 

 Of course, the phyllotaxy has very little to do with the ulti- 

 mate position of the blade; it holds true only for the origin 

 of the leaves in the bud. 



The students will be able to do but little with the ecological 

 explanation of the variations of shape, etc., and here the 

 teacher must give assistance when he can. It is better to 

 call attention to such questions, even if they cannot be solved, 

 than to omit them altogether. 



In making observations upon the plants, the students should 

 read over with each the account of the typical plant given 

 under 28 ; it is needful for them to have their attention 

 directed to each point, or they will miss important features. 



Experiment No. 4 is the well-known, valuable, and easy 



