712 THE PRINCIPLES OF SCIENCE. [CHAP. 



it belongs to the monometric system ; if not, we observe 

 whether the number of similar planes at the extremity of 

 the crystal is three or some multiple of three, in which 

 case it is a crystal of the hexagonal system ; and so we 

 proceed with further successive discriminations. To ascer- 

 tain the name of a mineral by examination with the blow- 

 pipe, an arrangement more or less evidently on the bifurcate 

 plan, has been laid down by Von Kobell. 1 Minerals 

 are divided according as they possess or do not possess 

 metallic lustre ; as they are fusible or not fusible, accord- 

 ing as they do or do not on charcoal give a metallic bead, 

 and so on. 



Perhaps the best example to be found of an arrange- 

 ment devised simply for the purpose of diagnosis, is 

 Mr. George Bentham's Analytical Key to the Natural 

 Orders and Anomalous Genera of the British Flora, given 

 in his Handbook of the British Flora? In this scheme, 

 the great composite family of plants, together with the 

 closely approximate genus Jasione, are first separated 

 from all other flowering plants by the compound character 

 of their flowers. The remaining plants are sub-divided 

 according as the perianth is double or single. Since no 

 plants are yet known in which the perianth can be said 

 to have three or more distinct rings, this division becomes 

 practically the same as one into double and not-double. 

 Flowers with a double perianth are next discriminated 

 according as the corolla does or does not consist of one 

 piece ; according as the ovary is free or not free ; as it is 

 simple or not simple ; as the corolla is regular or irregular ; 

 and so on. On looking over this arrangement, it will 

 be found that numerical discriminations often occur, the 

 numbers of petals, stamens, capsules, or other parts being 

 the criteria, in which cases, as already explained (p. 697), 

 the actual exhibition of the bifid division would be tedious. 



Linnaeus appears to have been perfectly acquainted 

 with the nature and uses of diagnostic classification, which 

 he describes under the name of Synopsis, saying : 3 



1 Instructions for the Discrimination of Minerals by Simple Chemi- 

 cal Experiments, by Franz von Kobell, translated from the German 

 by R. C. Campbell. Glasgow, 1841. 



* Edition of 1866, p. Ixiii. 



3 Philosophia Botanica (1770), 154, p. 98. 



