INTRODUCTION. 1 1 



It is clear, however, that whatever subsequent alterations 

 are made in the system, the construction remains fundamentally 

 that of Schimper and Braun, and must stand or faU with the truth 

 of the premises which govern the original fractional series ; and 

 these, as has been pointed out, are extremely vague, and have to 

 a great extent been rejected by Hofmeister and Sachs. 



Contemporaneously with Schimper and Braun, the problems of 

 phyllotaxis were being attacked by the brothers A. and L. Bravais, 

 with in some respects identical results.* 



Very scant justice has been done by Sachs -f to the remarkable 

 work of these French observers. The parts in which they 

 appeared to agree with Schimper and Braun have been accepted, 

 those in which they differed have been rejected. It is not too 

 much to say that in the latter case they were wholly correct, and in 

 the former they came under the same erroneous influences as the 

 rival German school. 



Thus, Sachs sums up by saying that their theories presented the 

 defects and not the merits of the Schimper-Braun system, ia that 

 they made use of mathematical formulae to an even greater extent 

 without paying attention to genetic conditions, and the whole was 

 " much inferior as regards serviceableness in the methodic descrip- 

 tion of plants to the simple views of Schimper." 



It is evident that Sachs' distaste for the whole subject prevented 

 him from going into the matter very carefully, as the first thing 

 that strikes the reader is the very definite attempt made by the 

 Bravais to actually measure the angles and confirm their results 

 experimentally. It was owing to failure in this respect that they 

 fell back on the method of orthostichies and on this basis erected 

 very consistent hypotheses. When orthostichies obviously failed, 

 they approached the actual truth much nearer than Schimper and 

 Braun. They thus distinguished two kinds of spiral phyllotaxis 

 (1), that in which orthostichies were present and rectiserial ; (2) 

 that in which the so-called orthostichies were obviously curviserial. 

 The former applied to cylindrical structures and was so far identical 

 with Schimper's theory, which was also based on mature cylindrical 



* Ann. Sci. Nat., 1837, p. 42. 



t History of Botany, Eng. trans., p. 169. 



