40 



curves of growth and temperature are represented on the same diagram, 

 so that one can easily tell the increment of growth for a given time along 

 with the factors of heat and light. This kind of diagram is especially 

 valuable if the experiment be written in a language that one does not 

 read readily, for the gist of the work can be gotten from the diagram with 

 but little help from the text. 



A great deal of mathematical work has been done in phyllotaxy. Th is 

 work consisted in the first place in imagining a line proceeding from one 

 of the older lateral members, traversing the stem to right or left, so as to 

 Include the points of insertion of all the successive lateral members in 

 the order of their age. This line, when projected, horizontally, was called 

 the genetic spiral, butas the line is a helix, its horizontal projection could 

 not be a spiral. 



Then in working out the law of the phyllotaxis, a series of fractions 

 were formed, the numerator expressing the number of complete revolu- 

 tions round the stem, starting from the point of insertion of a lateral 

 organ and extending to the organ directly above it; the denominator ex- 

 pressing the number of joints of insertion of lateral organs passed through . 

 It was discovered that The series of fractions expressing the most com- 

 mon divergences were successive convergents of the continued fraction, 

 and it was supposed that a natural law had been found, 

 but as it is necessary to construct new continued fractions 

 1 i for many of the divergence-, this proved fallacious. But 



1+ etc. as no relation has been found to exist between the method 

 and anything relating to plant life, the method has but little vahie, ex- 

 cept from the mnemonic point of view. Work on this subject was very 

 popular about twenty years ago, as it gave people an opportunity of prov- 

 ing that they knew their mathematics, it being somewhat generally sup- 

 posed at the time that anyone who could do his mathematics could easily 

 do his other work. 



In the latest bulletin* issued from the lnd. Exp. Sta., the subject of 

 which is the relation of number of eyes on the seed tuber to the product, 

 it was found that a relation existed between the eye of the seed tuber and 

 the number of stalks, that is, when the eyes formed an arithmetical series, 

 the number of stalks, per unit of weight, derived from them formed an 

 approximate hyperbolic series. To a scientific person this result means 



:: J. O. Arthur. Purdue Exp. Sta. Ind.. Xo. 12, 1892. 



