266 TRANSACTIONS OF THE AMERICAN INSTITUTE. 



well plowed; the trees planted 12 by 15 feet. They are well examined for 

 worms, and yet with all the care given, they die regularly at fbnr years old, 



'The Law of Phyllotaxis. 



Prof. S. D. Tillman gave a very interesting dissertation upon the law 

 which regulates the arrangement of leaves upon the stem of a plant. With- 

 out attempting to assign causes for the remarkable development, he pro-, 

 ceeded to show the several positions which leaves may assume with refer- 

 ence to the circumference of the stem. To obtain a clear conception of the 

 law it is only necessary for one to imagine that the vital force of the plant 

 ascends spirally beneath its bark, so that on rising a certain distance it 

 will have passed once around the wood of the stem. Now within the dis- 

 tance of one turn there will be either two or three leaves at equal distances 

 frona each other, which may be measured by the usual division of a circle, 

 into 360 degrees. If in the first case there are two leaves in one turn, they 

 will be 180 degrees apart. If there are three leaves, they will be 120 de- 

 grees apart. The itext order contains five leaves in two turns ; the next 

 eight leaves in three turns, the next thirteen leaves in five turns and so on. 

 If we represent this arrangement by fractions in which the numerator 

 expresses the number of turns, and the denominator the number of leaves 

 in such turns, we have the following series : 



1 1 2 3 _5 JL Xrp 

 '2' 3' 5' 8' 13' 2 1' ^^' 



Starting with the first two terms, it will be perceived that the sum of 

 two denominators form the new denominator of the next succeeding term, 

 and the sum of the two numerators form the next numerator. For example 

 |^-{-|=-|, and to find how far around the stem each leaf of the last order 

 measures, we must multiphy 360 degrees by three and divide by eight ; 

 the result shows that these leaves are 135 degrees apart, measuring around 

 the stem and not lengthwise. Lovers of flowers who watch with great 

 interest the development of beauty in form and color, will have their pleas- 

 ures heightened by a realization of the fact that for the arrangement of 

 leaves there is a fixed and immutable law. The design of the Creator, in 

 the countless forms and colors of flowers, cannot yet be so comprehended 

 as to express, by formula, the successive steps of development ; but of this 

 we may be assured, that all changes, whether according to the regular 

 course of nature, as far as known to us, or in apparent contradiction to it, 

 are the, direct result of physical causes, and that Order reigns supreme 

 while beauty pervades the endless variety of the vegetable kingdom. 



Clean Culture. 



The Chairman read the following communication to the Massachusetts 

 Ploughman, by S. P. Maybury, Cape Elizabeth, Maine: 



Clean culture is a term that most of farmers either do not understand the 

 import of or do not care to practice. To such I write this as of import- 

 ance. They will see if they practice. 



On my tour to the White Mountains, in August, I paid particular atten- 

 tion to the treatment which was bestowed upon apple trees. In most of 

 the towns which I passed through they paid little heed except to trim them, 



