326 Mathematical Nature of Phyllotazis. [June, 
tion of the relative geographical distribution of Io and Angitrema, 
taken in connection with obvious resemblances in the shells de- 
tected by Mr. Reeve, seem to, favor the-suggestion that Angi- 
trema is but a minor phase of Io. In habits the animals, so far 
as is known, are somewhat similar to each other, with this differ- 
ence, that Angitrema is fitted to dwell in more quiet waters than 
the necessities of Io require. 
Taken in another aspect, the inquiry why Io should be confined 
apparently to the head-waters of the Tennessee River can be an- 
` swered (in the proverbial Yankee style) by offsetting the inquiry 
why a curious group of shells with a fissured lip should be found 
only in the Coosa River in Alabama. This, like much more that 
might be made the subject of inquiry, is a part of the unwritten 
history of Io that remains to be investigated. 
The reader who may desire to refer to a summary of what has 
been written on species of Io will find such information as is 
available for the purposes of a naturalist in a work entitled Strep- 
omatide, by G. W. Tryon, Jr., Smithsonian Miscellaneous Col- 
lections, No. 253, 
ee 
A POPULAR EXPLANATION (FOR THOSE WHO UNDER- 
STAND BOTANY) OF THE MATHEMATICAL NATURE 
OF PHYLLOTAXIS. 
BY THE LATE CHAUNCY WRIGHT.? 
TAKS, by the finger and thumb of your right hand, hold of a 
spike of Plantago major, Lepidium Virginicum, or other 
flower-cluster with symmetrically crowded flowers, and with the 
finger and thumb of the left hand grasp it a little higher up, 8° 
as to include between the two hands a dozen or twenty buds on 
a piece of stem about equally tough from end to end. Twist the 
stem, and if it twists equally in all parts you will bring your 
buds into a small number of ranks, let us say 8. By twisting 4 
little in the opposite direction you will get them into 5 ranks. 
Twist harder, and if your stem is tough enough to stand the 
twist you will bring them into two ranks. Turn back to 8 rows, 
and twist harder in that direction ; you will fetch your buds into 
3 rows. Then twist still harder in that direction, and if you have 
an old, tough, plaintain spike, you may get the seed-vessels all 
into one row before your stalk is twisted off. 
1 This article was prepared by Mr. Wright several years ago, at Professor Gray's 
suggestion, In its manuscript form it has been found of much interest and value to 
the botanical students in Harvard College. It is here reprinted without change from 
Mr. Wright’s notes. 
