174 THE JOURNAL OF BOTANY 
NOTICE OF BOOK. 
Mathematische und mikroskopisch-anatomische studien tiber Blatt- 
stellungen. Von Dr. G. Van ITERson, Jun. Jena: Gustav 
Fischer. 1907. 8vo, pp. xii. 331, tt. xvi. 
A CAREFUL Sonaly of Dr. Arthur Henry Church’s treatise “On 
the Relation of Phyllotaxis to Mechanical Laws” seems to have 
led Dr. Iterson to reconsider and further to extend the geo- 
metrical and mechanical theories. The first and second parts of 
Ch 
tion of these formule to particular cases, for the urpose of 
numerical illustrations, and twenty- -one tables containing the 
ults o The author gratefully 
a) 
2 
— 
OQ 
S 
-_ 
2 
or 
his sister Agatha in working out some of the more difficult of the 
calculations. The second part of the book contains the botanical 
applications 
Tt has been ig oncmine ee! previous observers that the hori- 
zontal divergence betw uccessive leaves on the stem of a 
plant, when is same iy "indicat ed as a fraction of the circum- 
ference of the axis, can be approximately repre: mgt for the 
principal spiral, by a member of the following 
4,4, 2, 3 a, fh, 33, &e., the ultimate ae of the series 
3— v5 : 
being = ‘381966 and called “the limiting divergence” ; 
that is, when expressed in degrees, by one of the following 
gles :— 
180°, 120°, 144°, 135°, 138° 28’, 137° 9’, 137° 39’, &., to 
28". 
For the leaf-arrangement on a subordinate spiral the diver- 
proximately represented by a member of the 
following series :— 
1 1 2 3 5 if 
—, ——,, ————, ——, —— ke., to -, 
z z+r1 22-1 3z--2 52+3 aoe 
5—1 
‘where z is an integer, and % = ———— = °618034. 
2 
