202 THE JOURNAL OF BOTANY 
coaxial system of confocal ITT which form the ae 
walls. The author urges that the paraboloid shape of 
bis is Saapable of proof, and that a a ane founded on 
this principle does not satisfy the evidence deduced from Sachs’s 
drawings; he prefers the proposition (page 42) think. the genetic 
spiral is a icmp spiral, homologous “with line of current- 
iral-vortex, and that in such a system the action of 
orthogonal Horeed will be mapped out by other sittiogoenally inter- 
secting log. spirals,—the ‘ parastichics.’” 
he application of spiral-vortex construction is then arranged, 
followed by a demonstration that helices and spirals of Archimedes 
do not satisfy the requirements of ontogenetic observation. The 
vat portion of the first part contains a consideration of “ideal 
angles,” all of which follow from summation-series expressing 
‘values of continued fractions of the type 
1 
oT 
Be oa 
1 + 1, etc., 
where a oa be any whole or fractional number 
The second part deals with asymmetrical and symmetrical 
ueliobists; “hid dibsiineee Normal Fibonaci phyllotaxis. Il. 
Constant phyllotaxis. ILI. Rising phyllotaxis. IV. The sym 
metrical concentrated type. V. Asymmetrical least-concentrated 
type. VI. Symmetrical non- pstiet Las: type. VII. Multijugal 
types. VIII. Anomalous series. 
W. P. Hiern. 
Manual of the Flora of the Northern States and Canad By 
Nartuanre, Lorp Buses n, Ph.D. New York: Henry “Holt & 
Co. 8vo, cloth, pp. 1 
In this well ogee volume, Dr. Britton has supplied what we are 
sure must have been ‘‘a long felt want” among American botanists. 
The manuals of Asa Gray and Chapman for the Northern and 
Southern States respectively a excellent books, and have been 
of incalculable value in the past; but it was high time for a book 
which should be for the field what the Illustrated Flora is for the 
The 
its pre follows Engler & Prantl’s Pilatictnfaudlien ; the nomen nl 
ture follows the rules of what is known as see ‘Rochester Code,” the 
