THE DISTRIBUTION OF CALIFORNIAN MOTHS. 453 
twist we get z, another twist ;&, etc. Some of our cones, then, 
fall into the phyllotaxis of opposite leaves the same as though the 
stem were more or less twisted. The single cone of the European 
larch which indicated the fraction + (a fraction requiring a di- 
vision of numerator and denominator by three to reduce it to its 
lowest terms) falls under decussate whorls of three for its sim- 
plest fraction. 
I leave any further consideration of this matter showing the re- 
lations of the fractions to each other, etc., fo those who have a 
greater skill in mathematics than myself. My examples indicate 
that we may look for some curious series of fractions by diligently 
examining the phyllotaxis of a great number of plants of many 
different species. 
It would be interesting to know whether there are any cones 
which fall into series beginning with decussate whorls of four or 
more scales. 
ON THE DISTRIBUTION OF CALIFORNIAN MOTHS.* 
BY A. S. PACKARD, JR. 
Tue Phalænidæ (Geometrids) of California (including mre 
and Nevada) seem to be composed of four elements: (1) of spe- 
cies of genera exclusively American (North and South). ad 
are Cherodes, Sicya, Hesperumia, Tetracis, Azelina, Gorytodes 
and Metanema. Certain species of these, with several of Tephro- 
sia (a genus largely found in the New World) are the most char- 
acteristic of the Pacific slope of the United States. 
(2) The species next most characteristic belong to the following 
genera : — Halia, Tephrina, Selidosema and Heterolocha. Species 
of these groups occur in Europe, but especially (all except Halia 
which has a species (H. novaria) living in northern Europe) in 
southern Europe, around the Mediterranean Sea, western Asia, 
and Asia Minor; while species of Heterolocha occur in Abyssinia 
and South America (Quito). 
(3) The next group comprises a few arctic or circumpolar s 
cies of Coremia, Cidaria and Larentia, or of cosmopolite genera 
oo Extracted fom a communication presented to the Boston Society of Natural His- 
tory, May 7,1 
