156 REV. PROF. G. HENSLOW ON THE ORIGIN OF 
if the spiral were continued, would be the first number of the second cycle—is taken 
in to complete two, whorls of three parts each: the 144° being now changed to 120° 
hetween any two successive parts. 
Starting afresh with No. 7, 7 to 12 make the next two trimerous whorls, and so on. 
If there be tri-trimerous whorls, then the one cycle of $ divergence is taken together 
with the first number of the next, so that the result is 3--3--3. 
It will be observed that No. 21 falls over No. 1, this number of parts having required 
eight coils or circles; so that the whole of the floral whorls, calyx, corolla, stamens, and 
carpels utilize the 21 numbers, that is, a single cycle of 3°; ; though each pair of whorls 
was formed out of a single cycle of 2. The dotted lines show the positions of the parts 
of the whorls. 
The genus Anemone is one of an order characterized by having quinary flowers; and 
although it usually has six sepals, as in 4. Pulsatilla, they may vary from 5 to 9. 
Thus 4. nemorosa, ranunculoides, and Coronaria (in Malta) have often 5 sepals. The 
characteristic involucre of three parts has these on the 3 divergence. In A. Hepatica it 
takes the form of an extra whorl, so that with the 6 sepals it follows the 2 plan. 
In A. japonica each member of the involucre has a floral peduncle in its axil, while the 
calyx may have 3+3, 5, or more sepals. There is a well-marked internode between the 
innermost sepals and the stamens, showing that the origin of the calyx is noć due to the 
andreecium, but to the foliage; though now and then one or more stamens may be 
petaloid in part. Hence 4, 2, and $ are all represented in the calyx, the two latter 
divergences being especially characteristic of Dicotyledons. 
Turning to the foregoing list of examples, Lardizabala will illustrate the preceding 
observations ; and the reader will at once perceive the difference between such a flower 
and that of any common Morocotyledon, as of Alisma or of a Tulip, with ternary 
whorls. These Monocotyledonous perianths, representing calyx and corolla, consist of 
only two whorls of three parts each—the whole flower being represented as 3 . 3 . 3, 3 . 3; 
the periods marking off the four floral whorls, but the comma separating two distinct 
cycles of stamens. On the other hand, Rumex should be represented as deficient in the 
corolla, thus: 3+3 . [3+3] . 3+3 .3. The dislocation of the stamens (two being in 
front of each outer sepal) points to the absence of an intermediate whorl; the whole 
number of parts being 21, representing a cycle of the jj arrangement. Having once 
changed cycles of fives (2) into whorls of threes, or the one cycle of twenty-one parts (34) 
on the continuous spiral line, such can be increased in number upwards or downwards, 
by making additional “staminodal” petals as in Magnolia, or bracts may become 
petaloid and add trimerous whorls below the calyx, as occurs, e. g., in Berberidew and 
 Menispermes. In this latter order, the genera are mostly with 3+3 . 3+3. ¢, 8+8. 
9,9. But they may have the following numbers in the calyx, 3+3+3 ( Coscinium) ot 
—3+3843-+43 (in Botryopsis) (Benth. & Hook. fil. ‘Genera Plantarum’). 
Berberideæ have mainly di-trimerous whorls; but three genera are tetramerous. 
* Fours" can only be derived from “fives” by “symmetrical reduction" *. I would, 
* « Note on the Causes of the Numerical Increase of Parts of Plants,” Journ. Linn. Soc., Bot. vol. xvi. (1877) p. 20° 
