42 THE REV. GEORGE HENSLOW ON THE ORIGIN OF THE 
latter genus, it may be observed in passing, there is a frequent change from opposite to 
alternate leaves), that the numbers * fours,’ * fives,’ and ‘sixes’ are often found amongst 
the whorls of the flowers on the same Jessamine, Elder, Rue, &c., and, again, that there 
is the positive fact of opposite and whorled leaves passing into spiral on the same stem, as 
in Epilobium, there would thus seem to be а just inference that the great majority of 
instances of spiral phyllotaxis have taken their origin from whorled and opposite 
arrangements. 
Opposite Leaves generally fail to produce the 4 and $ arrangements.—On referring to 
the figures of the diagram (fig. 1), it will be seen that for MIRA leaves to become spiral 
and distichous (that is, to be represented by the fraction $) the third leaf, No. 2, must, as 
it were, pass through 90? in order that it may fallover the first (or 0). Similarly if 
decussate leaves were to pass into the spiral arrangement represented by 3, 2. e. to become 
tristichous, the fourth leaf, No. 3, must fall over the first. In all other cases the leaves 
have to shift through a much less angle than 90°. This may be the reason why 4 and $ 
are by no means common amongst Dicotyledons. On the other hand, they appear. 
particularly frequent amongst Monocotyledons. Тһе above failure in producing the 
1 and 1 arrangements is on the supposition that the spirals result from the conversion of 
а definite number of pairs of opposite leaves. Оп referring, however, to fig. 1, it will be 
seen that if leaf (0) be neglected, and No. 1 represent the first leaf, then the 4th is 
actually over the 1st, and thus will give rise to the $ plan. This may have been the 
origin of the tristichous arrangement amongst Dicotyledons, as well as of the ternary 
symmetry which occasionally occurs in the flowers of that class; but it is comparatively 
rare in both leaves and flowers; and this seems to correspond with the fact that it is 
usual to convert complete pairs into alternate leaves. Аз an additional faet it may be 
mentioned that other rare arrangements, such as 74, 74, $4, &c., which occasionally 
occur in nature, can be deduced from it, and lend proportional aid to the acceptance of 
the theory. This will be better seen by referring to the scheme appended to this 
paper (fig. 3). 
Before suggesting a eause for this latter fact, it would be as well to state that, in 
every case that I have examined, wherever leaves have to be represented by $ in 
Dicotyledons, I believe it is an effect produced by habit of growth resulting in an 
apparent production of the $ or $ arrangement. Thus, if the leaves on а shoot of Ivy 
growing against а wall be compared with those on a free (barren) branch, or the leaves 
of the common Yew with those of the * fastigiate" variety—or, again, comparing the 
leaves оп а horizontal bough of the common or Portugal Laurel with those on a shoot 
growing freely upwards, it will be seen at once how the usual and really or pice 
distichous arrangement reverts to the manner of growth represented by 2 or 2, thereby 
revealing the fact that in those (and probably all other) instances the leaves were not 
originally distichous, but have only acquired that arrangement by habit. 
l have, indeed, reason to suspect that it is only in those instances where the leaves of 
à branch lie in one and the same horizontal plane, from a peculiar habit of growth, that 
the $ and perhaps } arrangement occurs, and that this obtains mostly in а certain number 
of instances, where the leaves are broad and not dissected; for deeply gashed or com- 
