[142]

Hartfield

Spirality May 4th 1863

I see in Plum shoot (2/5) at very apex, buds decrease successively in size & pretty crowded —

In Lychnis (?) with opposite leaves, the exterior buds (seen with 1/10' lens) are exactly equal & not on centre of axis. The next 2 leaves being alternate well explained by crowding & requisite space being then granted —(Does not bundles of spiral vessels account for leaves running in lines: first establish this, & establish principle of alternation & in flowers & in rows of shillings & then go on to Spires) There is wider distinction between buds necessarily found on continuously growing axis & contemporarily formed when opposite or in whorls — I think spire would result from buds successively formed on growing axis, with centre requisite space between each?? Can alternation

[142v]

I must assume when only 2 or 3 leaves in spire there is not crowding enough to make alternation necessary on growing them; though it is enough in flower — But in whorl of 3 I must assume that there is crowding enough —

360 [x] 2 [=] 720 [÷] 5 [=] 144

In young Plum — shoots are ring of dots or groups of spiral sepals & not 5 defined groups

with opposite leaves the cotyledons determine first pair & then others alternate & then 3d pair alternate & so on.— With 3 leaves, whatever position of 3 first, the next 3 alternate & the next 3 above first three leaves.—

[143]

settle the definite angles? First make diagram of all angles [diagram]

Also draw 2/5, 3/8, 5/13, 8/21 thus [diagram]

& then 3/8 & so on & see if we have alternation; & so with 3/8 & 5/23.—

Then try such an angle as 160° 170, 154° & see if there would be alternation.— /over

[143v]

Take some other fraction & so as 3/5 or 4/7 1/2 1/3 2/5 3/8

If we take assume that leaf buds successively formed on continuously growing axis, at some definite angle from each other can hardly fail to form a spire; take alternate leaves (ie 180°) & it must be spire — Take 120° — so it will be — assume angle & continued growth & spires will follow.—

I have been looking at young stems of Honeysuckle with alternate leaves, & spiral vessels form about 12 groups in ring, so no explanation of leaf over leaf.— nor in Oleander in which 3 leaves are opposite to each other.