THE COTTAGE GARDENER AND COUNTRY GENTLEMAN, October 19, 1858. 
numerators equals tlie numerator of the third, and the sum of the 
first two denominators, the denominator of the third. Continu¬ 
ing the series by this rule, that is by adding together the nume¬ 
rators and the denominators of the last two fractions, the next 
fraction will be f. 
Now, will the next higher spiral with which we shall meet be 
a f spiral? Is this Nature’s law? Let us see. We find a long, 
straight shoot of Osage Orange in yonder hedge. If it be desti¬ 
tute of leaves, no matter, the thorns stand exactly in the same 
order as the leaves did, for they arc axillary thorns. Now pass 
we our thread from thorn to thorn, fastening it by a single loop 
to each, and another beautiful spiral is before us. Here neither 
the third, nor the fourth, nor the sixth leaf brings us to the com¬ 
pletion of our cycle, but the ninth does ! and in order to reach 
the ninth we have made three complete turns and passed eight 
leaves ! The fraction f, therefore, is the appellative of this, the 
Osage Orange-cycle; the angular distance between any two con¬ 
tiguous leaves is also f of a circle, or 135°, and the number of 
perpendicular rows of leaves will be 8, or the plant is 8-ranked. 
The next fraction in our series is 5-13, and this also we find 
verified in nature as the next higher mode of spiral arrangement. 
The leaves of the Houseleek, or of a young shoot of the White 
Pine, are thus arranged,—that is to say, the cycle of the House¬ 
leek, &c., consists of 5 turns and thirteen leaves, whose angular 
distance is 5-13 of 360°. 
But the older stems of the White Pine have their leaf-scars 
arranged after the next higher plan of Phyllotaxy,—viz., 8-21. 
Hence it would appear that the growth of the stem, after the 
first year, is accompanied by a spiral movement, in the same 
direction as its first development. We will now recapitulate 
these several plans with examples :— 
Plan i : Elm, Linden, or Lime; Indian Corn, Wheat, and all 
the Grasses. 
Plan £ : Alder, Bii’ch, Tulip, Orchis, Carex, and all the Sedges. 
Plan 2-5 : Apple, Peach, Pear, Cherry, Willow, Poplar, Oak, 
Hickory, Rose, &c. 
Plan : j : Osage Orange, Holly, Flax, Plantain, Aconite. 
Plan 5-13 : Eyes or buds in the tuber of the Potato, scales of 
the Pine cone, or leaves, of its annual shoots. Also Erigeron or 
Flea-bane. 
Plan 8-21 : Leaf-sears of Pine, leaves of Pitch Pine, Spruce. 
To trace out the formative spiral in the simpler plans, like that 
of the Alder or Peach, is very easy ; but to do so in cases of the 
5-13 or 8-21 arrangement requires the exercise of much care and 
skill. The following suggestions will be of use:—Suppose we 
have the stem of White Pine under trial. The spiral thread 
here winds against the sun. Its turns are rather close,—nearer 
together than the consecutive leaves are. The line from one scar 
to the next will vary but little from horizontal, and fall but little 
short of half a turn (8-21), and, when it is correctly coiled,— 
except in abnormal eases,—it will include every leaf-scar. 
The case of opposite leaves presents a new phase of the spiral 
arrangement. Here two leaves stand opposite each other at the 
same node or joint. The second pair above never stand exactly 
over the first part, but over the intervening spaces, and generally 
over the centre of those spaces, as seen in the Catmint, Boneset, 
Maple. Two spiral lines, therefore, instead of one, arise, and 
proceed up the stem together and parallel in such plants. In 
whorled leaves, like those of Trumpet-w r eed, where three or more 
leaves stand around the same node, we have three or more parallel 
spirals. 
Finally, we thus learn that the course of development in the 
growing plant is universally spiral, either evolving a single, 
double, or triple, &c., spire, prescribing with unerring exactness 
the position of each leaf, and consequently of each axillary bud, 
thorn, or branch. “ Marvellous are thy works, O Lord of Hosts ! 
in wisdom hast thou made them all!”—and it will be a long time 
before we shall have comprehended all of His works in the 
structure of the plant.— The Cineinnatus. 
ANECDOTE OF THE ROBIN. 
A FEW weeks ago an interesting account of the familiarity of 
the Robin was published, under the above heading, in the pages 
of The Cottage Gardener. With your permission, 1 will 
relate a similar instance, which has occurred here (Torquay). Mr. 
Sharland, who is a marble mason, and is nearly eighty years of 
age, is the occupier of a garden at Ellacombe, where he spends 
much of his time, amusing himself with the culture of flowers and 
fruits. About eighteen months ago he contracted an intimate 
acquaintance with a hen Robin, which would follow him to every 
part of the garden; and, when Mr. Sharland took a seat in his 
arbour, the little favourite woidd flit about in front, hopping 
from twig to twig, and alight, upon the same bench. By degrees 
this familiarity increased, and at length the Robin would actually 
pitch upon the old gentleman’s lap, and gather the crumbs, 
which he never failed to provide for his visitor. Five or six 
times in the week,—I might say, almost every day,—Mr. Shar¬ 
land, for the last eighteen months, has regularly visited his 
garden ; immediately on entering which he calls for his ‘‘ Bob,” 
and “ Bob ” as regularly appears, with every demonstration of 
delight. It. is worthy of notice, that this Robin mated in the 
spring; but neither her mate nor any of the members of her 
young family could be induced to partake of the fare daily pro¬ 
vided, which was spread out on the old gentleman’s lap, but 
would flutter about at the entrance, waiting for the dainty morsels 
to be thrown to them. The Robin does not appear to be intimi¬ 
dated by the presence of another party, as many persons, includ¬ 
ing myself, have accompanied Mr. Sharland to liis garden, and 
! witnessed the above facts for ourselves. As in the first case 
noticed in your pages, no attempt has ever been made to capture 
the bird.—J. T. W., Torquay. 
ON WASPS’ NESTS UNDER WATER. 
Mi attention has been called to Mr. Errington’s notice, at 
page 370, Yol. XX., concerning wasps’ nests, “under the water 
level—in fact, the young grubs over head in water and perfectly 
healthy.” I have found them so myself; but, of course, in such 
situations they soon perish ; and slight knowledge of wasps’ nests 
will convince any one that they must soon decay in water ; and, 
supposing that the grubs could live under it “ without air,” 
how could they find food, since they have no affinity to the lame 
of insects bred in water,—for instance, to those of cousin Johns. 
These find food where they are hatched, without the least care of 
the parent insects, while those of wasps are carefully fed; and 
I need hardly say that the yellow pests cannot dive under water. 
But the chief difficulty to be explained is, how came these nests 
to be immersed ? Perhaps they belonged to a larger and darker 
kind of wasps than the common ones, which are fond of building 
in the banks of rivers, and often make large cavities, to hold 
their nests, below the usual water level. In autumn, when the 
rivers increase, the lower combs, which contain the broods of 
drones and queens, are immersed, and left by the insects to perish. 
I should here note, that when the broods are found “ perfectly 
healthy” under water, they certainly have not been long there,— 
probably the nests had dropped down while in the act of being 
dug out. I have known them do so even from the tread of the 
foot above, especially after rain, which loosened the props of the 
paper-like structures. 
If Mr. Errington doubts what I have said respecting the 
difference of wasps, and he examines his nests, perhaps he may 
find them of the same texture and colour as those of the tree 
wasp. The nests of both, being exposed to damp, are of sounder 
texture than that of the common wasp, which, like the hornests’ 
nests, are made of the scrapings of decayed wood. These are 
fond of dry places for their nests; and I possess one, of the 
common wasp, which was taken from under the roof of a barn, 
about the Bize of a beehive.—J. Wighton. 
TO CORRESPONDENTS. 
Boite a Hocppe ( Miss Gilbert).— It may be had at Messrs. Burgess and 
Keys, Newgate Street, London. 
Transplanting Machine (C. 12.). — We suppose you hare Mr. 
M'Glaslien’s in your memory. It effects the removal of large trees ; but 
the same operation may be performed as effectually by much cheaper 
modes of operation. 
• Pears Unfruitful [J. A. C.).—Seurre Hose is Beurrc Bose, Beurre 
Fortunee is Fortunee. Most likely a good watering would hare saved the 
fruit, and caused the tree to grow. We would advise cutting the roots of 
the Jargonelle directlv, and also thinning the shoots, if at all thick. Most 
likely the Marie Louise will bear well next year. Thin out the young 
shoots not wanted. With such a warm summer, and your best Pear crack¬ 
ing, we fear you will do little good with it in your climate. If you do not 
like to change or graft it all over with what does suit, try what cutting the 
roots, and raising them nearer the surface will do. 
The Damson ( A New Subscriber ).— The insect which infested your 
Damson trees is Aphis pruni, an incorrigible pest, not easily got rid of. 
Many applications have been recommended for destroying it, but we never 
