The main branch always goes below, as is shown by the branch f n m, which does not go to f n o.

The forms of trees (408—­411).

408.

The elm always gives a greater length to the last branches of the year’s growth than to the lower ones; and Nature does this because the highest branches are those which have to add to the size of the tree; and those at the bottom must get dry because they grow in the shade and their growth would be an impediment to the entrance of the solar rays and the air among the main branches of the tree.

The main branches of the lower part bend down more than those above, so as to be more oblique than those upper ones, and also because they are larger and older.

409.

In general almost all the upright portions of trees curve somewhat turning the convexity towards the South; and their branches are longer and thicker and more abundant towards the South than towards the North.  And this occurs because the sun draws the sap towards that surface of the tree which is nearest to it.

And this may be observed if the sun is not screened off by other plants.

410.

The cherry-tree is of the character of the fir tree as regards its ramification placed in stages round its main stem; and its branches spring, 4 or five or 6 [together] opposite each other; and the tips of the topmost shoots form a pyramid from the middle upwards; and the walnut and oak form a hemisphere from the middle upwards.

411.

The bough of the walnut which is only hit and beaten when it has brought to perfection...

[Footnote:  The end of the text and the sketch in red chalk belonging to it, are entirely effaced.]

The insertion of the leaves (412—­419).

412.

OF THE INSERTION OF THE BRANCHES ON PLANTS.

Such as the growth of the ramification of plants is on their principal branches, so is that of the leaves on the shoots of the same plant.  These leaves have [Footnote 6:  Quattro modi (four modes).  Only three are described in the text, the fourth is only suggested by a sketch.

This passage occurs in MANZI’S edition of the Trattato, p. 399, but without the sketches and the text is mutilated in an important part.  The whole passage has been commented on, from MANZI’S version, in Part I of the Nuovo Giornale Botanico Italiano, by Prof.  G. UZIELLI (Florence 1869, Vol.  I).  He remarks as to the ‘four modes’:  “Leonardo, come si vede nelle linie sententi da solo tre esempli.  Questa ed altre inessattezze fanno desiderare, sia esaminato di nuovo il manoscritto Vaticano”.  This has since been done by D. KNAPP of Tubingen, and his accurate copy has been published by H. LUDWIG, the painter.  The passage in question occurs in his edition as No. 833; and there also the drawings are wanting.  The space for them has been left vacant, but in the Vatican