42 
NATURE 
| May 19, 1870 
largely to advance modern education; or Owens College, 
Manchester, whose students show so well the nature of 
the education they there receive by the honours and 
prizes they gain at the London University ; or many other 
flourishing colleges—should have their hands strengthened 
by Government help, In these institutions a thoroughly 
sound education, in all branches, is given. They have 
hitherto depended entirely on voluntary support, but the 
time has come when larger aid is needed to meet the 
modern requirements. Scholarships given by Govern- 
ment as incentives to work, and as helps to the many in- 
dustrious students whose means are limited ; stipends to 
professors, in order that they may obtain teaching assistance 
of a high character, of which they stand sorely in need, for 
it is absolutely impossible for them to teach effectively the 
large classes who place themselves under their guidance ; 
grants for apparatus, and enlarged accommodation for 
the extension of original research—these are subjects 
which must occupy the attention of any committee ap- 
pointed to inquire into the existing state of education. It 
is now pretty generally admitted by scientific men that no 
exclusively scientific education can meet our present re- 
quirements. On the Continent it is felt that it is only in 
universities and schools where a// branches of knowledge 
are taught, that a really scientific education can be given ; 
and we are glad to find that this opinion has gained 
ground in this country, together with a conviction that 
Science studies in their turn render students more apt in 
the acquisition of other branches of knowledge. 
In Germany there is a strong feeling against the estab- 
lishment of mere technical schools. It is maintained 
that boys should receive the same training up to a certain 
stage, and that they should afterwards enter for the 
special branch they design tofollow. Professor Kéchly, 
of Heidelberg, Professor of Greek, proposes that there 
should be a thorough but limited instruction in classics, a 
more extended development of mathematics, a course of 
instruction in the natural sciences, and systematic instruc- 
tion in modern languages. Professor Hofmann, who is 
well known in this country, considers that the best safe- 
guard against the vulgarising of Science, when it is taught 
with too special a regard to its applications, is to be found 
in a sound general school training ; and he believes that 
the old gymnasium system is of inestimable value. He 
asserts that in scores of instances he has seen youths 
who have come to the chemistry classes in the University 
of Berlin, with scarcely a knowledge of the meaning of 
the word chemistry, but who have been well trained in a 
gymnasium, in a short time completely surpass their 
fellows, who, in a school of another kind, have acquired 
considerable knowledge of the elements of chemistry. All 
the Polytechnic Schools of Germany are rapidly approach- 
ing the university type ;—the teaching of the principles of 
Science, and not of the applications, is becoming more 
and more the main object. 
LEONARDO DA VINCI AS A BOTANIST 
EW men have better earned the title of universal 
genius than Da Vinci. An ardent disciple of Nature, 
disdaining mere superficial knowledge, he went to the 
root of whatever he took up, and attained an intimate 
acquaintance especially with everything that bore on his 
beloved art of painting. And this art was understood by 
him in its widest sense. Not content with representing 
the mere outward appearance of Nature or of the human 
form, he considered it a part of his business as a painter 
to investigate the laws which produce those appearances 
or which govern that form in its healthy state. To the 
long list of his acquirements given in the catalogue of the 
Louvre collection, as painter, sculptor, architect, engineer, 
physicist, writer, and musician, may now be added that of 
botanist. In the first number of a new botanical journal, 
Nuovo Giornale Botanico Italiano, published at Florence, 
Sig. G. Uzielli has given some interesting extracts from a 
work by Da Vinci, from which he would appear to have 
anticipated the discovery of certain botanical laws gene- 
rally attributed to writers of a later age. These extracts 
are taken from a section of his great treatise on painting, 
entitled “On Trees and Vegetation,” which, however, is 
found only in one edition of that work, the Roman. The 
following are the points on which the originality of his 
observations deserves especial mention. 
1. The laws of Phyllotaxis, or of the arrangement of 
leaves on the stem. Da Vinci appears to have been the first 
to observe that the order of growth of the leaves is uniform 
in the same species ; and that their modes of arrangement 
can be divided into three principal forms—the opposite, the 
whorled or verticillate, and that usually denominated in 
text-books the alternate, but which should rather be called 
the spiral. He also pointed out that in the case of leaves 
growing in opposite pairs, they are generally arranged in 
a “ decussate ” manner, that is, each pair grows at right 
angles to the pairs immediately above and below it ; that 
when leaves are verticillate, those in each whorl are seldom 
in a direct line with those in the whorls immediately above 
and beneath ; and that a very common form of the spiral 
arrangement is that sometimes called “ quincuncial,” where 
the cycle is completed by five leaves, the sixth being in a 
direct line with the sixth above and beneath. Another 
observation of the great painter’s is, that inasmuch as 
branches grow from buds generated in the axils of leaves, 
the arrangement of the branches on the trunk necessarily 
corresponds to that of the leaves on the stem. 
In botanical works it is generally stated that Sir 
Thomas Browne, in his quaint little treatise “ The Garden 
of Cyrus, or the Quincuncial Lozenge,” published in 1658 
(a work not mentioned in Pritzel’s “ Thesaurus Litterature 
Botanicze”), was the first to describe the spiral disposition 
of leaves, which was afterwards noticed contempora- 
neously by Grew and Malpighi. Bonnet,* however, in 
1754 followed out the laws of phyllotaxis in a far more 
exact manner ; and the subject has been still further elu- 
cidated by Goethe, Schimper, Braun, Steinheil, the brothers 
L. and E. Bravais, and Martins. To Da Vinci, however, 
who lived from 1452 to 1519, is clearly due the priority in 
the discovery of these laws ; although, as might be ex- 
pected, many of his observations show a crudeness and 
imperfection which have been corrected by more recent 
writers. , 
2. The manner in which, from the structure of the trunk 
of exogenous trees, their age can be determined, This 
fact, although now familiar to unscientific persons, 
appears to have been unknown to the ancients ; since 
Theophrastus makes no mention of it, nor does Pliny, who 
* Bonnet, Ch., Recherches sur l’usage des feuilles dans les plantes, 
