174 
LETTERS: TC PHE “EDITOR. 
(Zhe Editor does not hold himself responsible for opinions ex- 
pressed by his correspondents. Neither can he undertake 
to return, or lo correspond with the writers of, rejected 
manuscripts intended for this or any other part of NATURE, 
No notice ts taken of anonvmous communications. 
Astronomy in the University of London. 
Ir seems desirable to call special attention to the change which 
has recently been made in the conditions with regard to astronomy 
for the B.Sc. Pass and Honours degrees of the University of 
London. This is the more important as, owing to an unfortunate 
slip of the much-overworked academic Registrar, the point was 
omitted from the published examination schedules, and 
has only been corrected by an attached slip in recent issues. 
The point is this, that in future astronomy is to be counted as 
an independent subject for the B.Sc. degree. It will rank 
equally with geology, botany or zoology. It is true that the 
Faculty of Arts has retained a certain amount of astronomy in 
its mathematical syllabus—in my opinion a very poor syllabus— 
which represents, not modern astronomy, but the condition of 
affairs in ‘‘ three day papers ” at Cambridge fifty years ago, when 
the University of London was founded. Why the Faculty of Arts 
does not insist also on a little antiquated geology and a little pre- 
Darwinian biology is cause for wonder. At any rate, the Faculty 
of Science has recognised that astronomy is a suitable subject 
for graduation, and we may hope that students of astronomical 
physics and theoretical and observational astronomy will realise 
that they can now specialise in London before graduating. A 
Pass student will be able to graduate by studying mathematics, 
physics and astronomy, and an Honours student by taking 
astronomy and ez/kex mathematics ov physics. We may 
hope that a school of astronomy will form itself in London 
free from the traditions of the Cambridge Mathematical Tripos, 
and recognising mathematics for the astronomer as ancillary 
only to observational and physical work. Kar PEARSON. 
University College, London, June 15. 
De Vriesian Species. 
THE recent work of Prof. H. de Vries on the origin of species by 
mutation has attracted a great deal of attention, although it 
cannot be said that the facts he presents are of a new kind, or 
that, taken by themselves, they prove anything about the origin 
of species. The great merit of the work is to be found in 
its clear presentation of the subject, with carefully worked out 
examples, at an opportune time. In former years botanists were 
not so ready as they are to-day to recognise apparently minor 
characters as specific, and the great variety of slightly modified 
plant forms passed almost unnoticed. It was not considered 
worth while to investigate the polymorphism of the old specific 
aggregates, and men like Jordan, who didso, were not regarded 
altogether favourably. The old conception of species seemed to 
give us a superabundance of plant types, taking the world over ; 
and many botanists thought, as one recently said to me, that it 
was impossible to catalogue and name the minor forms, decause 
they were infinitely numerous. However, there has arisen a 
new school, especially dominant in America, which recognises 
the fact that many of the old specific names cover a number of 
types which are readily distinguishable from one another. These 
may intergrade. but in many cases they do not seem to do so, 
and though the distinctions may seem small, they are perfectly 
constant. The result of the new investigations is in many cases 
to increase the number of recognised species four-fold, ten-fold, or 
more. Now when one comes to study these numerous species, it is 
evident that much of the difference is not absolute, but consists 
in different combinations of the same or similar characters, like 
the patterns of a kaleidoscope. With a little ingenuity, one 
could almost predict the characters of undiscovered forms. 
Heredity seems every now and then to take a new throw of 
the dice, with results exactly such as de Vries has described. The 
successful throws are those which give results adapted to the 
environment, and these, under the laws governing the survival 
of the fittest, give us what we proceed to describe as new 
species, 
The proof that species do thus originate is not to be found in 
garden experiments alone, but must be confirmed by field obser- 
vations. Unfortunately, the average systematic botanist seems 
to be much more interested in defending his ‘‘ new species ” than 
in asking whether they may not be ‘‘new” in a more literal 
sense than he imagines. Nevertheless, search will be made for 
NO. 1703, VOL. 66] 
NATURE 
[JUNE 19, 1902 
“de Vriesian species,” and thereby the true status of many 
described plants may be revealed. Two instances of such 
which have lately come to my notice may be worth recording. 
(1) Aelianthus petiolaris phenax (new variety). Rays 13, 
mustard yellow, 11 mm. diameter ; corollas and stigmas yellow, 
giving the flower a yellow disc, Found at Boulder, Colorado, 
August, 1901, growing in a field full of normal A. /efiolaris, 
with deep saffron-yellow rays about 8 mm. diameter, and 
corolla and stigmas a very dark wine red. I took both plants 
to the meeting of the American Association for the Advancement 
of Science at Denver, and showed them to an eminent botanist 
who knows the flora of Colorado well, and is not regarded as a 
“splitter.” I said, ‘‘these appear to be forms of one 
species.” ‘*Oh, no,” he replied, ‘‘one is a Helianthus, the 
other a Rudbeckia!” However, the flowers were carefully 
examined in company with Prof, Pammel, and were also shown 
to Miss Eastwood, and no doubt remained that the new variety 
was really an offshoot from /#. fetiolaris, which had probably 
originated where it was found. The variation is the more 
interesting because in the sunflowers (Helianthus) the colour of 
the disc is used as a character to separate groups of species. 
(2) Ribes cereum viridior (new variety). Plant perhaps more 
resinous ; tube of calyx shorter, pale greenish, stigma exserted 
beyond petals. Fruit deep red, small, perfectly spherical. 
Found (first by my wife) between San Ignacio and Las Vegas, 
New Mexico. A clump of bushes presenting these characters 
(observed in two seasons) grows only a few yards away from 
plenty of what Mr. Coville considers genuine 2. cereum, witha 
longer calyx-tube, streaked with purplish pink, and fruit a little 
larger and more inclined to be oblong. I was at first quite sure 
I had a valid species in this zzr¢dzor variety, and Mr. Coville, 
before we got the fruit, thought the specimens might be his 
R. mescalerium, which has black fruit. Now, however, it 
appears reasonably certain that the plant represents a de Vriesian 
“* species” or mutation. Miss Eastwood has lately described a 
somewhat similar mutation of a Californian species, under the 
name (2bes sertceum viridescens. T. D. A. COCKERELL. 
East Las Vegas, New Mexico, U.S.A., May 22. 
Formula for the Perimeter of an Ellipse. 
THE formula given by your Queensland correspondent 
(Nature of April 10, p. 536) for the perimeter of an ellipse is 
not at all objectionable on the score of degree of approximation, 
It leads, however, to another, which for practical purposes is 
much preferable. If for shortness’ sake A be written for 
log 2/ log 47, he says in effect that the perimeter of an ellipse 
with semi-axes @ and 4 is approximately equal to the circum- 
ference of a circle of radius 
(22s 
2 
Now A= 3010300/*1961199, two convergents to which are 3/2 
and 20/13. Taking the former of these—a course which entails 
the extraction of no roots other than the square and the cube— 
we obtain the following result:—The perimeter of an ellipse 
is approximately equal to the circumference of acircle the radius 
of which is the semi-cubic mean of the semi-axes of the ellipse 
(see Messenger of Math., xii. pp. 149-151 ; Proc. Manchester 
Lit. and Phil. Soc., February 1, 1go0r), 
But by far the best result of this kind known to me may be 
put in the shape of a rule as follows :—To obtain the radius of a 
circle the circumference of which will be a close approximation to 
the perimeter of a given ellipse, diminish twenty-one times the 
arithmetic mean of the semi-axes of the ellipse by twice the 
geometric mean and thrice the harmonic mean and divide the 
remainder by 16. As an illustration of the value of this, 
we may take the classical example where z=1 and 6="8. The 
three means A, G, H, referred to in the rule are then “o) NS; 
8/9 and 
_ 18°9 —(1°7888544 — 2°6666666) 
16 4 
= 18:9 ~ 474555210 
16 
= 144444790 
TOM ee 
= °90277993. - - 
