52 
being caused to move in a larger orbit than that de- 
scribed by it while still a part of the sun’s mass,” and 
the author suggests the action of comets carrying off- 
portions of the nebulous border of a sun, as they struck 
it in the direction of its motion at a suitable moment. 
The fifth and last article, in the results of which Dr. 
Smith expresses confidence other than he shows in respect 
of his earlier excursions into heterodox and quasi- 
heterodox physics, is devoted to “the laws of river- 
flow.” Residence on the banks of the Mississippi 
enabled him to discover the formula of a double spiral 
action, by which to explain the elevation of the middle 
of a stream, the drift of floating material from the sides 
and of sunken material to the sides, the shape and 
depth of the eroded channels, the different speed of 
diverse portions of the current. This piece of at any 
rate unborrowed speculation appears not unworthy of 
consideration. Ee Webs 
Das Heidelberger Schloss und Seine Garten in alter 
und neuer Zeit und der Schlossgarten zu Schwetzingen. 
By H. R. Jung and W. Schroder. Pp.74. (Berlin: 
G. Schmidt, 1898.) 
IN this work we have an historical account of the gardens 
and castles of Heidelberg—the famous German university 
town, and its less well-known neighbour Schwetzingen. 
The authors are both gardeners, and, although the book 
is written chiefly from a garden point of view, a good 
deal of space is given to purely historical matter. 
Judging from the photographs, the gardens at Schwet- 
zingen seem to be far more beautiful and natural than 
those of Heidelberg, where grottoes, shrines, and various 
other architectural devices appear to be the leading 
features, and not always ornamental ones either. To 
those interested in the history of very old and famous 
gardens, this treatise may be of use ; and it will not take 
up much space on the library shelf, being only about a 
quarter of an inch in thickness. It is well printed and 
illustrated, and is practically free from misprints ; the 
only one of any importance being at p. 47, where Azalea 
appears as Aralea. Were it not that there is a genus 
Aralza, this slip would not be worth mention. 
JOHN WEATHERS. 
Graduated Test-papers in Elementary Mathematics. By 
Walter J. Wood, B.A. Pp. 71. (London: Macmillan 
and Co., Ltd., 1899.) 
THERE are forty test-papers in this collection, each con- 
taining questions in arithmetic, Euclid, and algebra. At 
the head of each test are notes stating the parts of the 
subjects required in order to solve the questions. The 
papers are primarily intended to test the progress of 
students preparing themselves for the examination in first 
stage mathematics of the Department of Science and 
Art, and Departmental teachers will find them of real 
value for that purpose. In the lower mathematical forms 
of secondary schools, also, the papers should be of ser- 
vice, as many of the questions have been selected from 
the papers of public examining bodies mostly favoured 
by such schools. Care appears to have been taken in 
selecting and arranging the questions, and answers are 
given to all the questions in arithmetic and algebra. 
The Story of the British Race. By John Munro. Pp. 242. 
(London: George Newnes, Ltd., 1899.) 
SoME time ago Mr. Munro wrote “The Story of 
Electricity” for this library of useful stories. In this 
volume he transfers his attentions to the science of 
anthropology, and expresses in his preface the hope that 
his book will “tend to destroy some errors regarding the 
origin and pedigree of the nation which have infected life 
and literature for ages.” The volume should be the 
means of creating an interest in the study of mankind, in 
addition to imparting a knowledge of the nature of the 
races in the British Islands. 
NO. 1542, VOL. 60] 
NATURE 
[May 18, 1899 
LEITERS TO THE EDITOR. 
[The Editor does not hold himself responsible for opinions ex: 
pressed by his correspondents. Neither can he undertake 
to return, or to correspond with the writers of, rejected 
manuscripts intended for this or any other part of NATURE 
No notice ts taken of anonymous communications. | 
Fourier’s Series. 
I HAVE M. Poincare’s authority to publish the accompanying 
note regarding the applicability of Fourier’s series to discon- 
tinuous functions, and send it accordingly for publication in 
NaTurRE. A, A. MICHELSON. 
MON CHER COLLEGUE,— Comme je l’avais prévenu vous avez, 
: Y sin xz 
Prenons d’abord J’integrale See as 
tout a fait raison. 
0 
dont la limite pour y=o0 est m/4, 0, — 7/4 selon que z est positif, 
nul ou négatif. 
Faisons maintenant tendre simultanément z vers 0 et y vers 
Vinfini de telle fagon que zy tende vers a. La limite sera 
ag 
| Si *dx qui peut prendre toutes les valeurs possibles depuis 
ones 
O jusqu’a ik Sue 
o 7 
: Cheer pe sin £2 
Si nous prenons maintenant 7 termes dans la série —— 
z 
en faisant tendre simultanément z vers o et # vers l’infini de 
telle fagon que le produit #z tende vers a, cela sera évidem- 
ment la méme chose ; et la différence entre la somme et l’integ- 
rale sera d’autant plus petite que z sera plus petit. Cela se voit 
aisément. Tout a vous, 
(Signed) POINCARE. 
A Note upon Phosphorescent Earthworms. 
It has been long known that earthworms may be phosphor- 
escent. So long ago as 1836 Prof. Duges described, under 
the name of Lumébricus phosphoreus, a worm which showed this 
peculiarity. In 1887 Prof. Giard showed that a worm prob- 
ably identical with this, and, if so, not a Lumdérzcus at all, was 
marked luminous, especially when the soil was disturbed in the 
vicinity. Giard named the species Photodrzlus phosphoreus. 
It has been met with and noticed to be luminous by two other 
observers. Quite recently (Zoolog. Jahrbiicher,xii., 1899, p. 216) 
Dr. Michaelsen, of Hamburg, ascertained that this species of 
Giard is really identical with Aicroscolex modestus of Rosa, 
The multiplication of names is hardly the fault of Prof. Giard, 
since the genus AZicroscolex had only been instituted a few 
months before his genus Photodrzlus. This species, unlike the 
majority of its congeners, which are chiefly congregated in 
Patagonia, and there very abundant, is not only European, but 
also occurs in England. It seems also to be, at least usually, 
phosphorescent. I received some time since, through the 
kindness of Mr. Carleton Rea, a few small earthworms from 
_ the neighbourhood of Worcester, which were undoubtedly a 
Microscolex, and at least not much different from AZ, modestzs. 
Mr. Rea informed me that they were phosphorescent, with a 
‘light emitted exactly similar to that of the glow-worm.” 
They could be stimulated to show this light by ‘‘ stamping the 
lawn.”’ It has been suggested that this phosphorescence in 
earthworms is really due to photogenic bacteria entangled in 
the slime upon the skin. Possibly such an explanation may 
account for the occasional phosphorescence of <Adlolobophora 
Joetida (the ‘‘ Brandling”’), observed by Vejdovsky. But the 
regularity, and the mode of excitation, of the luminosity seems 
to show that Aicroscolex is phosphorescent in its own right. 
FRANK E. BEDDARD. 
ON THE CHEMICAL CLASSIFICATION OF 
THE VSPARSA 
ie the attempts made to classify the stars by means 
of their spectra, from Rutherford’s time to quite 
recently, the various criteria selected were necessarily 
for the most part of unknown origin ; with the exception 
of hydrogen, calcium, iron, and carbon, in the main 
chemical origins could not be assigned with certainty to 
1 By Sir Norman Lockyer, K.C.B., F.R.S. A paper read at the Royal 
Society, May 4. 
