JUNE 26, 1902] 
Prof. Mackenzie is an idealist in his general position, 
though he evidently realises the difficulties which beset 
an over-hasty idealism, and states his result in an 
avowedly tentative form. 
Histoire des Mathématiques dans  Antiquité et le Moyen 
Age. Par H.G. Zeuthen. Traduite par J. Mascart. 
Pp. xvi + 296. (Paris: Gauthier-Villars, 1902). Price 
fr. 7. 
THIS translation of Prof. Zeuthen’s well-known and 
deservedly popular work has been revised by the author, 
and several interesting notes have been added by M. Paul 
Tannery. The greater part of the volume deals with the 
mathematics of the Greeks, especially their geometry ; 
the Elements of Euclid, in particular, are analysed in 
considerable detail, and discussed with intelligence and 
sympathy. Conservatives who still rally to the cry of 
“Euclid, and nothing but Euclid,” may be respectfully 
invited to study, with the help of such comments as Prof. 
Zeuthen’s, the actual text of the Elements, which is now 
easily procurable in Heiberg’s excellent edition. It 
ought, on the one hand, to increase their admiration of 
the Greek geometer, and, on the other, to convince them 
of the absurdity of supposing that a garbled travesty of a 
portion of his work is the best introduction to geometry 
to put into the hands of the English schoolboy. Another 
interesting section is that which deals with the mathe- 
matics of the Arabs. It is difficult to claim for them any 
very substantial contributions to the science; but they 
showed themselves apt pupils both of the Greeks and of 
the Indians, they kept the study of mathematics alive 
when Christian Europe was passing through its darkest 
age of ignorance and superstition, and they powerfully 
helped on the subsequent revival. Yo Moslem scholars, 
and their enlightened rulers, modern Europe owes a debt 
which is not always sufficiently realised. M. 
A la Conguéte du Ciel! Contributions Astronomiques 
de F.C. de Nascius, en Quinze Livres, Livre Deuxiéme 
(fascicule 6 et dernier.) Pp.84. (Nantes : Imprimerie- 
Libraire, Guisthau, 1902.) 
M. F. C. pe Nascius has favoured us from time 
to time with copies of his astronomical contribu- 
tions, which are to extend when complete to fifteen 
volumes. Since each volume consists of numerous parts, 
it will be easily understood that no inconsiderable task 
awaits the reader who aspires to a complete mastery of the 
author’s methods and teaching. Only one small part of 
the second volume lies before us, but we confess that we 
are utterly unable to comprehend its purpose or to do 
justice to the ingenuity that apparently underlies its 
construction. The general conception seems to be 
remotely connected with Bode’s law, but is far more 
difficult of apprehension, for with this is connected a 
discussion of the ‘‘triangle of divine harmony,” while 
over the whole hovers a bewildering but awe-inspiring 
theme which is expressed as algorithmic. It will, 
perhaps, be sufficient to say that the object of the author, 
if object he has, is by some simple manipulation of 
figures to produce quantities that shall approximate to 
various astronomical constants, such as the periods and 
distances of the planets. For example, he sets out to 
establish or reproduce the period of sunspots, which 
he gives at I1ll years. The triangle of divine 
harmony is, we are assured, admirably adapted 
for this species of discussion. This triangle happens, 
fortunately, to be right-angled, and two sides have the 
values 69 and 17°89. There is a good deal about the 
number 69, which we are very solemnly assured is equal 
to 64 + 5, and it is no doubt entirely one’s own fault if 
he fails to correctly apprehend its true significance, but 
17°89 seems to be introduced here for the first time, at 
least in this volume, and one may be excused if he fails 
to perceive its actual bearing. Our author handles these 
NO. 1704, VOL. 66] 
NATURE 
199 
quantities in the following way. The area of the divine 
triangle is first found, this is then doubled to get a paral- 
lelogram, and the side of a square found the area of 
which is equal to the tenth part of that parallelogram. 
This side has for its numerical value 117110! and the 
author congratulates himself on his success. 
For many years, we are afraid, M. de Nascius has 
laboured on similar lines, which are destined to bring 
him or his readers little profit, but which he will no 
doubt pursue so long-as he can trace his figures. It is 
nearly thirty years, he tells us, since he first placed a 
hesitating foot on the path which was destined to lead 
him to such brilliant discoveries. Let us hope that he 
has been frequently cheered by finding some close co- 
incidence between his calculations and observed facts, 
and that his delight has been as keen as that experienced 
by other physicists who have trod a more legitimate road 
and been led to more valuable results. 
EETTERS TO THE EDIMOR: 
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 notzce 2s taken of anonvitous communications. | 
Mr. Marconi’s Results in Day and Night Wireless 
Telegraphy. 4 
READING a brief account of these results in the Zvmes of 
June 14, I perceive that Signor Marconi advances in explana- 
tion of the greater distance at which night signals were received, 
that the day signalling is affected by diselectrification of the 
transmitting elevated conductor. 
If—as I gather—Signor Marconi is referring to his observa- 
tions made at positions in the Atlantic, west of England, the 
waves lravelling westward, may not ether drift in the earth’s 
orbital path be concerned in producing the effects observed ? 
The waves advancing against the orbital zther stream in the 
day time, with it at night, might be supposed to give rise to 
conditions analogous to those which affect the transmissibility 
of sound against or with a high wind. It will assist if we 
assume a retarded cether drift near the earth’s surface and free 
motion above. But still, the difficulty in this explanation resides 
in the very great magnitude of the effects observed. 
I write merely by way of suggestion, and in very considerable 
ignorance of almost every particular involved in this explanation. 
JEeLN: 
Geological Laboratory, Trinity College, Dublin, June 17. 
Remarkable Sunsets at Madeira. 
THE last few evenings we have witnessed here some beautiful 
sunsets, closely resembling the sunsets observed after the 
Krakatoa eruption, which I remember well, ze. there is the 
same large area of beautiful pink haze in the west and high up 
in the sky at and immediately after sunset. The first sunset 
which I felt certain was of the above character I noticed on 
Friday, June 6. On June ro and yesterday the display was 
particularly striking. There were indications, I believe, of the 
pink glow on one or two evenings before June 6, but as there 
were a good many clouds about it was difficult to feel certain of 
the special character of the sunsets. F. W. T. KRown. 
Funchal, Madeira, June 12. 
THE INSTITUTION OF ELECTRICAL 
ENGINEERS’ DEPUTATION ON ELECTRICAL 
LEGISLATION. 
WE published an article a short time ago (NATURE, 
vol. Ixvi. p. 35) on the report of the committee 
appointed by the Institution of Electrical Engineers to 
inquire into the cause of this country’s backwardness in 
electrical industries, and stated that it had been decided 
to ask the Prime Minister to receive a deputation on the 
subject. This deputation, after being once or twice 
postponed, waited upon the President of the Board of 
Trade, the Right Hon. Gerald W. Balfour, M.P., on 
