March 23, 1871 | 
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Lunar Halos: their Origin and Prognostic Significance | condemned by ‘* The Reviewer,” is almost identical with that of 
M. W. DE FONVIELLE is, no doubt, right in attaching impor- 
tance to the study of these phenomena of refraction, depending 
as they do, upon the polarisation of atmospheric vapour. Rightly 
interpreted, they afford one of the most certain indications of 
weather change, especially in regard to rain; but the popular 
notion of their being precursors of storms is certainly exaggerated. 
In reply to hee inquiry made by M. de Vonvielle, I may say 
that the distance between the observers of the singular forms of 
this phenomenon, and seen on January 4th (and of which asketch, 
furnished by me, was inverted by the printer) was about two 
statute miles. I have ascertained that the two arcs in my own 
sketch corresponded with the largest and the smallest circles in 
the drawing of your other correspondent. I saw nothing of the 
intermediate intersecting arc, almost vertical* in his drawing. 
M. de Fonvielle does not, however, remark on the fact that 
the great circle of 90° had the moon in its circumference. Allow 
me also to ald that in my own sketch the apparent diameter of 
the moon and of the imperfect paraselene are exaggerated ; the 
object of the drawing being to show the relative magnitude and 
position of the two circles. The innermost circle in both drawn 
ings was about 45° to 50°—in fact an ordinary lunar halo. All 
my observations (for many vears) have pointed to the inference, 
which I may call a law, ‘‘ That halos indicaée a change of lempera- 
ture, and are indicative of transition from dry to wet as well as 
from wet to dry.” I shall be Lappy to forward M. de fonvielle 
further information if desired. 
Aigburth, Liverpool, March 20 SAMUEL BARBER 
i in S Ss 
Science School 
In the last number of your paper a correspondent, ‘‘ W., 
asks for information respecting ‘‘any school adapted for young 
boys whose parents wish to give them an education embracing 
the physical sciences and modern languages, ou some such plan 
as that of the Realschule of Germany.” Will you permit me to 
state that the International College at Spring Grove was estab- 
lished with precisely this object, and to a prospectus of this 
college, which I send you, I would direct the attention of your 
correspondent. ‘he scheme of science instruction for this college 
was drawn up by Professors Huxley, Tyndall, and Williamson, 
and for upwards of four years past has been carried into operation 
as closely as circumstances permit. 
Tsleworth 
” 
W. F.B. 
In reply to “ W.” will you allow me to forward you a pro- 
spectus of Craufurd College, Maidenhead, in which an education 
is given embracing the physical sciences and the modern languages. 
Having many years ago visited the Realschule of Offenbach, and 
attended the classes of several of the professors in that school, I 
have no hesitation in expressing my opinion that a comparison of 
the merits of the two schools would not be unfavourable to the 
former. ANGLICUS 
Morell’s Geometry 
As a considerable part of your number of February 23 is 
devoted to comments on a little publication just issued by me, 
‘The Essentials of Geometry,’ I must request you in courtesy 
to insert these lines in order to set right one misconception. 
‘<The Reviewer” (p. 323) passes certain criticisms on the defini- 
tions and enunciations, as well as demonstrations, of the book, 
describing the former as having salient incongruities, ard the 
latter as being nonsense. ‘These are strong expressions, but my 
present purpose is not to expose the fallacy of the remarks in the 
review, but to point out the fact noticed in the preface, and over- 
looked by the reviewer, that all the proofs in the work are taken 
from French and German sources (p. viii.) 
I may add that those sources are the most approved in neigh- 
bouring countries, and though I have not given my references in 
every case, I have done so in so many cases that any person of 
ordinary discrimination might have inferred that every statement 
and proof advanced had some high authority for warrant. It is 
to be regretted that the ‘* Reviewer” overlooked this, for in his 
haste to condemn a method for which he has an antipathy, he has 
been betrayed into accusing some even of the leading British as well 
as foreign geometricians as guilty of salient incongruities, and of 
writing nonsense. ‘Thus the definition of a plane angle, though 
* See Nature, Jan. 26. 



Dr. ‘Thomson in his edition of Euclid (1835), Def. 7, and the 
Note tu it which runs: “A rectilinear angle is the degree of 
opening or divergence of two straight lines which meet one 
another.” Nor does Euclid’s original definition of an angle dilfer 
in conception from that given by. me, ywvia éorly 7} mpds aAAijAas 
Tov ypauuav KAlois; for this word KAlvew contains the notion of 
revolution, that is, of more or less. Compare my second dcfi- 
nition of an angle. —Zssentials, No. 68, p. 40. 
Again, the enunciation and demonstration of the two funda- 
mental theorems of parallels are qualified as sheer nonsense, and 
yetthe whole passage is textually the same as Amivt’s, including 
the parts printed in italics. Further, the proof of the equality of 
triangles at p. 44, condemned as a violation of the common rules 
oflogic, is based on the previous pages 42,43, overlooked by 
“The Reviewer,” and agrees almost word for word with Legendre, 
and absolutely with M. Bos, Professor of the Lycée St. Louis at 
Paris, and successor of Amiot. (See his ‘‘ Memento du Dac- 
calaureat es Lettres,” 1866-68, p, 183. Partie Scientifique.) 
It would take up too much time and space to gu further into 
the matter in dispute, but I wish it to be clearly understood, with- 
out denying the right of “ The Reviewer” to attack the book in any 
way that is fair and reasonable, that it is neither one nor the 
oiliec to make Mr. Morell the object of all the attacks when he 
is far too honoured in being treated as the substitute for many of 
the first geometers of the present age on whom the punishment 
desceuds, 
Lvery statement and proof in the work has for its warrant 
some high authority, and the basis of the work and most parts of 
it to which no special references are given in foot-notes are taken 
from a digest published by University examiners and Doctors of 
Science on the Continent. 
Now, Sir, as the present letter does not presume to enter ona 
discussion of the merits or demerits of the work, butis simply an 
explanation of an essential point underlying the whole question 
and overlooked by ‘* The Reviewer,” I must, as I have said 
before, request these remarks to be inserted in NATURE to set 
right the nustake about the authorship and authority of the book. 
If Nature will have the courtesy to give me a little more 
space on a future occasion, I hope to show on my own authority 
that I have good arguments for what has been advanced. 
March 15 J. R. MoreLi 
Work and Force 
As I hope to hear more of Mr. Highton’s arguments at the 
meeting of the Literary and Philosophical Society of Manchester 
before this is printed, 1 will content myself now with noticing 
but two points. 
The first is his attempt to defend himself from the charge of 
confusing Work and Force ; there are other passages in his 
writings which lead to this somewhat serious conclusion ; but 
the vagueness of the expression ‘‘the total of the force used” 
would suffice to make anyone suspect some such confusion. I 
presume that a ‘‘total of force” is still force, and can therefore 
be no more equivalent to work than to a time or a space. 
The other point is the sentence ‘* this only shows that one of 
the laws of thermu-dynamics is inconsistent with the doctrine of 
the mechanical equivalence of heat.” If Mr. Highton knew 
that the first law of thermo-dynamics simply asserted this 
equivalence he would surely have expressed the proposition 
differently. As it stands in formit is very much t ie same as it he 
had said that one of Newton’s laws of motion was inconsistent 
with the principle that a particle acted on by no forces will move 
uniformly in a straight line. 
If he had known what the laws were, he would hardly have 
said that they were inconsistent with the very principle which the 
first asserts, and which the second, as usually stated, involves. 
Of course, these lines are not meantas an answer to Mr. 
Highton’s letter, but merely to show that he really does not quite 
understand the theory he criticises. 
March 18 J. Hopkinson 
INVINCIBLE ignorance is said to be excusable. This must be 
my plea, when I say that I have read over again Sir W. Thom- 
son’s paper in the “ Philosophical Magazine ” of Feb. 1854, and 
that I cannot see but that it leads to perpetual motion more 
than anything I have ever written, 
Ii. Il1cuTon 
