Sept. 21, 1871] 
NATURE 
405 
TT lO 
the best beginning. I believe that, on the contrary, unless the 
demonstrative and deductive principles of the science are soon 
introduced to the student’s notice, he is likely to acquire a dis- 
taste for the subject. 
I was learning, under an infliction of practical geometry (at 
school}, to detest the very sight of a box of mathematical instru- 
ments, when a fortunate ilIness kept me at home fortwo or three 
years. I believe that Euclid, as it would have been introduced 
ito me at school, would have rendered my dislike for mathematics 
‘complete. But becoming possessed of a Simson’s ‘‘ Euclid,” 
sand veading it instead of learning it for ‘‘class,” I found geometry 
ithe most enjoyable of subjects. Ina very few months I came to 
tthe end of the book, and I have never lost the liking for geometry 
which I had by that time acquired. 
Let it not be supposed, however, that I advocate the claims of 
Euclid as a text-book. The first, third, and sixth books might 
indeed be retained—with certain omissions and modifications ; 
but the second and fourth books (setting asidea few propositions) 
are monstrositres of clumsiness.* The fifth, eleventh, and twelfth 
could never be generally used in their present form. But 
whether a totally new text-book be adopted or Euclid he modi- 
fied, | am convinced that until the demonstrative and deductive 
nature of the science is recognised the interest of the student will 
not be excited. 
While, however, my own experience will not permit me to 
believe that a cour-e of practical constructions is a suitable in- 
troduction to geometry, I certainly agree with Mr. Wilson in 
regarding cireful constructions as of the utmost importance to the 
learner. But, in my judgment, the processes of construction 
should accompany, not precede, the study of some demonstrative 
and deducrive treatise. 
J believe the chief difficulty under which we labour at present, 
resides in the fact that, owing tothe small encouragement given 
to the study of geometry at ovr Universities, we have, even 
among our ablest mathematicians, very few able geometricians. 
One cannot read the Cambridge text-books of mathematics— 
written though these are, in many instances, wih singular 
ability—without becoming convinced of this. So soon as a 
geometrical construction is introduced we recognise the clearest 
traces of maptitude. The fact iss ill more clearly evidenced in 
treatises professedly geometrical. I take up an edition of Euclid, 
prepared by a very eminent mathematician, a senior wrangler, 
and, opening at random the portion relating to deductions, I find 
the following problem :—‘“‘ Required to draw a circle through a 
given point to touch two intersecting lines; ” and to solve this 
obvicus thiru- book pr..blem the aid of the sixth book is called in. 
But it is hardly to be wondered at that university mathe- 
maticians ar~, as a rule, not strong in geometry, for the study of 
geometry is very litile encouraged by university tutors. Indeed, 
an aptitude for geometrical methods is generally regarded as more 
mischievous than useful in the Tripos. I can remember the hints 
I myself received on this point. A few instances may perhaps 
interest your readers, 
The first hint was given me in the lecture-room bya high 
wrangler (an excellent geome'rician). The following proposition 
had been submitted—‘‘ A ball is placed on a horizontal plane, 
above which is a luminous point ; show that the length of the 
minor axis of the ball’s elliptic shadow depends only on the 
height of the luminous point above the plane.” I wrote for 
answer that the fact is obvious, because two sloping planes 
touching the bal], and with a horizontal intersection through the 
luminous point, must clearly have the same slope wherever the 
ball is placed. The proof was acc+pted, and even regarded (to 
my infinite surprise) as ingenious ; but I was warned not to leave 
the safe track of analysis. 
The next hint was given me by my private tutor, a senior 
wrangler with fine (bu untrained) geometrical powers, on the 
score of my solving geometrically some problems relating to 
epicycloidal and hypercycloidal areas. 
The third hint was given me by a vacation tutor, also a senior 
wrangler, and was perhaps the best deserved of the three. He 
had set me a problem relating to a curve which chanced to be a 
projection of the four-pointed hypercycloid, and the problem was 
meant as an exercise in analytical processes. Knowing very 
li tle about these, I ven ured to proceed more meo. I first pro- 
jected the curve back again (so to speak). established the pro- 
perty in the case of the quadricuspid hypercycloid, and repro- 
* Allthe propositions of Book II , save f ur, may be established (usual y) 
in three lies from the first two, cof which they are in ‘act little more than 
corollaries. The main objection te the fourth bock reiates to the inscription 
and circumscription of the regular figures; but throughout the book the 
heavin sss of Euclid’s method is much felt. 

jected all my constructions on the original plane of the curve. I 
shall never forget the solemnity of the warning I received, 
The last case I shall refer to relates to a probability problem 
(the last in Todhunter’s “* Integral Calculus”) about a messenger 
and a shower of rain, the messenger’s “expectation” under 
ee stated conditions being expressed in the following pleasing 
orm :— 
“Ulett v, u ! 
( i ) log # + 2 
2 ci) te “ 

v I ut 
n 
From the day that I gave a geometrical solution of this problem 
(the logarithm coming out as a hyperbolic area) I was given up as 
a bad job, No wonder, indeed, for as a problem in the Integral 
Calculus it can be solved in half-a-dozen lines, 
So little encouragement is given to geometrical work, that I 
know instances where men who have taken very high degrees 
could not so've the easiest geometrical problems. Many indeed 
in my time (I believe Mr. Wilson would confirm this) in their 
second or third yearat Cambridge, scarcely know what has to 
be done with such problems—that is, even how to try to solve 
them. I wrote a l'ttle pamphlet four or five years ago, to show 
how such problems should be attacked, proceeding on the follow- 
ing plan:—I took the case of a beginner dealing with easy 
geometrical problems, and considered his difficulties and false 
steps, as well as the true demonstration ultimately evolved. I 
did this because I “had found it the only effectual course with 
pupils. To give problems, and on the pupil failing to solve 
them, to show him the solution, is utterly useless. One must 
listen to his reasoning, wrong or right, to the purpose or not— 
show him why it is wrong, or not effective towards the solution 
of the problem ; and so gradually guide him towards the correct 
solution, In the pamphlet I employed a corresponding method. 
Unfortunately (for me at any rate) Messrs. Longmans submitted 
this pamphlet to ‘‘a competent mathematician,” who imme- 
diately misunderstood my plan; took the imagined difficulties 
for real difficulties of my own, and solved for my behoof an 
immensely difficult problem—the first worked-out example in 
Potts’s Euclid. This achievement (far parenthése my pamphlet 
also) was then submitted to another competent mathematician, 
and he, excited to emulation, suggested another solution of a 
problem which a boy of twelve might safely attack. Finally, 
these labours were submitted to Messrs. Longmans and (signa- 
tures removed) to myself. So my pamphlet has remained in my 
desk ; for I thought better of it than to send it begging. 
We want geometricians more than text-books just now. If 
our universities would give geometry a reasonable position among 
the subjects for mathematical examination, we should probably 
soon have both. At present a man with geometrical tastes must 
either turn from his favourite subject during his university career 
(with small chance, perhaps, of resuming it) or must be content 
with but a small share of university success, 
Brighton, September 15 {R. A, PRocToR 

Captain Sladen’s Expedition 
In reply to F.R.S.’s inquiry in your issue of September 14, 
I may state that the last number of the ‘‘ Proceedings of the 
Zoological Society of London” (1871, part 1) contains several 
articles by Dr, John Anderson relating to discoveries made 
during Capt. Sladen’s expedition to Yunan, and that the next 
number (1871, part 2), which I am now preparing for the press, 
will contain others. 
It was Dr. 7iomas Anderson, Curator of the Botanic Garden 
at Cal.utta, whose untimely death we have recently to lament. 
Dr, Fehn Anderson (his brother) is, Iam happy to say, in good 
health at his official postas Curator of the Indian Museum and 
Professor of Comparative Anatomy at Calcutta, or was so, at all 
events, at the date of his last letters to me, about a month since. 
11, Hanover Square, Sept 16 P. L. SCLATER 

Deschanel’s Physics 
As regards the particular passage in my edition of Deschanel 
which I am challenged to defend by your Reviewer (NATURE, 
vol. iil. p. 343), his charge, which issomewhat obscured by rhetorical 
H=2 . 
embellishment, seems to be that in the factor a GGkees has not 
7 
been indicated that H and 4%, as well as 760, denote so many 
millimetres of mercury af zero. I think this was scarcely neces- 
sary, as the question whether the observed or reduced heights of 
the mercurial columns should be employed, is not one on which 
