March 23, 1871 | 
and price of either of these, which might be made the ground- 
work for lectures. As it is, we have been compelled to depend 
upon lectures alone, illustrated by experiments, in which the 
pupils themselves are allowed to have as much share as possible. 
I should be much obliged to any of your readers who could 
direct me to any text-book likely to meet the want I have indi- 
cated. We are now intending to combine with the subject named 
above a little Natural Philosophy ; and I may add, that we 
have already had, some time ago, a twelve months’ course on 
electricity, with experiments. 
I think, however, that the whole subject of Science Teaching 
in schools wants treating by some master hand; and if some 
such man as Prof. Tyndall, for instance, who, in addition to the 
highest scientific attainments, knows something about the practi- 
cal difficulties of the matter, would enter into the whole subject 
in your columns, advising what to teach, how to teach it, 
and what books to use, he would, I am sure, confer a real 
benefit upon Science. We have heard enough about the 
want of it; we want now to be told by competent authority how 
the want may be best supplied. And Iam able tosay from 
my own personal knowledge that there are heads of schools 
quite convinced of the importance of the subject, but utterly 
ignorant how to set about remedying it. Upon this point [ 
wish to be very emphatic, and indeed it was chiefly for the pur- 
pose of urging this that I began this letter, knowing as I do 
well, both from observation and experience, the practical diffi- 
culties of the subject ; difficulties which are much, very much, 
greater than your enthusiastic philosophers have any idea of. 
Thope, however, that if the subject be taken up at all, it will be 
by some one practically conversant with it, who can give advice 
which will be worth taking. 
M. A. 

Forms of Clouds 
CLoupy formations worthy of being noticed have been observed 
by me during the week. On the 8th I chanced to take a walk with 
M. Gustave Flourens, who has since been sentenced to death 
by court-martial. At five o’clock we witnessed many ribboned 
clouds parallel to each other, and so long that they appeared to 
radiate from a common focus. These ribboned clouds termi- 
cated abruptly just over our heads, and their extremities were 
noalescent, so that the appearance was one of a feather with the 
vanes of the quill emanating from one side. The wind was blowing 

perpendicularly to the vanes and parallel to the quill. This ac- 
cumulation of matter was evidently owing to the purity of the 
air on the other side of the singular cloud-edge. 
I witnessed again these phenomena on the 9th and on the 
roth of March, but not so well. On the gth and roth I also 
observed two solar halos well defined. The halo had a pecu- 
liarity of its own. The clouds adjoining the edge were tinged 
most delicately with violet on the south-easterly side. The evening 
was stormy and rainy, which is consistent with the theory I have 
advocated that halos are a prognostic of bad weather. 
W. DE FONVIELLE 

The Limits of Numerical Discrimination 
THE solution of the Problem “how many objects can a 
man count at once?” is not general, but depends especially on 
the grouping, position, angular distance, similarity and nature of 
the objects counted, as well as on the experience and health of 
the person who counts them. 
(This is written under the supposition that the word ‘‘ count” 
means ‘‘tell the number of,” not ‘‘ begin, one, two, three,” 
which of course cannot be done simultaneously.) 
NATURE 

405 
As an example of the operations performed in counting, take 
the card ‘‘ten of diamonds.” The player passes his eyes up and 
down it, recognises it to be the ten, discriminating it from the 
other cards, calls it by its name ‘‘ten,” and then, if he likes, can 
count separately the pips on the card. 
This is a case in which the number of the card is recognised 
as its name, and many others could be adduced in which much 
higher numbers arranged symmetrically could be recognised at a 
glance without counting. 
A person habituated to counting would divide the objects into 
groups with which he was best acquainted, in a way depending 
on their position. 
To show that running the eye over the object is not necessarily 
conscious, or the very operation of counting—If anyone on a 
fine sunny day looks through a latticed window for some time 
and then shuts his eyes, he will be able to count a great number 
of panes in the impression on his retina, or wherever it is. 
(Compare with this operation that of recognising a person after 
he has passed out of sight.) 
Looking at a collection of objects in counting by groups is 
governed by the same laws as looking ata single complex object, 
and naming follows after the object has been properly discrimi- 
nated. I can imagine that a person naturally gifted with a 
memory for form of a certain kind, could by practice at once 
recognise the number of a large quantity of coins scattered at 
random, inasmuch as the number would be sharply discriminated 
from the one higher and the one lower, just as a shepherd dis- 
criminates sheep, which to other eyes are alike, and if he can 
discriminate 36 from 35 and 37, there is no necessity for him to 
count 36 to say that 36 are there. That can be done afterwards. 
There should be no astonishment that anyone should possess this 
power, for after all what is it in comparison to the marvellous 
faculty we have of seeing highly complex objects at once, which 
we can analyse toa certain extent ; but in no way resolve into 
the elements of the synthesis. The discrimination between red 
and yellow, between one note and the next, seems to demand 
much finer powers of the memory; but we are not astonished 
at it. 
The explanation of many wonderful mental and manual feats 
depends on the same marvellous faculty of apprehending and 
considering as one that which formerly could be only considered 
as very many. Reading words, playing a musical instrument (whether 
with or without notes), writing, tying knots, doing needlework, 
the manufacture of every useful thing, all are acquired through 
the same faculty of changing several simple movements into one 
complex movement, which is treated as one, and can be named 
as one, even before it is analysed. It is only fair to infer that 
counting by groups is an art which may be learned, and, if worth 
the while, carried to a high degree of practical excellence. 
Your correspondent ‘‘J. B.” (March 9) illustrates Dugald 
Stewart’s view by the examples of two beans and two eyes ; 
these do not prove anything in regard to mental attention, but 
only that they were not both opposite the parts of the retina with 
which the observer could see most comfortably. If they had 
only a small but perceptible angular distance, and did not dazzle 
so as to tire the eyes, what he mentions would probably not have 
occurred. He could remember them both together and then 
count them as well as if he were actually looking at them. 
Eccles, March 14 Reavis 


Books Wanted 
CouLp you kindly inform me where I could obtain the fol- 
lowing works mentioned by Sir John Herschel in his ‘* Discourse 
on Natural Philosophy,” viz.—Bracconot, “Annales de Chimie,” 
and ‘* Dr. Prout’s Account of the Experiments of Professor 
Autenrieth, of Tubingen,” Phil. Trans. 1827. My efforts to 
obtain these books have hitherto been in vain; if you could assist 
me, I should feel much obliged. 
Newbridge, March 12 H. J. Watson 

Quinary Music 
Your correspondent, Beacon Lough, will find a very effective 
specimen of this division in the concluding Allegro to the glee 
“The Gipsy,” written by Wm. Reeve. W. R. M. 
The Earthquake 
THE earthquake, which caused considerable alarm throughout 
the North of England on the night of the 17th, was felt severely 
here between 11.5 and 11,10 P.M. The sky, which had been 

