166 
THE PHARMACEUTICAL JOURNAL AND TEANSACTIONS. 
[August SI, 1872. 
to the law of gravitation, the body would'move exactly as 
this calculation required. And if it were objected that 
the hody must be slightly magnetic or diamagnetic, while 
there are magnets not an infinite way off; that a very 
minute repulsion, even at sensible distances, accompanies 
the attraction ; it might be replied that these phenomena 
are themselves subject to exact laws, and that when all 
the laws have been taken into account, the actual motion 
will exactly correspond with the calculated motion. 
I suppose there is hardly a physical student (unless he 
has specially considered the matter) who would not at once 
assent to the statement I have just made; that if we 
knew all about it, Nature would be found universally 
subject to exact numerical laws. But let us just con¬ 
sider for another moment what this means. 
The word exact has a practical and a theoretical 
meaning. When a grocer weighs you out a certain 
quantity of sugar very carefully, and says it is exactly 
a pound, he means that the difference between the mass 
of the sugar and that of the pound weight he employs 
is too small to be detected by his scales. If a chemist 
had made a special investigation, wishing to be as ac¬ 
curate as he could, and told you this was exactly a 
pound of sugar, he would mean that the mass of the sugar 
differed from that of a certain standard piece of pla¬ 
tinum by a quantity too small to be detected by his 
means of weighing, which are a thousand-fold more 
accurate than the grocer’s. But what would a mathe¬ 
matician mean, if he made the same statement? He 
would mean this. Suppose the mass of the standard 
pound to be represented by a length, say a foot, mea¬ 
sured on a certain line; so that half a pound would be 
represented by six inches, and so on, and let the differ¬ 
ence between the mass of the sugar and that of the 
standard pound be drawn upon the same line to the 
same scale. Then if that difference were magnified an 
infinite number of times it would still be invisible. This 
is the theoretical meaning of exactness; the practical 
meaning is only very close approximation; how close, 
depends upon the circumstances. The knowledge then 
of an exact law in the theoretical sense would be equi¬ 
valent to an infinite observation. I do not say that 
such knowledge is impossible to man; but I do say that 
it would be absolutely different in kind from any know¬ 
ledge that we possess at present. 
, 110 doubt, that we do possess a great 
deal of knowledge of this kind, in the form of geometry 
and mechanics ; and that it is just the example of these 
sciences that has led men to look for exactness in 
other quarters. If this had been said to me in the last 
century, I should not have known what to reply. But 
it happens that about the beginning of the present cen¬ 
tury the foundations of geometry were criticized inde¬ 
pendently by two mathematicians. Lobatscheffsky and 
the immortal Gauss; whose results have been extended 
mid generalized more recently by Eiemann and Helmholtz 
ir ZT t0 Which these investigations leac 
is that, although the assumptions which were very pro 
“ ad , e the an cient geometers are practically 
exact-that is to say more exact than experiment car 
be-for such finite things as we have to deal witl 
and such portions of space as we can reach; yet th< 
truth of them for very much larger things, or very 
much s “aller things, or parts of space which are ai 
present beyond our reach, is a matter to be decided by 
experiment, when its powers are considerably increased 
I want to make as clear as possible the real state of this 
question at present, because it is often supposed to be i 
question of words or metaphysics, whereas it is a ven 
distinct and simple question of fact. I am supposed t< 
know then that the three angles of a rectilinear triangh 
are exactiy equal to two right angles. Now suppSs< 
that three points are taken in space, distant from on< 
another as far as the sun is from Sirius, and that th< 
shortest distances between these points are drawn so a: 
to form a triangle. And suppose the angles of thes< 
points to be very accurately measured and added to¬ 
gether ; this can at present be done so accurately that 
the error shall certainly be less than one minute, less 
therefore than the five-thousandth part of a right angle. 
Then I do not know that this sum would differ at all from 
two right angles; but also I do not know that the dif¬ 
ference would be less than ten degrees, or the ninth part 
of a right angle. And I have reasons for not knowing. 
This example is exceedingly important as showing the 
connection between exactness and universality. It is 
found that the deviation, if it exists, must be nearly 
proportional to the area of the triangle. So that the 
error in the case of a triangle whose sides are a mile 
long would be obtained by dividing that in the case I 
have just been considering by four hundred quadrillions; 
the result must be a quantity inconceivably small, which 
no experiment could detect. But between this incon¬ 
ceivably small error and no error at all, there is fixed 
an enormous gulf; the gulf between practical and 
theoretical exactness, and what is even more important, 
the gulf between what is practically universal and what 
is theoretically universal. I say that a law is practically 
universal which is more exact than experiment for ail 
cases that might be got at by such experiment as we 
have. We assume this kind of universality, and we 
find that it pays us to assume it. But a law would be 
theoretically universal if it were true of all cases what¬ 
ever, and this is what we do not know of any law at all. 
(To he continued.) 
FORMATION OF OZONE BY PLANTS.* 
BY C. BELLI!CCI. 
Scoutetten, Bineau, Kosmann, and De Luca, insti¬ 
tuted experiments from the results of which they inferred 
that plants are sources of ozone, whilst Cloez (Ann. 
Chem. Phys. 1856) on the contrary shows conclusively 
that the apparent ozone was due to other causes. He 
passed the aeriform products from the plants through 
two tubes placed side by side, and containing iodized 
test-paper; one of these was exposed to the action of 
light, and the test-paper became coloured, whilst in the 
other which was protected from the light, it remained 
unaltered, showing that the action was due, not to ozone 
evolved from the plants, but to the effects of moisture, 
ox yS en > an( l light on the test-paper. The author has 
carefully repeated the experiments of Cloez, and devised 
new ones, in which he introduced into a large Woulfe’s 
bottle containing water saturated with carbonic anhy¬ 
dride, and to which a small quantity of potassium iodide 
and starch was added, sprigs and leaves of the following 
plants: Taxus baccata, Juniperus virginiana , Abies vul¬ 
garis, Thuja orientalis , Trunus laurocerasus , Buxus sem¬ 
per virens, , and Char a fcctida. The apparatus was then 
placed in bright sunshine, but no change was observable 
in the liquid, proving that the green parts of plants do 
not evolve ozone under the influence of the solar rays. 
NICOTINE AN ANTIDOTE TO STRYCHNIA. 
A case of poisoning by strychnia which was success¬ 
fully treated with nicotine, has been published in the 
‘ British Medical Joumal ’ by the Eev. Dr. Houghton, 
F.R.S., of Trinity College, Dublin. When the treatment 
commenced, the patient, a lad nineteen years of age, was 
violently convulsed, his pupils were dilated and his arms 
and legs were rigid. The nicotine was administered in 
drop doses in whisky-punch every half-hour. After the 
second dose the paroxysms were less violent; and when 
he had taken four doses he was much better, and even¬ 
tually he recovered. The poisoning was caused by the 
lad picking up and eating an egg which had had 
strychnia introduced into it, and been placed in a garden 
for the purpose of poisoning magpies. 
* ‘ Gazzetta Chimica Italiana,’ i. 687-690., and ‘Journ. 
Chem. Soc. 
