September 7, 1872.] THE PHARMACEUTICAL JOURNAL AND TRANSACTIONS. 
183 
that happens when a gas is compressed. We know that 
a gas consists of a vast number of separate molecules, 
rushing about in all directions with all manner of veloci¬ 
ties, hut so that the mean velocity of the molecules of 
air in this room, for example, is about 20 miles a minute. 
The pressure of the gas on any surface with which it is 
in contact is nothing more than the impact of these small 
particles upon it. On any surface large enough to he 
seen, there are millions of these impacts in a second. If 
the space in which the gas is confined he diminished, the 
average rate at which the impacts take place will he in¬ 
creased in the same proportion; and because of the 
enormous number of them, the actual rate is always ex¬ 
ceedingly close to the average. But the law is one of 
statistics; its accuracy depends on the enormous num¬ 
bers involved; and so, from the nature of the case, its 
exactness cannot be theoretical or absolute. 
Nearly all the laws of gases have received these sta¬ 
tistical explanations; electric and magnetic attraction 
and repulsion have been treated in a similar manner; 
and a hypothesis of this sort has been suggested even 
for the law of gravity. On the other hand, the manner 
in which the molecules of a gas interfere with each other, 
proves that they repel one another inversely as the fifth 
power of the distance; so that we have found at the 
basis of a statistical explanation a law which has the 
form of theoretical exactness. Which of these forms is 
to win ? It seems to me again that we do not know, and 
that the recognition of our ignorance is the surest way 
to get Tid of it. 
The world in general has made j ust the remark that | 
I have attributed to a fresh student of the applied 
sciences. As the discoveries of Galileo, Kepler, Newton, 
Dalton, Cavendish, Gauss, displayed ever new phenomena 
following mathematical law, the theoretical exactness of 
the physical universe was taken for granted. Now when 
people are hopelessly ignorant of a thing, they quarrel 
about the source of their knowledge. Accordingly many 
maintained that we know these exact laws by intuition. 
These said always one true thing, that we did not know 
them from experience. Others said that they were 
really given in the facts, and adopted ingenious ways of 
hiding the gulf between the two. Others again deduced 
from transcendental considerations sometimes the laws 
themselves, and sometimes what through imperfect in¬ 
formation they supposed to be the laws. But more 
serious consequences arose when these conceptions de¬ 
rived from physics were carried over into the field of 
biology. Sharp lines of division were made between 
kingdoms and classes and orders; an animal was described 
as a miracle to the vegetable world ; ^specific differences 
which are practically permanent within the range of 
history, were regarded as permanent through all time; 
a sharp line was drawn between organic and inorganic 
matter. Further investigation, however, has shown 
that accuracy had been prematurely attributed to the 
science, and has filled up all the gulfs and gaps that 
hasty observers had invented. The animal and vegetable 
kingdoms have a debatable ground between them, oc¬ 
cupied by beings that have the character of both and 
yet belong distinctly to neither. Classes and orders 
shade into one another all along their common boundary. 
Specific differences turn out to be the work of tkne. The 
line dividing organic matter from inorganic, if drawn to¬ 
day, must be moved to-morrow to another place; and 
the chemist will tell you that the distinction has now no 
place in his science except in a technical sense for the 
convenience of studying carbon compounds by them¬ 
selves. In geology the same tendency gave birth to the 
doctrine of distinct periods, marked out by the character 
of the strata deposited in them all over the sea; a doc¬ 
trine than which, perhaps, no ancient cosmogony has 
been further from the truth, or done more harm to the 
progress of science. Refuted many years ago by Mr. 
Herbert Spencer, it has now fairly yielded to an attack 
from all sides at once, and may be left in peace. When, 
then, we say that the uniformity which we observe in 
the course of events is exact and universal, we mean no 
more than this, that we are able to state general rules 
which are far more exact than direct experiment, and 
which apply to all cases that we are at present likely to 
come across. It is important to notice, however, the 
effect of such exactness as we observe upon the nature 
of inference. When a telegram arrived stating that Dr. 
Livingstone had been found by Mr. Stanley, what was 
the process by which you inferred the finding of Dr. 
Livingstone from the appearance of the telegram ? You 
assumed over and over again the existence of uniformity 
in nature. That the newspapers had behaved as they 
generally do in regard to telegraphic messages ; that the 
clerks had followed the known laws of the action of 
clerks ; that electricity had behaved in the cable exactly 
as it behaves in the laboratory ; that the actions of Mr. 
Stanley were related to his motives by the same unifor¬ 
mities that affect the actions of other men; that Dr. 
Livingstone’s handwriting conformed to the curious rule 
by wdiich an ordinary man’s handwriting may be recog¬ 
nized as having persistent characteristics even at diffe¬ 
rent periods of his life. But you had a right to be much 
more sure about some of these inferences than about 
others. The law of electricity was known with practi¬ 
cal exactness, and the conclusions derived from it were 
the surest things of all. The law about the handwriting, 
belongingtoa portion of physiology which is unconnected 
with consciousness, was known with less, but still with 
considerable accuracy. But the laws of human action 
in which consciousness is concerned are still so far from 
being completely analysed and reduced to an exact form, 
that the inferences which you made by their help were 
felt to have only a provisional force. It is possible that 
by-and-by when psychology has made enormous advances 
and become an exact science, we may be able to give to 
testimony the sort of weight which w T e give to the in¬ 
ferences of physical science. It will then be possible to 
conceive a case which will show how completely the 
whole process of inference depends on our assumption 
of uniformity. Suppose that testimony, having reached 
the ideal force I have imagined, were to assert that a 
certain river runs up hill. You could infer nothing at 
all. The arm of inference would be paralysed, and the 
sword of truth broken in its grasp; and reason could 
only sit down and wait until recovery restored her limbs 
and further experience gave her new weapons. I want 
in the next place to consider what we mean when we 
say that the uniformity which we have observed in the 
course of events is reasonable as well as exact. 
No doubt the first form of this idea was suggested by 
the marvellous adaptation of certain natural structures 
to special functions. The first impression of those who 
studied comparative anatomy was that every part of the 
animal frame was fitted with extraordinary completeness 
for the work that it had to do. I say extraordinary, be¬ 
cause at the time the most familiar examples of this 
adaptation were manufactures produced by human in¬ 
genuity ; and the completeness and minuteness of natural 
adaptations were seen to be far in advance of these. 
The mechanism of limbs and joints was seen to be adapted 
far better than any existing ironwork to those motions 
and combinations of motion which were most useful to 
the particular organism. The beautiful and complicated 
apparatus of sensation caught up indications from the 
surrounding medium, sorted them, analysed them, and. 
transmitted the results to the brain in a manner with, 
which at the time I am speaking of no artificial contriv¬ 
ance could compete. Hence the belief grew amongst 
physiologists that every structure which they found must 
have its function, and subserve some uselul purpose ‘ r 
a belief which was not without its foundation in fact, 
and which certainly (as Dr. Whewell remarks) has done 
admirable service in promoting the growth of physiology. 
Like all beliefs found successful in one subject, it was 
carried over into another ; of which a notable example 
