_ 400 
ae 
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a gord rule to say nothing but good of the dead, it is a better 
one to say nothing at all of the living, 
I have already alluded to the mathematical treatment of 
electricity and magnetism. The aid of mathema ics here was 
not required to confirm a theory, tut rather to prepare the way 
for one. The complicated laws, regulating the attractions of 
electric and magnetic bodies, and of bodies cariying electric 
currents, have by the aid of mathematics been reduced to their 
simplest form, and electrical units have been connected with 
the ordinary mechanical units. This interesting branch of 
physics will furnish us with an example of the services which 
mathematics has rendered in directing the efforts of experi- 
menters into the proper groove. We need cnly compare the 
magnetic measurements which were made during the last century 
with those made in our own time. While the early investiga- 
tions gave us only a series of numbers impossible to interpret 
without a large quantity of accessory data, which are generally 
omitted, modern measurements, even when made by non-mathe- 
maticians, have generally been suggested by mathematical calcu- 
lations and very often serve a useful purpose, 
I have hardly alluded, as yet, to the science of dyramics, 
which is the foundation of all applications of mathematics. Its 
progress has been s'eady since the time of Galileo, but all the 
marvellous results arrived at by Newtcn and his followers, 
results which first showed the great fertility of applied mathe- 
matics, are too familiar to need any enumeration from me. The 
modern researches in hydrodynamics may perhaps not as yet 
have led to any definite result of physical interest, but they are 
rapidly progressing towards that end, and we may look forward 
to an increasing number of physical discoveries made by the aid 
of mathematics. 
In tracing the history of some of our modern theories, I have 
followed the usual plan of presenting the history of science as 
illustrated by the discoveries of our great scientific men. It is 
necessary, however, to draw attention to the fact, and I have 
tried to keep this point in view throughout this discourse, that it 
is not always the most conclusive arguments which carry the day, 
and that secondhand thinkers have often had a more potent in- 
fluence in shaping the course of scientific history than those to 
whom we now justly ascribe the greater merit of discovery. In 
cur historical studies, therefore, we ought to direct our attention 
not less to that which has influenced public opinion, than to the 
actual soundness and originality of each discoverer. 
If we ransack old books of science we often come across 
passages of long-forgotten writings, in which, when they are 
properly construed, when new meanings are given to old words 
and obscure expressions are freely translated, we may trace a 
faint prophetic glimmering of a modern theory. Such passages 
have a peculiar charm for the student of scientific history ; they 
are oftenthe only reward for much patient and otherwise use- 
less reading, and are interesting as showing the almost boundless 
ingenuity both of him who made the statement and of him who 
interpreted its meaning. But those who are fond of this process 
of exhumation onght not to forget that two parties are necessary to 
every advance in science—the one that makes it and the one that 
believes in it, and the course of history is as much affected by 
the second class as by the first. 
* A jest’s prosperity lies in the ear 
OF him that hears it, never in the tongue 
Of him that makes it.” 
A scientific man, in so far as he influences the progress of 
science, caunot be far ahead of his time, and though his writings 
may be read and admired centuries after his death, he will have 
written in vain if he has not been appreciated by bis contem- 
poraries or by those who immediately followed them, For our 
present purpose, then, we must consider not so much those 
mathematical arguments which appear now to us the most con- 
clusive ones, but such as did appear conclusive to those whose 
opinion they were meant to affect. But if we try to discover 
what arguments have had the greatest power in removing old 
preju ices and in causing a solid advance in science, we find that 
they have often been of the most flimsy nature. Analogies, 
sometimes not even good ones, have succeeded where solid 
reasoning has failed, prejudices have been overcome only by 
other prejudices, and a rough illustration of a point of secondary 
importance may have made a previously obscure theory look 
more familiar, though not more clear, to the popular mind. 
What, for instance, has the existence of Jupiter’s four satellites 
to do with the question whether the earth turns round the sun 
or the sun round the earth? Yet the discovery of these satellites 
Ci ng ae ae 
‘NATURE 
~~ Ue 
[ Feb. 23, 1882 
2 PY, 
has produced a greater revolution in favour of the Copernican 
theory than anything else that Galileo wrote on the subject. 
If we look at the history of science from the point of view 
suggested by these considerations, we find that in addition to the 
legitimate influence of mathematics which we have traced, its 
practical effects, through less reasonable causes, have often been as 
powerful, The statement that in science authority is of no avail 
against argument, is one the proof of which must be looked for 
in the future, rather than in the past. There can be little doubt 
that authority has had a great effect in all scientific revolutions, 
and the authority of mathematicians was always greater than 
that of other men of science. Men are thoroughly convinced in 
one of two ways only ; either by a train of reasoning which they 
can fully appreciate, or by one which is entirely above their 
comprehension, To those who are particularly amenable to the 
second kind of proof, mathematics has always been a magic 
power. Many results first obtained by the help of advanced 
mathematics have since been deduced by more elementary rea- 
soning, but it seems questionable whether the original author 
would have been as successful in overcoming the inertia of his 
contemporaries, if he had confined himself to language intelligible 
to the greater number of his reeders. It is no doubt due to this 
cause that mathematical papers have brought wifh them more 
widespread convincing power than we should now feel inclined 
to accord to them. The papers of Young, in which he avoided 
mathematical symbols, may appear to us sufficient to establi-h 
the undulatory theory of light; the arguments of Sir Humphry 
Davy, the experiments of Joule, may seem absolutely conclusive 
in favour of the mechanical theory of heat; but although the 
mathematical investigations of Fresnel, Clausius, and Thomson 
could be appreciated only by a much smaller number of readers, 
they had a more powerful influence in turning the scale of public 
opinion in favour of the modern ideas. Jt seems sometimes 
almost as if it required an experimentalist to convince a mathe- 
matician, and a mathematician to convince the general world. 
It is impossible to enter into greater detail or to exemplify more 
amply the assertions which 1 have made without touching on 
delicate and controversial matters, but on the present occasion it 
seemed to me to be specially fitting to point out that the course 
of science is as much affected by the appreciative faculty 
of receptive minds as by the creative faculty of the discoverer. 
It is given to few only to take an active and successful part in 
the preduction of scientific work, The young man who begins 
life with the idea of making a name as a scientific discoverer is 
like the little girl in Puch who intended to become a profes- 
sional beauty. They may both be successful, but if so, it will 
depend as much on the ready appreciation of their contempo- 
raries as on themselves. The advance of science takes place 
through many channels, and each generation has its own part to 
play. Particular ideas, particular faculties are wanted at par- 
ticular times, and no one can foretell where success will be. 
Men who are now quoted as shining lights would have passed 
away unnoticed had they lived at other times, and many a life 
has been one of patient but unsuccessful work, because its ener- 
gies were devoted to a subject which was barren, or at least lay 
fallow fora time. No one, for instance, who has attempted to 
read through J. B. Morinus’ work (and I doubt whether any one 
has ever got beyond the attempt) can fail to notice in him quali- 
ties which might have made a successful discoverer. In his 
method of determining longitudes by lunar distances Morinus 
has left us a lasting legacy. During the greater part of bis life, 
however, his energies were devoted to the study and application 
of astrology, and all the labour spent on that subject was thrown 
away, although he did his best to make his own prophecies come 
true, and, having predicted the end of the world for a certain 
year, went through with his share of the proceedings, and died 
a natural death at the appointed time. A friori, there was no 
reason why astrology when married to mathematics should not 
have produced a healthy progeny, and looking especially to the 
state of science at the time, we can have little fault to find with 
the old astrologers ; it is only the long and sad experience of 
their failure and disappointment that has given us the right to 
laugh at their unproductive efforts. 
History then does not teach us any royal road to success. But 
more important for the ultimate progress of truth than a solitary 
success is the training of the faculty which enables the scientific 
man to judge correctly, and to appreciate the results of those 
who strike out new roads and extend the boundaries of know- 
ledge. It seems to me to be one of the chief objects of an 
institution like this to bring up men, who, by conscientious con- 
