820 
method of interpolation will serve the same purpose, 
as well as save a very tedious calculation. Perhaps too 
much importance has been assigned to the “ probable 
mean error” of a single observation deduced from 
many individual errors by the same theory. If a 
man has but one shot at a target, it is perfectly un- 
certain (by hypothesis) whether that shot be one of 
his best, or one of his worst, or one of his middling 
ones. But as there are more middling hits than 
very bad or very good ones, there is a certain dis- 
tance which it will be safe to bet (i. e. for which the 
probability is }), that he will not exceed; though it 
would be a strange occurrence indeed, if he exactly 
struck the ring in question. This is all thatis meant 
by the phrase “ probable error ;” it is an entirely 
artificial number, which serves to give a sort of nume- 
rical value of the skill of the performer, but is other- 
wise of no importance. Its application has sometimes 
been strangely mistaken. Even the “rule of least 
squares’”’ is often misapplied, and empirical laws al- 
together false have been deduced from it ; for it is 
rare in practice that the chances of error of observa- 
tion of a varying quantity are the same throughout 
the limits of observation. 
Probable 
error. 
Res ; But those applications of the doctrine of proba- 
of Testi. » bility which pretend to give us a measure of our belief 
mony and in the constancy of natural laws, in the confidence due 
of Design. to testimony and to the teachings of history, in the 
proofs of design in cosmical arrangements,—are 
inquiries which, from their connection with meta- 
physics, religion, and morals, havehad a higher interest 
for mankind at large than ordinary problems about 
cards and dice. To these Laplace paid peculiar 
attention ; and the reputation of his name tended to 
create in others a belief that the analysis he so power- 
fully wielded could communicate a portion of its 
certainty to the data subjected to it, and gave a 
currency to many of his conclusions to which we 
believe them by no means entitled. Professor Play- 
fair, one of the most ardent of Laplace’s admirers, has 
recorded (in a criticism in the Edinburgh Review, of 
the works we are considering) his total dissent from 
Laplace’s doctrine that the transmission from age to 
age of the historic record of a fact diminishes its credi- 
Laplace’s bility in a geometrical ratio. But a Cambridge 
ppt mathematician and speculative philosopher of singu- 
oe ae penetration, Mr Leslie Ellis, has most formally 
assailed! the principle of nearly all Laplace’s esti- 
mates of our expectation of events arising from causes 
unknown or assumed to be so, such, for instance, as that 
a common cause determined the revolution of all the 
planets in one direction. The subject of the meta- 
physics of probability evidently requires a complete 
reconsideration ; and, owing to the singular subtlety of 
MATHEMATICAL AND PHYSICAL SCIENCE. 
(Diss. VI. 
the matter, it is one which few persons are competent 
to handle. The state of health of Mr Ellis leaves us 
little hope of his resuming the inquiry; but two 
eminent mathematicians, Mr De Morgan and Mr 
Boole, have published considerable works chiefly 
bearing upon it. 
As an implement bearing upon discovery in (87.) 
science, the Calculus of Probabilities has as yet been Probability 
of little service. Whilst Laplace tries to indicate how {, ae. i 
it guided his researches connected with planetary irre- covery. 
gularities, every one sees at a glance that, with the 
data before him, common sense must have outstripped 
analysis, Laplace has called the doctrines of pro- 
bability “ good sense reduced to calculation.” What 
is to be feared is, that the calculation should outstrip 
the good sense. 
(88.) 
Laplace’s 
V. Fifthly, We are to consider Laplace’s charac- 
ter as a general physicist and as a writer. shaceslall 
In the former respect he stands in a higher posi- as a phy- 
tion than that usually attained by eminent analysts. sicist, and 
In fact, if we compare him with any of his own ®§ 82 4U- 
generation, we find him not only better acquainted ~~" 
with physical principles, and more scrupulous in 
taking account of them in his mathematical discus- 
sions, but even possessing skill and interest in ex- 
periments. The Calorimeter for measuring the capa- 
cities of bodies for heat was the joint invention of 
Lavoisier and himself; at least their memoir does 
not assign to either a predominant share in it,? and 
their determinations of the expansions of the metals 
by heat seem also to have been made in common. 
His happy discovery of the chief or sole cause of the Memoirson 
discrepancy between the theoretical and observed Heat, in 
velocity of sound (due to the heat developed by com. Soho” 
pression) would alone have given him a just reputa- Lavoisier. 
tion, so anxiously had the matter been debated, and 
so much was it involved in a purely mathematical 
intricacy. Even in his great work on physical as- 
tronomy he takes a peculiar pleasure in embracing 
topics of terrestrial physics. We there find discussed 
the theory of barometrical measurements, the ques- On Baro- 
tion of atmospheric tides, the laws of capillary attrac- metrical 
tion, and the constitution of the gases. As to the first Measure- 
of these topics he made a practical improvement On Capill 
the formula of his predecessors, so that his rules are Attraction, 
in fact stillin use. As regards capillary attraction, & Astrono- 
he was materially anticipated by Young, who evi- pees 
dently considered his principles to have been pirated ; 
yet his theory, though obscured by a display of re- 
dundant mathematics, was a real improvement. His 
theory of tides, and that of atmospheric refractions, 
though closely connected with physical astronomy, 
were in fact not less so with the doctrines of hydro- 
1 Cambridge Transactions, Vol. VIII. The writer of these pages has also given his reasons for dissenting from the argu- 
ments of Michell (which have been sanctioned by the authority of Laplace) on an astronomical question as discussed by the 
Theory of Probabilities. 
See Philosophical Magazine for December 1850. 
® Dr Black, the discoverer of latent heat (who was probably well-informed), states in a letter to Watt that he believes 
Laplace to have been the inventor. 
See Correspondence of Watt on the Decomposition of Water, p. 66. 
