(38.) 
Solutions of 
Cuap. II., § 1.] 
a new form of construction, are experiments on the 
resources of nature under new conditions. 
In fact, even in comparatively simple cases, we 
mechanical Cannot set forces to act on matter, or dispose mat- 
as of ma- 
thematical 
problems 
sometimes 
manifold. 
(39.) 
ter so as to resist force, without doing not only what 
we intend to do, but also a great deal more. Man 
may put powers in motion which he is unable to 
control ; and whilst he calculates confidently upon 
the effects of such and such dispositions of force or 
resistance, he may overlook consequences equally 
necessary, because resulting from laws of nature 
which are either unknown to him, or the magnitude 
of which he had overlooked, in considering those only 
which he required. A complicated mechanical con- 
trivance may be compared to the mathematical solu- 
tion of a problem. It represents commonly a great 
deal more than is meant to be derived from it. It 
may represent several distinct results, some possible, 
some impossible, and of the former only one, it may 
be, congruous to the real conditions of the problem 
proposed. In mechanics, the laws of nature are 
as impatient of control as the laws of quantity in 
geometry, and the engineer may find, too late, that 
nature has solved his problem differently from what 
he expected. But even when successful, it is to be 
presumed that his own contrivance contains within 
it results unforeseen by himself. If he is wise he 
will become a student in his own workshop. The 
material contrivances are indeed his own, but the 
powers which they awaken or distribute are beyond 
his control. Even if his reading of the equation be 
strictly correct, there may remain in the backgrouud 
others no less important. 
The considerations here imperfectly laid before 
the reader are intended to justify the introduction of 
certain practical topics into the present Dissertation, 
which, though many readers will see their insertion 
without surprise, or would have been sorry to find 
them omitted, others possibly may think more or 
less independent of, and separable from a scheme 
already sufficiently extensive and intricate, if con- 
fined to mere subjects of scientific doctrine, to the 
exclusion of its applications, My chief reason for 
including such subjects as the steam-engine, the 
strength of materials and some great examples of 
PHYSICAL ASTRONOMY—LAGRANGE. 
809 
construction, and the electric telegraph, is that 
these important practical improvements are both 
historically and logically interwoven with the pro- 
gress of pure or abstract physics. They have be- 
sides impressed upon the character of scientific dis- 
covery of the last hundred years a peculiar stamp 
which it would have been absurd to ignore while 
endeavouring, within a moderate compass, and in the 
plainest language, to convey a vivid though compre- 
hensive sketch of the advancement of Natural Philo- 
sophy during this and the preceding, or rather two 
preceding generations. 
It is not to be imagined that the difficulty of the 
problems which occupy the speculative philosopher, 
or the comprehensiveness of mind required for their 
solution, diminishes in any degree as we descend 
from the regions of pure science to the walks of every- 
day life—from the vast periods and majestic motions 
which astronomy enables us to explain and predict, 
to the common details of the workshop and the rail- 
way. In fact, the former are to be regarded as the 
simpler investigations, whilst our terrestrial agents 
have their effects modified by the diversified states of 
aggregation and various mechanical properties of mat- 
ter, and by the numerous modifications of force arising 
from heat, electricity, or magnetism, to which it may 
be exposed. We have as yet made but an insignificant 
advance towards that completer system of Natural 
Philosophy of which Newton’s will form but one 
section, in which all the properties of matter and 
their consequences shall be as well understood as the 
particular property of gravity is at present. Many of 
these are to be learned by daily observation of the 
effects which occur in the ordinary progress of civi- 
lization amongst us. We are continually perform- 
ing experiments on a great scale and on purely com- 
mercial principles, which no individual philosopher 
or merely scientific society could have ventured to 
attempt. And in the midst of these appeals to 
experience, unexpected results are frequently occur- 
ring which send us back once more to the study of 
first principles, which, indeed, while they confound 
the empiric, do but establish the reputation of the 
philosophic engineer, who seldom fails to turn them 
to good account, both in his theory and practice. 
CHAPTER II. 
PHYSICAL ASTRONOMY AND ANALYTICAL MECHANICS. 
$1. Lagrance.—Variation of Parameters—A pplication to Physical Astronomy. The Stability 
of the Planetary System; Laplace; Poisson. Moon's Libration. 
The period of Lagrange’s most celebrated labours 
Dissertation, it might have been excusable, with so 
extends so far back into the preceding century, that great a mass of matter before us, to have passed 
having been already mentioned in Sir John Leslie’s them over without farther notice. But they are so 
VOL. 1. 
5k 
(40.) 
Lessons of 
ordinary 
experience. 
