CHAP. II., 1.] 



PHYSICAL ASTRONOMY LAGRANGE. 



11 



a new form of construction, are experiments on the 

 resources of nature under new conditions. 

 (38.) j n f ac f even j n comparatively simple cases, we 



Solutions of . j. 



mechanical canno ; se * forces to act on matter, or dispose mat- 

 as of ma- ter so as to resist force, without doing not only what 

 thematical we intend to do, but also a great deal more. Man 

 sometimes mav P u * P owers * n motion which he is unable to 

 manifold, 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 background 

 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 



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 (40.) 

 problems which occupy the speculative philosopher, Lessons of 

 or the comprehensiveness of mind required for their experience 

 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. LAGRANGE. Variation of Parameters Application 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 



c 



