PERTU11BATION EXPLAINED. 



Such, then were in fact the means by which the discovery of the 

 planet, since called Neptune, was made; a discovery which was 

 incontestably one of the most signal triumphs ever attained by 

 mathematical science, and which marked an era that must be for 

 ever memorable in the history of physical investigation. 



If the planets were subject only to the attraction of the sun, 

 they would revolve in exact ellipses, of which the sun would be 

 the common focus ; but being also subject to the attraction of 

 each other, which, though incomparably more feeble than that 

 of the presiding central mass, produces sensible and measurable 

 effects, consequent deviations from these elliptic paths, called 

 PERTURBATIONS, take place. The masses and relative motions of 

 the planets being known, these disturbances can be ascertained 

 with such, accuracy, that the position of any known planet at any 

 epoch, past or future, can be determined with the most surprising 

 degree of precision. 



If, therefore, it should be found, that the motion which a 

 planet is observed to have is not in accordance with that which 

 it ought to have, subject to the central attraction of the sun, 

 and the disturbing actions of the surrounding planets, it 

 must be inferred that some other disturbing attraction acts 

 upon it, proceeding from an undiscovered cause, and, in this 

 case, a problem novel in its form and data, and beset with diffi- 

 culties which might well appear insuperable, is presented to 

 the physical astronomer. If the solution of the problem, to 

 determine the disturbances produced upon the orbit of a planet 

 by another planet, whose mass and motions are known, be re- 

 garded as a stupendous achievement in physical and mathe- 

 matical science, how much more formidable must not the converse 

 question be regarded, in which the disturbances are given to 

 find the planet. 



Such was, nevertheless, the problem of which the discovery of 

 Neptune has been the astonishing solution. 



Although no exposition of the actual process by which this great 

 intellectual achievement has been effected, could be comprehended 

 without the possession of an amount of mathematical knowledge 

 far exceeding that which is expected from the readers of works 

 much less elementary than the present, we may not be altogether 

 unsuccessful in attempting to illustrate the principle on which an 

 investigation, attended with so surprising a result, has been 

 based, and even the method upon which it has been conducted ; 

 so as to strip the proceeding of much of that incomprehensible 

 character, which, in the view of the great mass of those who con- 

 sider it, without being able to follow the steps of the actual 

 investigation, is generally attached to it, and to show at least 



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