MECHANICS AND USEFUL ARTS. 43 



discoverer of the new world made the inhabitants of the old cast their eyes 

 over lands and seas far distant from those he had traversed; lands and seas 

 of which they could form to themselves no conception, any more than they 

 had been able to comprehend the course by which he led them on his grand 

 enterprise. In this achievement, and in the qualities which alone made it 

 possible, inexhaustible fertility of resources, patience unsubdued, close med- 

 itation that would suffer no distraction, steady determination to pursue paths 

 that seemed all but hopeless, and unflinching courage to declare the truths 

 they led to, how far soever removed from ordinary apprehension, in these 

 characteristics of high and original genius, we may be permitted to compare 

 the career of those great men. But Columbus did not invent the mariner's 

 compass, as .Newton did the instrument which guided his course, and enabled 

 him to make his discoveries, and his successors to extend them by closely 

 following his directions in using it. Nor did the compass suffice to the great 

 navigator without making any observations, though he dared to steer with- 

 out a chart; while it is certain that by the philosopher's instrument, his dis- 

 coveries were extended over the whole system of the universe, determining 

 the masses, the forms, and the motions of all its parts by the mere inspection 

 of abstract calculations, and formulas analytically deduced. The two great 

 improvements in this instrument which have been made the calculus of 

 variations by Euler and La Grange, the method of partial differences by D'- 

 Alembert we have every reason to believe were known, at least in part, to 

 Newton himself. His having solved an isoperimetrical problem (finding the 

 line whose revolution forms the solid of least resistance), shows clearly that 

 he must have made the coordinates of the generating curve vary, and his 

 construction agrees exactly with the equation given by that calculus. That 

 he must have tried the process of integrating by parts in attempting to gen- 

 eralize the inverse problem of central forces before he had recourse to the 

 geometrical approximation which he has given, and also when he sought the 

 means of ascertaining the comet's path, which he has termed by far the most 

 difficult of problems, is eminently probable, when we consider how naturally 

 that method flows from the ordinary process for differentiating compound 

 quantities, by supposing each variable in succession constant; in short, dif- 

 ferentiating by parts. As to the calculus of variations having substantially 

 been known to him, no doubt can be entertained. Again, in estimating the 

 ellipticity of the earth, he proceeded upon the assumption of a proposition 

 of which he gave no demonstration (any more than he had done of the iso- 

 perimetrical problem) that the ratio of the centrifugal force to gravitation 

 determines the ellipticit} 7 . Half a century later, that which no one before 

 knew to be true, which many probably considered to be erroneous, was exam- 

 ined by one of his most distinguished followers, Maclaurin, and demonstrated 

 most satisfactorily to be true. Newton had not failed to perceive the neces- 

 sary effects of gravitation in producing other phenomena beside the regular 

 motion of the planets and their satellites in their course round their several 

 centres of attraction. One of these phenomena, wholly unsuspected before 

 the discovery of the general law, is the alternate movement to and fro of the 

 earth's axis, in consequence of the solar (and also of the lunar) attraction 

 combined with the earth's motion. This libration, or nutation, distinctly 

 announced by him as the result of the theory, was not found by actual obser- 

 vation to exist till sixty years and upwards had elapsed, when Bradley proved 

 the fact The great discoveries which have been made by La Grange and La 

 Place upon the results of disturbing forces have established the law of peri- 



