SEQUEL TO THE EPOCH OF NEWTON". 447 



places were better represented by a circle than by a parabola : and 

 Lexell, a celebrated mathematician of Petersburg, found that a motion 

 in a circular orbit, 'with a radius double of that of Saturn, would satisfy 

 all the observations. This made its period about eighty-two years. 



Lalande soon discovered that the circular motion was subject to a 

 sensible inequality : the orbit was, in fact, an ellipse, like those of the 

 other planets. To determine the equation of the centre of a body 

 which revolves so slowly, would, according to the ancient methods, 

 have required many years ; but Laplace contrived methods by which 

 the elliptical elements were determined from four observations, within 

 little more than a year from its first discovery by Herschel. These 

 calculations were soon followed by tables of the new planet, published 

 by Nouet. 



In order to obtain additional accuracy, it now became necessary to 

 take account of the perturbations. The French Academy of Sciences 

 proposed, in 1789, the construction of new Tables of this Planet as its 

 prize-question. It is a curious illustration of the constantly accumu- 

 lating evidence of the theory, that the calculation of the perturbations 

 of the planet enabled astronomers to discover that it had been observed 

 as a star in three different positions in former times ; namely, by Flam- 

 steed in 1690, by Mayer in 1750, and by Le Monnier in 1769. De- 

 lambre, aided by this discovery and by the theory of Laplace, calcu- 

 lated Tables of the planet, which, being compared with observation for 

 three years, never deviated from it more than seven seconds. The 

 Academy awarded its prize to these Tables, they were adopted by the 

 astronomers of Europe, and the planet of Herschel now conforms to 

 the laws of attraction, along with those ancient members of the known 

 system from which the theory was inferred. 



The history of the discovery of the other new planets, Ceres, Pallas, 

 Juno, and Vesta, is nearly similar to that just related, except that their 

 planetary character was more readily believed. The first of these was 

 discovered on the first day of this century by Piazzi, the astronomer 

 at Palermo ; but he had only begun to suspect its nature, and had not 

 completed his third observation, when his labors were suspended by a 

 dangerous illness; and on his recovery the star was invisible, being 

 lost in the rays of the sun. 



He declared it to be a planet with an elliptical orbit ; but the path 

 which it followed, on emerging from the neighborhood of the sun, was 

 not that which Piazzi had traced out for it. Its extreme smallness 

 made it difficult to rediscover; and the whole of the year 1801 was 



