LAPLACE. 147 



and 1769, on which occasions France — not to speak of stations in Eu- 

 rope — was represented at the isle of Kodri^o by Pingrc; at the isle of 

 San Dooiingo by Fleurin ; at California by the Abbe Ohappe ; at Pon- 

 dicherry by Legentil. At the same epochs p]ngland sent IMaskelyne to 

 St. Helena ; Wales to Hudson's Bay ; Mason to the Cape of Good 

 Hope ; Captain Cooke to Otaheite, &c. The observations of the south- 

 ern hemisj^here, compared with those of Europe, and especially with the 

 observations made by an Austrian astronomer. Father Hell, at Ward- 

 hus, in Lripland, gave, for the distance of the sun, the result which has 

 since figured in all treatises on astronomy and navigation. 



No government hesitated in furnishing academies with the means, 

 however expensive they might be, of conveniently establishing their ob- 

 servers in the most distant regions. We have already remarked that 

 the determination of the contemplated distance appeared to demand 

 imperiously an extensive base; for small bases would have been totally 

 inadequate to the purpose. Well, Laplace h^s solved the problem nu- 

 merically, without a base of any kind whatever. He has deduced the 

 distance of the sun from observations of the moon made in one and the 

 same place ! 



The sun is, with respect to our satellite, the cause of perturbations which 

 evidently depend on the distance of the immense luminous globe from the 

 earth. Who does not see that these perturbations would diminish if the 

 distance increased ; that they would increase, on the contrary, if the dis- 

 tance diminished ; that the distance finally determines the magnitude 

 of the perturbations ? 



Observation assigns the numerical value of these perturbations , 

 theory, on the other hand, unfolds the general mathematical relation, 

 which connects them with the solar parallax, and with other known ele- 

 ments. The determination of the mean radius of the terrestrial orbit 

 then becomes one of the most simple operations of algebra. Such is the 

 happy combination by the aid of which Laplace has solved the great, the 

 celebrated problem of parallax. It is thus that the illustrious geometer 

 found for the mean distance of the sun from the earth, expressed in 

 radii of the terrestrial orbit, a value diifering only in a slight degree from 

 that which was the fruit of so many troublesome and expensive voyages. 

 According to the oi^iuion of very competent judges, the result of the in- 

 direct method might not imjjossibly merit the preference.* 



The movements of the moon proved a fertile mine of research to our 

 great geometer. His penetrating intellect discovered in them unknown 

 treasures. He disentangled them from everything which concealed them 

 from vulgar eyes with an abilitj' and a perseverance equally worthy of 



'Mayer, from the principles of gravitation, (Ttieoria LunsE, J7(>7,) computed the value of 

 the solar parallax to be 7". 8. He remarked that the error of this determination did not 

 amount to one-twentielh of the whole, whence it followed that the true value of the parallax 

 could not exceed 8". 2. Laplace, by an analogous process, dotermined the parallax to be 

 8''. 45. Encke, by a profound discussion of the observations of tlie transits of Venus in ITGl 

 and 1769, found the value of the same element to be 8".r)77G.— Tkanslatoh. 



