DETERMINATION OF THE SOLAR PARALLAX. 335 



Laplace has solved the problem numerically 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 con- 

 trary, if the distance diminished ; that the distance finally 

 determines the magnitude of the perturbations ? 



Observation assigns the numerical value of these per- 

 turbations ; theory, on the other hand, unfolds the general 

 mathematical relation which connects them with the solar 

 parallax, and with other known elements. The determi- 

 nation 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, ex- 

 pressed in radii of the terrestrial orbit, a value differing 

 only in a slight degree from that which was the fruit of 

 so many troublesome and expensive voyages. According 

 to the opinion of very competent judges the result of the 

 indirect method might not impossibly merit the prefer- 

 ence.* 



* Slayer, from the principles of gravitation (Tlieoria Lunce, 1767), 

 computed the value of the solar parallax to be 7"-8. He remarked 

 that, the error of this determination did not amount to one twentieth 

 of the whole, whence it followed that the true value of the parallax 

 could not exceed 8"-2. Laplace, by an analogous process, determined 

 the parallax to be 8/'-45. Encke, by a profound discussion of the 

 observations of the transits of Venus in 1761 and 1769, found the 

 value of the same element to be 8''-5776. Translator. 



