Biographies of distinguished scientific men. First series

by F. Arago

No government hesitated in furnishing Academies with the means, however expensive they might be, of conveniently establishing their observers 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 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 contrary, if the distance 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 elements. 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 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 preference.[36]

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 every thing which concealed them from vulgar eyes with an ability and a perseverance equally worthy of admiration. The reader will excuse me for citing another of such examples.

The earth governs the movements of the moon. The earth is flattened, in other words its figure is spheroidal. A spheroidal body does not attract like a sphere. There ought then to exist in the movement, I had almost said in the countenance of the moon, a sort of impression of the spheroidal figure of the earth. Such was the idea as it originally occurred to Laplace.

It still remained to ascertain (and here consisted the chief difficulty), whether the effects attributable to the spheroidal figure of the earth were sufficiently sensible not to be confounded with the errors of observation. It was accordingly necessary to find the general formula of perturbations of this nature, in order to be able, as in the case of the solar parallax, to eliminate the unknown quantity.

The ardour of Laplace, combined with his power of analytical research, surmounted all obstacles. By means of an investigation which demanded the most minute attention, the great geometer discovered in the theory of the moon's movements, two well-defined perturbations depending on the spheroidal figure of the earth. The first affected the resolved element of the motion of our satellite which is chiefly measured with the instrument known in observatories by the name of the transit instrument; the second, which operated in the direction north and south, could only be effected by observations with a second instrument termed the mural circle. These two inequalities of very different magnitudes connected with the cause which produces them by analytical combinations of totally different kinds have, however, both conducted to the same value of the ellipticity. It must be borne in mind, however, that the ellipticity thus deduced from the movements of the moon, is not the ellipticity corresponding to such or such a country, the ellipticity observed in France, in England, in Italy, in Lapland, in North America, in India, or in the region of the Cape of Good Hope, for the earth's materials having undergone considerable upheavings at different times and in different places, the primitive regularity of its curvature has been sensibly disturbed by this cause. The moon, and it is this circumstance which renders the result of such inestimable value, ought to assign, and has in reality assigned the general ellipticity of the earth; in other words, it has indicated a sort of mean value of the various determinations obtained at enormous expense, and with infinite labour, as the result of long voyages undertaken by astronomers of all the countries of Europe.

I shall add a few brief remarks, for which I am mainly indebted to the author of the Mécanique Céleste. They seem to be eminently adapted for illustrating the profound, the unexpected, and almost paradoxical character of the methods which I have just attempted to sketch.

What are the elements which it has been found necessary to confront with each other in order to arrive at results expressed even to the precision of the smallest decimals?

On the one hand, mathematical formulæ, deduced from the principle of universal attraction; on the other hand, certain irregularities observed in the returns of the moon to the meridian.