PHYSICAL AND MATHEMATICAL SCIENCES. 331

principle of gravitation. But if this were perfectlyexact, the principle could not be true. The existenceof certain deviations was absolutely necessary to makeout the case. If, then, these could be calculated by thetheory, and the results found to agree with observation,the most perfect and satisfactory proof would be fur-nished. But this, as it may well he imagined, was afield of research of the most extensive and bewilderingkind: the different paths of investigation to be pursuedwere perplexed in the utmost intricacy, and the com-putations of the most difficult nature ; Newton, how-ever, found the means of overcoming those difficulties,to a sufficient extent to carry him satisfactorily throughthe investigation of the most important cases. Thesewere principally those inequalities of the moon’s motion,some of which were of sufficient amount to have beennoticed (as we have before seen) by the ancient astro-nomers, and which we’re now ascertained with consider-able accuracy. The greater phenomena, then, of theplanetary motions, constituted one class of proofs ofNewton’s theory. But these would be incomplete andunsatisfactory, without those of the second kind, de-rived from the theory of “ perturbations,” as they aretermed. Of these, the lunar inequalities formed themost conspicuous portion, and which occupied largely theattention of Newton. It is true that the investigationof the planetary system is thus involved in much diffi-culty and intricacy, which would not belong to it wereit restricted to exact elliptic motion ; and there areprobably many to whom the simplicity of the absoluteelliptic orbits would afford the most powerful evidence,but who might turn away with impatience from the la-borious details of the theory of perturbations. Few ofthese, again, are of such magnitude as to appear to anordinary apprehension worth the labour bestowed uponthem ; nevertheless, it must be borne in mind, thaton their successful exposition, the truth of the whole sys-tem essentially depends.

Besides the force of the earth, or rather of the mutual