As the means for making observations on the heavenly bodies become more and more exact, astronomers are compelled to introduce new refinements into their calculations; new inequalities are discovered, and the computation of those whose sources are already known has to be carried to a greater number of approximative steps.

Discussions on the amount of solar parallax, of aberration and of nutation, are now carried on to the third and fourth decimal fraction of a second; with such a refinement of computation, it seems almost impossible to proceed too far in the refinement of theoretical deductions, and on that account, it may not be inopportune to discuss the influence which the sun's and moon's attraction exert upon the direction of the plumb-line.