Kojjal Sucielij. 381 



But, in Jlie author's opinion, enough is shown to indicate the neces- 

 sity and propriety of a revision and correction of all the experiments 

 hitherto made with the pendulum, either for the determination of its 

 absolute length, or for ascertaining the true figure of the earth ; and 

 that for this purpose, the true correction must be found from actual 

 experiment in each particular case ; since, with very few exceptions, 

 it cannot be determined by any mathematical deduction. 



Mr. Daily then proceeds to point out some singular discordances 

 arising from the knife-edge mode of suspending the pendulum, where 

 the same knife-edge and the same agate planes are employed. From 

 which he is led to infer that the pendulum furnished with a knife-edge 

 and agate planes, as at present constructed, is a very inadequate in- 

 strument for the delicate purposes for which it was originally intended^ 

 and that a more rigid examination of that part of the instrument is 

 requisite, before we can rely witli confidence on the accuracy of the 

 results obtained by it. 



Some anomalies are then pointed out in the magnitude of the arc 

 of vibration, and some remarks offered on the supposed inadequacy of 

 the usual formula for determining the correction for the arc; but the 

 autlior considers it desirable that further experiments should be 

 made for the more accurate determination of this point. 



In conclusion, the author expresses a doubt of the rigid accuracy 

 of the length of the seconds pendulum, as deduced from the recent 

 experiments of Captain Sabine. 



To the whole are appended tables exhibiting the details of all the 

 experiments made by the author, and the corrresponding results. 



A Paper was read, entitled, " Researches in Physical Astronomy," 

 by John William Lubbock, Esq. V.P. and Treas. R.S. 



The present paper contains some further developments of the 

 theory of the moon, which are given at length, in order to save the 

 trouble of the calculator, and to avoid the danger of mistake. The 

 author remarks, that while it seems desirable, on tiie one hand, to 

 introduce into the science of physical astronomy a greater degree of 

 uniformity, by bringing to perfection a theory of the moon founded on 

 the integration of the equations employed in the planetary theory, it 

 is also no less important, on the other hand, to complete, in the latter, 

 the method hitherto applied solely to the periodic inequalities. Hi- 

 therto those terms in the disturbing function which give rise to the 

 secular inc(|ualities, iiave been detached, and the stability of the 

 system has been inferred by means of the integration of certain 

 equations, which are linear when the higher ])ovvers of the eccentri- 

 cities are neglected ; and from considerations founded on the varia- 

 tion of the elliptic constants. But the author thinks that the stability 

 of tiie system may be inferred also from the expressions which result 

 at once from the direct integration of the dift'erential equations. The 



led to infer that, in the case of spheres, cylinders, and other bodies sus- 

 punded by rods of diHurcnt diameters, the value of tlie factor depends not 

 oidy t)u lliu body a|)|;ended to such rod, hut that the rod itself lias a con- 

 sideraMc influence on the result, except it be a very fine wire ; when its 

 edctl becomes merged in that of the appended body. 



