AS AFFECTING PRECESSION AND NUTATION. 3 



with faots of nature ; or ratlicr to exhibit their phiusiblc claims to be so. I will 

 content myself with remarking tliat if we turn to any treatise on the figure of the 

 earth (regarded as fluid) we find the motion of rotation disregarded and for it, what 

 is in reality though not in name, the repulsive force of Sir Wm. Thomson's fixed 

 "rcpellino- line" substituted.' If the problem be what superimposed form a 

 forei<'-n attraction (e. g. of the sun or moon) will develop, we encounter again as 

 the sole and (alle.o-ed) sufHcient substitute for the rotary motion this same repre- 

 sentative of "centrifugal force." This last problem is not one of pnre equilibrium; 

 for the sought-for forms are incessantly shifting, involving thereby other violiom 

 than the conventional centrifugal-force-generating one of rotation. Nevertheless, 

 the required configurations on a fluid spheroid are sought for on tlie repelling-line 

 theory and are in fact nothing else but the " small elliptic deviation superimposed 

 on the great polar and equatorial ellipticity" of the hyi)othetIcal case in § 25 

 "Rigidity of the Earth." Nay more, we find it admitted (Mec. Cel., Vol. 11.", Ch. 



nuiiiications on "vortex rings" in the same magazine. In the Transactions R S. Ed., 1868 and 1809, 

 are papers " On Yortex Motion" by the same author. It is, however, the latter mentioned consider- 

 ation, the "quasi-rigidity," by wliich the " light" is thrown; "vortex rings" are certainly not without 

 noticeable exhibitions of that quality. 



' I believe there to be no pli)-sicist who has not had occasion sometimes to fault the uses of, and 

 attributes conferred upon, this "centrifugal" force, so called; which proceeds from a special mani- 

 festation of the quality of matter we call inertia; i. e., that manifestation offered by the resistance 

 of a 7novi»g body to dejlection from its rectilinear path, creating an exigency for force which may 

 explicitly, but invertedly, enter into our analysis, or not, according as the amount of dejlection is, 

 or is not, a datum. In {e. g.) the problem of equilibrium of figure of a rotating fluid, the exigency 

 is for force to compel the dejlection belonging to the rotary or circular motion of the fluid i)articles; 

 which requirement is given in terms of distance of the particle from axis and of the angular velocity 

 of rotation Disregarding the motion (and hence its exigency) we create an equivalent exigency by 

 introducing an equal and opposite " centrifugal force, so called," and thus determine the fgurc, 

 winch furnishes by its integral attraction the required deflecting force. 



v'' 

 The resistance to deflection to given curvature is measured by ; but if the radius of curvature 



r (the reciprocal of the deflection), be unknown, the force of inertia cannot be thus expressed. We 



have then to use the more general forms (for rectangular co-ordinates) -j^, -J, -,j (or -, , etc.), 



which express the inertia of deflection towards the plane normal to the co-ordinate axis indicated, 

 Jrum any linear direction of the velocity, v. A study of these expressions, in connection with the 

 value and direction of v, will show that they are (like the explicit form of the centrifugal force) the 

 equivalents of an inertia measured by the deflection into the square of the velocity. Their use 

 excludes the introduction of the first expression even where it is known. (See also Airy, " Tides 

 and Waves," § 79.) 



Whatever idea we may attribute to that mysterious thing called "force," there can be no doubt 

 that, as used by all the authorities on nieehanics, as something which has direction, measurable in- 

 tensity, and whicii implies an equivalent reaction, the so-called centrifugal force possesses all these 

 attributes. Hence we find in the Nat Philos. of Tliomson and Tait not only the "repul.-^ion from 

 the axis in simple proportion to distance" {i. e., the identical repelling line force of " The Rigidity 

 of the Earth" article), but we find, § 800, "the potential of the centrifugal force;" and. § S13, the 

 same problem "dealt with by the potential method ;" and this not merely where it is a question of 

 C(piilil)rium of form when the only motion is that which exacts a so-expressed deflecting force; but 

 when it is one which involves the identica] "small elliptic deviation" or superimposed tidal form 

 of § 25 of the above treatise. Cf Prof. Tait's lecture on " Force" (" Nature," Feb. 28, 1877). 



