Let the curve passing through C represent a portion of the orbit of the earth, and S the sun. From the principles laid down, the density of the ethereal medium increases outward as the square roots of the distances from the sun. Now, if we consider the circle whose centre is C to represent the whole terral vortex, it must be that the medium composing it varies also in density at different distances from the sun, and at the same time is rotating round the centre. That half of the vortex which is exterior to the orbit of the earth, being most dense, has consequently most inertia, and if we conceive the centre of gravity of the earth and moon to be in the orbit (as it must be) at C, there will not be dynamical balance in the terral system, if the centre of the vortex is also found at C. To preserve the equilibrium the centre of the vortex will necessarily come nearer the sun, and thus be found between T and C, T representing the earth, and ☾ the moon, and C the centre of gravity of the two bodies. If the moon is in opposition, the centre of the vortex will fall between the centre of gravity and the centre of the earth, and have the apparent effect of diminishing the mass of the moon. If, on the other hand, the moon is in conjunction, the centre of the vortex will fall between the centre of gravity and the moon, and have the apparent effect of increasing the mass of the moon. If the moon is in quadrature, the effect will be null. The coefficient of this inequality is 90′, and depends on the sun's distance from the moon. When the moon is more than 90° from the sun, this correction is positive, and when less than 90° from the sun, it is negative. If we call this second correction C, and the moon's distance from her quadratures Q, we have the value of C = ±(90′ × sin Q)/R. [Illustration: Fig. 11] This correction, however, does not affect the inclination of the axis of the vortex, as will be understood by the subjoined figure. If the moon is in opposition, the axis of the vortex will not pass through C, but through C′, and QQ′ will be parallel to KK′. If the moon is in conjunction, the axis will be still parallel to KK′, as represented by the dotted line qq′. The correction, therefore, for displacement, is equal to the arc KQ or Kq, and the correct position of the vortex on the surface of the earth at a given time will be at the points Q or q and Q′ or q′, considering the earth as a sphere. [Illustration: Fig. 12]