part of its rotation that the meridian of P passes through the star); also let S' be another star in the plane of the earth's orbit, and in the direction corresponding nearly to the earth's solstitial position. And suppose (in conformity with the assertion that we have made all along, but which we shall now subject to the severest proof) that the earth's axis remains strictly parallel to itself in its motion round the sun, with no other motion than those which we have described as produced by precession and nutation. And suppose that with a mural circle at P we observe the zenith-distances of the stars S and S' when they pass the meridian of P, and apply the proper corrections for refraction; and then, by applying corrections for the effects of aberration, we find the place in which the star would have been seen if unaffected by the earth's velocity: and by applying corrections for precession and nutation, we find the zenith-distances which the stars would have had if the position of the earth's axis had not been affected by precession and nutation. Now, if our assumption (that the earth's axis has no motion but those depending on precession and nutation) be correct, the result of the observation of the star S', whatever be its distance, will be, that its corrected zenith-distance when observed on the meridian will be the same whether the earth be at E', E", E'", or E"". This is found to be strictly in agreement with the results deduced from actual observation, so that it is certain that the earth's axis has no motion but those depending on precession and nutation. Moreover, for the vast majority of stars in all parts of the heavens, when the same corrections are applied, the corrected meridional zenith-distances are found to be the same whatever be the position of the earth in its orbit;
