Page:Philosophical Transactions - Volume 095.djvu/283

Rh The sum of the real motions required, with the apex of the solar motion above mentioned, is less in this Table than that in the former by 0",50343.

In these calculations we have proceeded upon the principle of obtaining the least possible quantity of real motion, by way of coming at the most favouraUe Situation of a solar apex, and have proved that the sum of the observed proper motions of the six principal stars, amounting to 5",3534, may be the result of a composition of two other motions, and that the real motions of these stars, if they could be reduced to their smallest possible quantities, would not exceed 0",9559.

But as I do not intend to assert that these real motions can be actually brought down to the low quantities that have been mentioned, it will be necessary to show that the validity of the arguments for establishing the method I have pursued will not be affected by that circumstance. In the first place then, we should consider that although the great proper motions of Arcturus, Procyon, and Sirius, are strong indications of their being affected by parallax, it does not follow, nor is it probable, that the apparent changes of the situation of these stars should be intirely owing to solar motion; on the contrary, we may reasonably expect that their own real motions will have a great share in them. Next to this, it is evident that in the case of parallactic motions the distance of a star from the sun is of material consequence; and as this cannot be assumed at pleasure, we are consequently not at liberty to make the parallactic motion s p in Fig. 1, equal to the line s m of the same figure; hence it follows, that the real motion of the star cannot be from m to a, as the foregoing calculations have supposed; but will be from p to a. It is however very evident, that if m a be