I made about 250 observations of ẞ Draconis; which I find correspond as well with the hypothesis, as those of y; but since the positions of both these stars, in respect to the solstitial colure, differ but little from each other, it will be needless to set down the observations of B. I shall therefore proceed to lay down some observations of a small star that is almost opposite to y Draconis in right ascension, being the 35th Camelopardali Hevelii in the British Catalogue. Mr. Flamsteed indeed has not given the right ascension of this star; but that being necessary to be known, in order to compute the change of its declination arising from the precession of the equinox, I compared the time of its transit over the meridian, with that of some other stars near the same parallel; by which I found that its right ascension was 85° 54′ at the beginning of the year 1737.

This small star was compared with the same point of the limb of my sector, as y Draconis; and the 2d column, in the following table shows how many seconds it was found to be south of that point, at the time of each respective observation. The other columns contain, as in the foregoing table, the equations that are necessary to find what its mean distance from the same point would have been, on the 27th day of March, 1727, which is exhibited in the last column. The whole number of my observations of this star did not much exceed 40; the greatest part of which were made before the year 1730; in some of the following years none were taken; and only a single one in any other, except in 1739. However, their correspondency seems sufficient to evince the truth of the hypothesis: for if the mean of these, contained in the table, be taken, not one, among the rest of the observations, will differ from it more than 2′′.

a

The observations of the foregoing stars are the most proper, to prove the change of the inclination of the earth's axis to the plane of the ecliptic; those which follow will show in what manner the stars, that lie near the equinoctial colure are affected, as well as others that are differently situated, with respect to the cardinal points of the equator. Some of these stars are indeed more remote from the zenith than I would have chosen, if there had been others, of equal lustre, in more proper positions; because experience has long since taught me, that the observations of such stars as lie near the zenith, do generally agree best with one another, and are therefore the fittest to prove the truth of any hypothesis. I shall begin with those near the vernal equinox. & Cassiopea was compared with the point marked 34° 55'; and at first was found to be more southerly, but afterwards became more northerly than that point, as in the following table; the last column of which shows its mean distance south of that point on the 27th of March, 1727. The observation of the 23d day of December, in the year 1738, differs 3" from the mean of the others; as does also another, that was taken 5 days after this; neither of which being marked as uncertain, I judged it proper to insert one of them, though it gives the mean place of the star near 2 seconds more northerly than any other, in a series of above 100; all of which correspond, with the mean of these here recited, within less than 2"; excepting two, that give the stars mean distance almost 3" more southerly;. but these last mentioned are marked as dubious; and indeed they appear to have been bad, by comparing them with several others that were made near the same time, from which they differ almost 2′′".

1

T

Though I have taken no observation of Persei since the 22d day of January 1740; yet as this star is very near the zenith, and a sufficient number were made about the times when the equation, resulting from the hypothesis, was at its maximum; I judged it proper to insert some of them in the next table; the last column of which shows how much the star's mean distance was south of 38° 20′ on the 27th day of March, 1727. Among near 60 observations I meet with 2 only that differ from the mean of these, so much as 2"; and those differ almost as much from the mean of others, that were taken near the same time: so that the hypothesis seems to correspond, in general, with the observations of this star, as well as with either of the foregoing.

After the last recited observations, it may perhaps seem needless to add those of a Persci, which is farther from the zenith; but however, as this star lies very nearly at an equal distance from the equinoctial and solstitial colures, and the series of observations of it is somewhat more complete than that of Persei; I shall insert one at least, for each year in which it has been observed; by which it may appear that the hypothesis solves the phenomena of stars in this situation, as exactly as in others: for if a mean be taken of the numbers in the last column of the following table, which expresses the mean distance of the star south of

41°5′, on March 27, 1727, it will agree within 2 seconds, with every one of 80 observations that have been made of this star.

Having already given examples of stars lying near both the solstices and the vernal equinox; I shall now add the observations of one that is not far from the autumnal equinox, viz. Ursa Majoris, the brightest star in that part of the heavens which approaches the zenith of Wansted within a degree; and which, by reason of its lustre and position, gave me the opportunity of making my series of observations of it, more complete than of many others. This star was compared with the point marked 39° 15', and was south of it as in the following table; in which it is seen, that the observations of the years 1740 and 1741 give the polar distances 3" greater, than the mean of the other years. Had there been only a single observation taken in either of those years, part of this apparent difference might have been supposed to arise from their uncertainty; but as there were 8 observations taken within a week, either before or after the 3d day of June 1740, which agree well with each other; and 3 were made within 20 days in September 1741, which likewise corresponded with each other; I am inclined to think that the beforementioned differences must be owing to something else, besides the error of the observations. This phenomenon therefore may deserve the consideration of those gentlemen, who have employed their time in making computations relating to the quantity of the effects which the power of gravity may, on various occasions, produce. For I suspect, that the position of the moon's apogee, as well as of her nodes, has some relation to the apparent motions of the stars that I am now speaking of.

α

My series of observations of several stars abound, of late years, with so many and long interruptions, that I cannot pretend to determine this point; but probably the differences before taken notice of in the observations & Cassiopea, and some others, that I have found also among the observations of other stars, that are not here recited, may be owing to such a cause; which though it should not have any large share of influence, may yet, in certain circumstances, discover a 3 K

VOL. IX.

hypothesis that pays no regard at all to it. But whether these differences do arise from the cause already hinted at; or whether they proceed from any defect of the hypothesis itself in any other respect; it will not be very material in point of practice; since that hypothesis, as it was before laid down, appears to be sufficient to solve all the phenomena, to as great a degree of exactness as we can in general hope or expect to make observations. For if I take the mean of all the numbers in the last column of the following table for Ursæ Majoris, and compare it with any one of 164 observations that were taken of it,

the difference will not exceed 3 seconds.

It

may

be perceived, by inspecting the tables which contain the observations. of a Cassiopea and Ursa Majoris, that the greatest differences that occur in them may be diminished, by supposing the true pole of the equator to move round the point P, in an ellipsis, instead of a circle. For if the transverse axis, lying in the direction Ac, be 18", and the conjugate, as DB, be about 16"; the equations, resulting from such an hypothesis, will make the numbers in the last columns agree with each other, nearer than as they now stand. But since this would not entirely remove the inequalities in all the positions of the moon's nodes, I shall refer the more accurate determination of the locus of the true pole to. theory; and at present only give the equations for the precession of the equinoctial points, and the obliquity of the ecliptic, as also the real quantity of the an