However, subsequent observations appear to render it probable that part of these appearances in stars of consi derable zenith distance, may arise from refraction.
Dr. Brinkley also states in this paper, that he considers the circumstance of the Greenwich mural circle, showing the same arch between a Lyrx and 7 Draconis in summer and winter, as the strongest objection that had been ad vanced against the results from the Dublin circle. But a recent examination having been made of the observations of the Greenwich circle, it appears that in each of the years 1812, 1813, 1814, and 1815, the arch between Pola ris above the pole and Lyrx in summer being compared with the same arch in winter, there results almost ex actly the same parallax for Lyrx, as has been found by Dr. Brinkley. This changes the nature of the objection. The objection, if any, against the Dublin circle, should now be, that it gives no parallax for 7 Draconis, whereas the Greenwich circle gives it the same as for a Lyrx.
Dr. Brinkley, anxious to obtain all possible exactness, pursued the observations, and front the great number which he had accumulated of certain stars, it occurred to him that they might be applied to finding the solar nota tions, as well as the parallax and aberration. lie has pub lished a paper on this subject, in the fourteenth volume of the Transactions of the Royal Irish Academy.
One of the principal objections to his results, was the difficulty of ascertaining with certainty quantities so small. The constant of aberration had evidently been obtained by him with great exactness, but the degree of exactness was not precisely known. Now, the constant of solar nu tation is known from theory with certainty to be nearly half a second, a quantity smaller than he had found for the parallax of certain stars; therefore, if the same ob servations should be found to give the solar nutation ex act, a most satisfactory argument would be had for the exactness of the parallax.
He remarks, " The solar notation goes through all its states twice in the course of a year; therefore, it appears impossible to suppose that, if any cause should occasion the instrument to show deviations explained by parallax which did not actually exist, it should not derange the solar notation, and cause the result of an investigation of its quantity to turn out quite erroneous.
"This method of investigation, which I have applied to several stars, has produced the most satisfactory re sults.
" There will not, I conceive, remain the smallest doubt with any one who examines the processes which have been used, that the observations have ascertained the quantities of parallax, with considerable exactness, of the Stars a Lyre, a Cygni, and Arcturus, and that the paral laxes of 7 Draconis and Ursx Majoris arc extremely small. That 7 Draconis is at least seven or eight times more distant than a Lyre." Dr. Brinkley shows that the constant of solar nutation deduced from theory, does not differ one-tenth of a second from 0"51. He shows, that if the constant of lunar nuta tion=9"50+y, the constant of solar nutation=0"506 13 y. Now y is certain to six-tenths of a second; there
fore the solar nutation is certain to less than one-tenth of a second by taking it = 0"51.
He supposes it unknown, and The constant of aberration = 20'25 + The constant of parallax = p.
The correction of the mean zenith ? dist. of the star known nearly, S — e.
From each observation he obtains an equation of the form e-Ff x-fg p+1, k=0, containing four unknown quantities, e, x, p, and z.
Thins, for a Lyre 333 equations of this kind arc ob tained. These equations arc reduced to 4, by the method of making the sums of the squares of the errors a mini mum.
quirt', the difference between the constants of aberration for y Draconis and Urstc Majoris.
The constant of aberration for a Lyrae, comes out The mean of the constants of aberration in the table of 13 stars above given, is 20"37. Therefore those who con tend, by arguments certainly of great weight, that the velocity of light of all the stars is the same, will admit that the constant of aberration has been determined with great exactness by the observations of a Lyre.
The parallax of this star appears also established in the most conclusive manner. It is difficult to imagine a se verer test for the exactness of any philosophical experi ment, than that to which the observations of this star have been submitted. There are three apparent motions of this star, depending on the place of the sun, and va riously mixed together. Two of these, the aberration and solar nutation, have been separated from each other, and from the third, (the parallax,) and ascertained to the ex actness probably of the 1-loth of a second. Can it be doubted that the third. the parallax appearing to amount to I", I, has also been. ascertained with nearly equal ex actness ? • It remains to mention the method of computing the effects of the parallax of the fixed stars as to changes or declination, right ascension, &c. This may be very shortly explained. It is easily understood that, by the effect of parallax, each star appears nearer the sun by Semi-diam. of earth's orbit.
an arch = X sin. angular Star's distance.
dist. of star from the sun = p sin. angular dist. of star from sun.
Also, (not considering the eccentricity of the Earth's Orbit) by the elect of aberration, each star appears to ap proach the point of the Ecliptic behind the sun by an mean vel. of earth.
arch = vel. of light. X sin. ang. dist. of star from point of Ecliptic 90° behind the sun = 20", 25 sin. ang. dist. of star from that point. Hence, if A represent the effect of aberration on a star when the sun's longitude is O + 90°, h A 20, 25. will be the effect of parallax, when the sun's longitude is 0. This is evidently true, whether the effect in declination, in right ascension, or in latitude or longitude, be required. Thus the tables of aberration are easily made to apply to finding the effects of parallax. It is only necessary to compute the aberration, for (sin. longi 2 tude x 90°) and the result multiplied by 25 will give the effect required.