79; and for the thermometer without, from 24 to 80. The difference of these extremes being divided by 8, will show the corrections for the former to every 6°, and for the latter to every 7°; and assuming that the variations are in a reciprocal ratio to the degrees of the thermometer, I propose the following formula. Putting h for the degree of Fahrenheit's thermometer, then 49°-hx,0024, when below the mean; 49°— h° ×,0023, when above the mean; will be the correction for the thermometer within; and 45hx,0021, the correction for the thermometer without. The Tables II. and III. show the near agreement of the observed and the equated factor, found as above. The barometer at its mean state may continue to be taken at 29,6 inches; and the mean point of the thermometer without, will then be at 45°. The thermometer within, which has been assumed at 50° for the mean state, from observation, appears to be at 49°; and supposing the barometer and thermometer to vary reciprocally, as the former in inches and the latter in degrees, the mean point of each is in an inverse ratio to the other, and might be changed if thought expedient. Indeed it appears from the mean of more than 1000 observations of these circumpolar stars, at all seasons, that the mean state of the barometer is 29,85, and of the thermometer 59°; yet, as the sum of the two corrections would still be the same, there cannot be occasion to alter the mean point of the former, especially as this might not be a general rule for every climate. It has very rarely happened, that I could make any observation, when the barometer has been below 29 inches, which causes the mean state to be so high as 29,85; but it may be otherwise in places,

where the atmosphere is not so charged with vapours, as that of this country.

I have, in the Table IV. shewn the mean refractions, according to various authors; the first column contains those of Mr. SIMPSON, from the observations of Dr. BEVIS; the second, those of Dr. BRADLEY, by his formula, tang. ≈ — gr × 57′′; but this quantity having been found, from later observations, to have been too small; the third column contains the same formula, into 58",107; yet the refractions, at low altitudes, will be found too great, and this excess has been corrected by M. PIAZZI, using arbitrary equations, which will bring them nearer to the truth, as shown in the fourth column. The more uniform correction of the whole will be, as I have proposed in the above theorem, by increasing the coefficient of r; a corollary from which will be drawn, that the increment of the tangents near the horizon will cause the equations of M. PIAZZI to vanish. The fifth column contains the refractions of the French tables; and the sixth, my own; viz. tang. z -3.3625г × 58",1192.

On inspection of this table, it will appear, that the refractions by different formula do not vary considerably, so far as 80°; and thence to 87°, my deductions are rather in excess of the French tables; below which, mine are rather less. Whether this arises from the defect of the formula, I cannot determine; since the wall of Greenwich park being above my horizon, I cannot observe lower than 88: however, so far as 88°, the formula I have proposed, agrees with observation.

Blackheath, 22 Jan. 1810.

S. GROOMBRIDGE.

Thermometer within.

Factors for the correction of the Refraction, the mean result

Factors for the correction of the Refraction, equated from the

mean of the above, according to the proposed formula.

Table IV. The mean astronomical Refractions, according to

85 9 10 9 52,50 10 3,18

86 11 5 87 13 44 88 17 43 89 23 50 90 33

11 49,77 12 1,95 11 42,6 11 48,3 11 52,21

14 34,61 14 48,78 14 18 34.30 18 50,59 18 24 28,14 24 46,42 23 032 59:43 33 18,52 32

25,1 14 28,1 14 31,75 2,7 18 22,2 18 19,19 46,1 24 21,2 23 46,77 3,033 46,3 31 27,87

XI. Extract of a Letter from the Rev. John Brinkley, D. D. F. R. S. Andrew's Professor of Astronomy in the University of Dublin, to the Rev. Nevil Maskelyne, D. D. F. R. S. Astronomer Royal, on the annual Parallax of a Lyræ.

I HAVE

Read April 12, 1810.

HAVE now had sufficient experience of my eight feet circle, to be highly satisfied with it, and have arrived at one conclusion, that it is of importance in astronomy.

My observations on a Lyræ for the purpose of discovering an annual parallax now amount to 47 in number, viz. 22 near opposition, and 25 near conjunction, and the mean of these gives a result of 2,"52 as the parallax of the annual orbit for that star, and I have no doubt that it exceeds 2".

My observations of different circumpolar stars, and of the same star in different states of the thermometer, seem to require a small alteration in the numbers of Dr. BRADLEY'S formula for refraction.

The formula so altered is

Refraction =56,"9 × tang. {Zen. dis. - 3,2 Refr.} height of barom.

500 450+ther.

X 29,6

By means of this formula, the observations of circumpolar stars considerably distant, give the same co-latitude to a great degree of exactness.