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To determine the refractions on the first arc, White Horse and Whiteham Hills, we have the distance between those stations 88662,2 feet, which subtends an arc of 14' 32" nearly.

To determine those on the second, we have the distance between Brill and Arbury Hill = 146530 feet, subtending an arc of 24′ 3′′,9: those on the third, Wendover and Arbury Hill, 210628 feet = 34′ 35′′; and, for finding the refractions from the two last tables, we have the distance from Broadway Beacon to Epwell = 80611,4 feet, which subtends an arc of 13′ 11′′ nearly.

The depressions and elevations were all taken to the ground, excepting those which are marked with asterisks. At White Horse Hill and Whiteham Hill, lamps were used at the hours of 9 and 10: they were also made use of at Arbury Hill and Brill at 9 o'clock. In the first instances, the lamps were placed (the centres of them) 14 feet from the bottoms of the respective instruments; and in the last 2 feet.

The height of the transit telescope above the ground was always 5 feet; therefore, an allowance must be made, at each station, for the angle which that space subtends at its corresponding one; this premised, the refraction will be found from one of the two following rules, viz. if A be the contained arc, and D d the observed depressions, the quantity answering to the refraction, R, will be expressed by A-D-d; or, if one of the angles should A+c-d; these rules give the


be an elevation, e, then R refractions in the following table.


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Refractions found from the preceding Angles of Elevation and Depression.


Barom. Therm.

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in. pts.

29,5 58,0 9A. M.
29,5 61,010

29,5 58,111

29,5 57,012

29,5 57,0 3 P. M.

29,6 55,6 4

29,6 54,5 9

Refraction. pts. cont arc.

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3. Arc.

Arbury Hill and Wendover.

Barom. Therm Hours.

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4. Arc.

Broadway Beacon and Epwell.

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On examining the refractions obtained on the first arc, we perceive them to have been tolerably regular from 3 o'clock till 8; the mean being part of the contained arc. The height of Whiteham Hill is 576 feet, and that of White Horse Hill 893 feet, above the level of the sea : the ray passes, therefore, through a tract of air considerably elevated, as the country between the stations is, for the most part, flat and low.

The air is not often clear enough, or sufficiently free from tremulous motions, for these delicate observations. On the present occasion, however, the state of it was highly fit for the purpose; and, as care was taken, I am of opinion an error of more than 3", taking that of the arch of altitude into the account, cannot have obtained in any of the angles. The refractions at 9 and 10 o'clock are less than at the preceding hours; but this does not appear to have been owing to any change in the refractive power of the air throughout the whole extent of the ray, because the depression of Whiteham Hill, from the other station, varied little at those hours. These changes in the observed angles of elevation at Whiteham, (44′′ and 42′′ being the differences,) without corresponding ones at White Horse Hill, prove that some partial alteration, from floating strata, had taken place in the refraction near the former station. Whoever considers the matter, must perceive a case may be constructed in which this will take place, causing a great variation in one of the angles, whilst the other apparently remains the same: and this suggested the idea, that to afford any accurate conclusions in this way, a long series of observations would be necessary. It furthermore appears, that dew could not have caused these differences at Whiteham Hill, since the same cause would equally operate to vary the observed angles at White Horse Hill; but those remained nearly the same.

The refractions on the second and third arcs, I consider as most accurate, on account of the great distance between the stations; and also as more to be depended on, from the circumstance of the ray generally passing 300 feet above the ground.

The fourth arc affords another instance of the refraction varying at one station, and remaining constant at the other. This, no doubt, was owing to the intervention of some partial stratum of air, nearer to Epwell than Broadway Beacon. The refractions, deduced from these contemporary observations are certainly inconclusive. The mean refractions, (neglecting the fourth arc) brought under one point of view, will be as follows.

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If the air had been in a quiescent state, previous to and also at the times when these observations were made, it might be expected that the differences of altitudes in the stations would be obtained, tolerably near the truth, barometrically. The remarks in the tables appertaining to the first and second arcs, shew that such opportunities offered; but those which belong to the third, prove the wind to have been fresh; and, as the space between the stations which constitute the extremities of that arc is 34 miles, nearly, it is not to be expected that a true result should be obtained. The differences of altitudes of the stations constituting the extremities of the two first arcs, obtained by means of the observed angles of elevation and depression, as well

as from the heights of the mercury in the barometer, will be as follows.








The little done on this subject, points out the necessity of doing more; it therefore remains with me to observe, that I shall lose no opportunity of employing the apparatus committed to my charge in the best and most diligent manner, both as relating to matters of refraction, and to all others connected with the Trigonometrical Survey.

Obs. Ang.





In the Introduction, page 2, it is stated that this Account would be comprized in three Sections, but it was afterwards thought more convenient to divide it into four.

Printed by W. Bulmer and Co.
Cleveland-row, St. James's.

In Page 45, line penult. dele and Prittlewell. 14, for 1792, read 1772.


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