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These theorems, however simple their algebraic expressions, it must immediately be seen, become for the most part complicated and unintelligible when geometrically enunciated. They are indeed (if we may in any case be allowed to consider a curve as unidentified with its equation) properties rather of the equations of the conic sections, than of the curves themselves,-of a limited number of disjoined points determined according to a certain law, rather than a series of consecutive ones composing a line.

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JOHN F. W. HERSCHEL.

Slough, Oct. 6, 1812.

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III. Observation of the Summer Solstice, 1812, at the Royal Observatory. By John Pond, Esq. Astronomer Royal, F. R. S.

Read November 12, 1812.

As it is intended that a minute description of the mural circle lately erected at the Royal Observatory, when completely finished, shall be laid before the Royal Society, I think it unnecessary to accompany this communication with

any

other remarks on its construction, than such as are absolutely necessary to render the annexed observations intelligible; being only anxious to take an early opportunity of transmitting the result of the observations of the sun, made at the last summer solstice. For, notwithstanding the instrument was at that time in a very unfinished and imperfect state, I have reason to think, that the observations made with it were much more exact than could have been made with any other instrument hitherto constructed: the uncertainty of the result, as far as the instrument itself is concerned, does not, I believe, exceed a small fraction of a second ; but I think it necessary to offer a few remarks on the elements of the computation, by which the result is obtained.

The distance of the sun from the pole at the moment of the solstice, may either be considered as a simple arc, or as composed of two others, namely, the distance of the sun from the zenith, and the distance of the zenith from the pole. From the construction of instruments which take their point of departure from the position of a plumb-line or level, it is a genera

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