238 PHILOSOPHICAL TRANSACTIONS. [ANNO 17 Of. 



We are now to speak of the most important business performed this year ; that 

 of making observations to determine the distance of the Scilly Isles from the Land's 

 End. To do this as accurately as possible, it became necessary to find stations 

 affording the longest base. The hill near Rosemergy, called the Watch, and the 

 station near St. Buryan, are certainly the most advantageous places, because all the 

 islands can be seen from both ; but we could not avail ourselves of the former, as 

 difficulties almost insuperable would have attended an attempt to get the instrument 

 upon it. Another station was therefore selected, on Karnminnis, near St. Ives ; a 

 spot as well situated as the place spoken of, provided all the islands could be seen : 

 this however does not prove to be the case, St. Martin's Day-Mark being the only 

 object in the Scilly Islands visible from Karnminnis. 



From the stations near the Land's End, Sennen, and Pertinney, as well as that 

 above-mentioned, St. Buryan, St. Agnes' Light-house, and 2 objects in St. Mary's, 

 were observed ; and as the means by which all their distances are determined, ex- 

 cept those of the Day-Mark, from the shortness of the bases, though the longest 

 that could be found, are exceptionable, while we were engaged in that part of the 

 operation now spoken of, the air was so unusually clear, that we could sometimes, 

 with the telescope of the great theodolite, discover the soldiers at exercise in St. 

 Mary's island.. In the present and former seasons, such stations were selected and 

 observed, as were judged to be proper for the future use of the small instrument ; 

 and as we had experienced, in the early stage of this survey, much delay and dis- 

 appointment from the white lights not being always seen when fired on distant 

 stations, we have since substituted lamps and staffs in their stead. The operations 

 of the present year were continued till October, when the party returned to 

 London. 



A list is here given of the angles observed in this quarter in the year 17 Q6. After 

 which is set down the demonstration of M. de Lambre's Formula in the Con- 

 noissance des Temps of 1793, for reducing a distance on the sphere to any great 

 circle near it, or the contrary ; by Nevil Maskelyne, d. d. f. r. s. and Astronomer 

 Royal. 



Put A = angle subtended by 2 terrestrial objects ; a = the same reduced to the 

 horizon ; h, A the 2 apparent altitudes : if either is a depression, it must be taken 

 negative. By spherics, c, a = c, a . «, h . c, A + s, h . s, A. 



Put A = a -f- da, where da signifies a — a, and not their differential. 



By trigonometry c, a = c, a . c, da — s, a . s, da = c, a X (l — vs, da) — s, a . s, 

 da = c,a — c, a X Is 1 , 4- da — s, a . s, da (by theorem above) = c, a . c, h . c, A 

 -f- s, h . s, h '.' s, da + Is 1 , ^da .'t, a = 't, a — 't, a . c, h . c, A — s, h . s, h X 

 cosec. a = t\ a — 't, a X CK, (h — A) + -Kj (h + A) — cosec. a X (ic, (h — h) 

 — ±c, (h -f h)) because t\ a = +% ±a — ±t, 4-a ; and cosec. a = ^t\a + ±t, -j-a) 

 = 0& i« - M *«) X (1 - -K, (h - k) - ±c, (h + h)) - (*%ia -f- ->./, ± a ) 

 X U-c, (h — h) — ic, (h + h)) = ft, -j-a x (1 - c, (h - A)) — ±t, ±a x 

 (1 — c, (h + A)) = +% ±a X vs, (h — A) — ±t, \a X vs, (h -f- A) = %+a . s\ 4. 

 (h - A) - t, +a . s\ 4. (h + A). 



