5 74 
Mr. Airy on the 
There are some measures in which such extraordinary 
disturbances appear to have existed, that it seems desirable 
to examine and extend them : of these, the most remarkable 
is that made by Lacaille at the Cape of Good Hope. And 
perhaps in speaking of the probable effects of local attraction, 
I may be permitted to allude to one of a different kind in 
England. This is the correction which it has been found 
necessary to apply to the longitudes of places in England, 
as deduced from the observations made at Beachy Head and 
Dunnose. For this investigation I prefer the method of 
Dalby, explained in the Philosophical Transactions for 1790 
and 1795, to any other; as being unobjectionable on the 
ground of accuracy, and as applying to any surface in which 
the intersections of the normals at the two stations with the 
earth’s axis, or with a line parallel to the earth’s axis, are 
not very distant. The difference of longitude is then made 
to depend on this case of spherical trigonometry ; given two 
sides ( a, b ) and the sum of the opposite angles ( A -f- B ) , to 
a — b 
cos. 
find the third angle (c). The formula is, tan. — = — b cos. £ 
cos. T— 
2 
In this instance a= colatitude of Dunnose = 39° 22' 52 ",69 ; 
h — colatitude of Beachy Head = 39 0 15' 36 ", 29 ; A 4* B = 
sum of observed azimuths = 178° 52' 51"; hence C = 
i° 2 6' 47", 87. And if the errors in the observed quantities 
a, h, A, B, were $ a, $ h, $ A, $ B, the error in C would be 
cos. 
a . — b 
cos. 
cos. 
^4-B 
cos. ■ 
cos. 
fl b 
sin. 
o cl -4- b 
cos . 2 ! 
(sin. b. 
Sa + sin. a. $ 6) = -1,293 ($A-\- £ B) +,0103. $a + ,0104.^6. 
Now the chronometer observations for the difference of 
