Analyses of Books- 
153 
In the course of the survey several determinations were made of distances mea- 
sured by General Roy. The following table contains the particulars of the compa- 
rison. General Roy’s distances are corrected for the difference of Captain Rater’s and 
the imperial standard. It is further to be noted, that the differences are solely attri- 
butable to differences in the measurement of the angles ; as the distance of Hanger 
Hill from Severndroog Castle, the first side of the present triangulation, is assumed 
to be as determined by General Roy. We have added a column giving in round 
numbers the ratio of the differences. 
General 
Roy. 
Captain 
Kater. 
Diff. 
Ratio. 
Fairlight to Frant, 
113850.6 
113857.3 
6.7 
T y i? o 5 
Fairlight to Tenterden, __ 
71577.2 
71580.8 
3.5 
2 0 0 0 0 
Fairlight to Folkstone, — 
154802.7 
154807.0 
4.3 
I 
36000 
Dover to Notre Dame, Calais, 
137459.4 
137472.0 
12.6 
TTo o o 
Notre Dame, Calais, to Fiennes, 
45222.7 
45221.0 
1.7 
1 
2 6000 
The distances of the several stations from the meridian and perpendicular of 
Greenwich being calculated ; Captain Kater proceeds to the determination of the differ- 
ence of longitude and latitude. For this purpose he thinks the most convenient formulae 
yet proposed, are those given by Oriani, in his Opusculi Astronomici, published at Milan 
In 1826. They are as follows. 
Let a = semi major axis of the Earth. 
b = semi minor axis. 
e — the eccentricity 
M = the distance in feet from the perpendicular to the meridian, at Green- 
wich. 
P = the distance in feet from the meridian of Greenwich. 
M 
l> Sin I" 
P 
r ~ b Sin 1" 
L = the latitude of Greenwich. 
^ = the latitude of the foot of the perpendicular let fall from the given 
station on the meridian of Greenwich. 
<p = the required latitude of the given station. 
« -- the required longitude of the given station. 
Then 1. X= L ± m ( 1— e* + § e 3 Cos. 3 (L ±j)) 
2. if/= p (1 — fe* Sin 2 A) 
3. Sin <p = Sin A Cos. 
4. Tan.a='^4-(l— ^-Cos.= X ) 
Cos. X V 2 
In attempting to determine the value of the perpendicular degree, by means of 
observed azimuths and co-latitudes ; a result is obtained which “ must be erroneous 
about one hundred fathoms.” It is shown, that to account for such an error, it is 
only necessary to suppose the azimuths erroneous to 2", a degree of accuracy which 
Captain Kater thinks cannot he predicated of any azimuth determined by observa- 
tion of the pole star. Any error of the level would be increased ; and besides the 
ordinary errors attributable to the level there may he irregularity of local attraction, 
Mich as at Arbnry occasioned the plummet of the sector to he drawn 5J” out of the 
vertical. Any slight uncertainty of polar distance would be doubledin the azimuth, 
•o which if we add lateral refraction affecting the position of the object to which it 
is referred, we shall agree with Captain Kater, that observations of the pole starve 
totally unworthy of credit, at least in the latitude of England. He considers obser- 
vations of a star when near the east or west point of the horizon as more eligible, 
