DEGREE. 
Let PGM oie VIt. ris 56.) be the sapere of 
Greenwich ; then if M B be the prrallel to th rpen- 
dicular bat Oe Ccaick, we hav 
269.328 feet. A herelore; taking 
for the a iewaet of the degree on the meridian, as derived from 
the difference of latitude between Greenwich and Paris, ap- 
plied to the ney arc eee the latitude a Paris 
8° so! 14"), GM= 15"20; confequently the 
latitude of the san “M (that of Gea being 51° 28' 40") 
is 50° 44’ 24”.74, and the co-lat. PM = 39° 15! 35.26. 
With mae to the arc MB, for the prefent p ae it 
is not of confequence on what hypothefis it ey obtained. 
But if 61,173 fathoms be affumed for the le eng a of a de- 
gree of a great pa perpendicular to the merid 
ther M'B = 9’ 37’ pe the latitude of B, bao cad. 
will be found 50° 44! oe 
gain (fig. 57+), let W 'B be the arc of a great circle 
perpendicular to the meridian ben ae at B, meet- 
ing that of Dunnofe in W, and let D R be another arc of a 
great circle ie to cn ean of Dunnofe in D, 
meeting that o -head in R: then we fhall have two 
{mall {pheroidical aa WBD and RBD, having in 
each two ang e8 given, namely, WD B= 81° 56’ 53”, and 
’ 58”, in the triangle WBD; and D 
= DR = 8°3'9", in the triangle D B 
and théfe reduced to the angles formed by the chords, sive 
the following triangles for computation ; namely, 
An 
bs 
WED = 6° 55’ 57%.2 
In the triangle W BD {wo B= Sr 96 52.4 
DWB — go! 7 10.4 
BDR= 8 3' 6 
In the triangle BD R {DBE = 83 4 
DRB=88 52 53 
In which it muft be noted, that the reduced angles are 
given to the neare 
Again, let BI an a DE be the parallels of latitude of 
Srelmeay and Dunnofe, meeting the meridians in 
E: then to find L W and E R, we have two fma!l triangles, 
that may te confidered as plane ones, namely, 
EDR, in which the angles at W and R are given nearly. 
Now the excefs of the three angles above 180° in the tri- 
angle D.BW, confidered as a ipherical one, is 5” nearly. 
Therefore ee angle D W B will be g1° 7’ 12” "nearly. Hen ce 
BWL= 8° 52 48”, confequently = 90° 33°36", 
2336". “Ll beeion with the chord of the 
= eet 
nd LB Ww = 
arc WB = 336,115.6 wis we get 
which added to W D, as found above, gives i es 6 feet, 
for the diftance between ae parallels i Beachy- nea and 
Dunnofe. Again, in the triaugle D B R, confidered as a 
{pherical one, the excefs is about 3 
Hence, from the two obferved oe at D and B, namely, 
83° 4/2", we get the third angle BRD = 
be 0° 33 
90° 33! 32°75 (DER); therefore an ae chord ‘se the 
336,989 feet, we get R E = 3288.2 feet, which 
B Ras found above, leaves 44,2589 feet for 
the meridional arc or the diftance between the parallels 
of Beachy-head and Dunnofe, which is nearly the fame as 
ore. 
This method of determining a diftance between the pa- 
Heap is fuffictently corre&. t the fame conclufion may 
ced from a different Sheek thus :— 
es the pesea of longitude, or the angle at P, 
found o hypothefis of the earth? 8 figure, and likewife 
she eines of Pa -head and Dunnofe; with thefe com- 
be 
pute the oe of the points R. and W: then it will he 
found that the arc R E is +3.” greater tran L W, and +2," 
on the meridian | is nearly a foot » RE is 5 tect more thaa 
475 4 .i— 
LW. Hence - = 5 a 40973 4 = 44257.8 is the 
diftance between the- eats hea is very nearly the 
fame as found by the cther meth Tt feems, therefore, 
that whatever be the value of a Me between thle parallels 
in parts of a degree, the diftance between ther is obtained 
{afficiently near the truth. Therefore, taking 60 851 fathoms 
for the length of a er on the meridian, we get the arc 
fubtended by 4 8.9 feet = 7’ idee which fubtracted 
from , Ys 50° 44! 23" 715 
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Since the fum of the horizontal angles P DB +PBD 
(Plate VII. jig. 55.) is nearly the fame as the 
which would be found on a fphere, we find the 
angles for fpherical computation, as follows:—The co- 
lauitudes ef D and B, or : e arcs D P ‘and B P, are 
g9° 22! 52% 69, and 39° 15/ 36".29; therefore half their 
fom is 39° 19! 14.495 aa half their difference 3’ 38".2 
—Half t a 
§ 
between Beachy-head and Dunnofe, or the ang e 
Ve hav 1 
"3° 20 43". e € now two angled tri iangles €s 
(jg. 57- Ms which may be confidered ees name ely, 
P BW and PDR, im which the angle at the pole, P, is 
iven, ae ee a fides P Band PD; therefore ufing 
thefe data a, we find the arc BW = 54’ 56" 21, and the arc 
DR= 55’ 4".74- e chords of the two pee 
arcs are about 34 feet lefs than the arcs themfelves: there 
fore BW = 36,1 11g.1 feet, and DR = 336,983.5 fe, 
And by proportioning thefe ar a to their relpective values 
in fathoms, we get the length o f the degree of the great 
circle perpendicular to aes meridian in the middle point be-« 
tween W and 5182.8 fathoms, ae in the middle 
point between R an 1,181.8 Therefore 
61,182.3 fathomsis the length of a degree eat the great circle 
perpendicular to the meridian, in latitude 50° 41’, which 
is nearly that of the middle point Siete omen yenead and 
unnofe. 
Of the aati of an Are of the ae an between Dun» 
nofe in the Ifle of Wight, and Cliften in Yorkfbire. 
The account of this important part of Be Englith furvey 
was drawn up by colonel Mudge, and read before the royal 
fociety ia June 180 
The length of the meafured arc was more than 196 
The triangles extended along a line exadtly 
They were conittru€ted, and obferved in 
the fame manner as in the former part of the furvey, 
and depending on the fame bafcs, namely, “Hounflow- 
heath and Salibury -plain. But, to add greater fecurity to 
the northern triangles, a bafe was meafured on Miterton 
Car, near the northern extremity of the bafe, with the fame 
as in the former operations, 
at had been meafured ; 
thowgh it would not have a prudent to have ot: 
fo eflential a verification, yet, bad all the calculations been 
made 
