DEG 
DEG 
4t)S 
crating, blessing, and sanctifying, is taken 
from him : lie erases the marks of the ton- 
sure in the same manner, which a barber 
completes by shaving his head all over. 
Degradation, in painting, expresses the 
lessening the appearance of distant objects in 
a landscape, in the same manner as they would 
appear to an eye placed at that distance from 
them. See the articles Perspective and 
Painting. 
DEGRADED CROSS, in heraldry, a 
cross divided into steps at each end, dimi- 
nishing as they ascend towards the centre, 
called by the French peronnee. 
DEGREE, in geometry, a division of a 
circle, including a three hundred and sixtieth 
part of its circumference. 
Every circle is supposed to be divided into 
three hundred and sixty parts, called de- 
grees, and each degree divided into sixty other 
parts, called minutes; each of these minutes 
being again divided into sixty seconds, each 
second into thirds, and each third into 
fourths, and so on. See the articles Minute, 
Second, &c. 
By this means no more degrees or parts 
are reckoned in the greatest circle than in the 
least that is ; and therefore if the same angle 
at the centre be subtended by two concentri- 
cal arches, as many degrees are counted in 
the one as in the other ; for these two arches 
have the same proportion to their whole pe- 
ripheries. 
A degree of the meridian on the surface of 
the globe is variously determined by various 
observers. 
Ptolemy fixes the degree at 68j Arabic 
miles, counting stadia to a mile. The 
Arabs themselves, who made a computation 
of the diameter of the earth, by measuring 
the distance of two places under the same 
meridian, in the plains of Sennar, by order 
of Almamon, make it only 56 miles. Kep- 
ler, determining the diameter of the earth by 
the distance ol two mountains, makes a de- 
gree 13 German miles ; but his method is 
far from being accurate. Snell, seeking the 
diameter of the earth from the distance be- 
tween two parallels of the equator, finds the 
quantity of a degree by one method 57,064 
Paris toises, or 342,384 feet ; by another me- 
thod 57,057 Paris toises, or 342,342 feet. 
The mean between which two numbers M. 
Picard found by mensuration, in 1669, from 
Amiens to Malvoisin, the most certain ; and 
he makes the quantity of a degree 57,060 
toises, or 342,360 feet. However, M. Cas- 
sini, at the king’s command, in the year 1700, 
repeated the same labour; and measuring the 
space of 6° 18', from the observatory at 
Paris, along the meridian, to the city of Col- 
iioure in Roussillon, that the greatness of the 
interval might diminish the error, found the 
length of the degree equal to 57,292 toises, 
or 343,742 Paris feet, amounting to 365,184 
English feet. 
And with this account nearly agrees that of 
our countryman Norwood, who, about the 
-year 1635, measured the distance between 
London and York, and found that distance 
905,761 English feet; the difference of lati- 
tude being 2° -28', hence he determined the 
quantity of one degree at 367,196 English 
feet, or 57,300 Paris toises, or 69 miles, 288 
jards. 
DEG 
! M. Cassini, the son, completed the work 
of measuring the whole arc of the meridian 
through Prance, in 1718. For this purpose 
he divided the meridian of France into two 
arcs, which he measured separately. The 
one from Paris to Collioure gave him 57,097 
toises ; the other, from Paris to Dunkirk, 
56,960 ; and the whole arc from Dunkirk to 
Collioure 57,060 ; the same as M. Picard’s. 
M. Muschenbroek, in 1700, resolving to 
correct the errors of Snell, found by particu- 
lar observations, that the degree between 
Alcmaer and Bergen-op-zoom contained 
57,033 toises. 
Messieurs Maupertuis, Clairaut, Camus, 
Mourner, and Outheir, of France, were sent 
on a northern expedition; and began their 
operations, assisted by M. Celsus, an emi- 
nent astronomer of Sweden, in Swedish Lap- 
j land, in July 1736, and finished them by the 
end of May following. They obtained the 
measure ot that degree, whose middle point 
was in lat. 66° 20' north, and found it 57,439 
toises, when reduced to the level of the sea. 
About the same time another company of 
philosophers was sent to South America, viz. 
messieurs Godin, Bouguer, and Condamine, 
i of France, to whom were joined don Jorge 
j Juan, and don Antonio de Ulloa, of Spain. 
J 1 hey lett Europe in 1735, and began their 
; operations in the province of Quito, in Peru, 
! about October 1736, and finished them, after 
j many interruptions, about eight years after, 
j 1 he Spanish gentlemen published a separate 
i account, and assignedfor the measure ofa de- 
I gree of the meridian at the equator 56,768 
I toises. M. Bouguer makes it 56,753 toises, 
| when reduced to the level of the sea; and 
j M. Condamine states it at 56,749 toises. 
| M. La Caille, being at the Cape of Good 
i Hope in 1752, found the length of a degree 
! of the meridian in lat. 33° 18' 30" south, to 
\ be 57,037 toises. In 1755 father Boscovich 
I found the length of a degree in lat. 43° north 
! to be about 56,972 toises, as measured be- 
tween Rome and Rimini, in Italy. In the 
year 1740 messrs. Cassini and La Caille 
again examined the former measures in 
France ; and after making all the necessary 
corrections, found the measure of a deiajjb, 
whose middle point is in lat. 49 a 22' north/ to 
be 57,074 toises ; and in the lat. of 45° it was 
57,050 toises. 
In 1764 F. Beccaria completed the mea- 
surement of a portion of the meridian near 
Turin ; from which it is deduced that the 
length of a degree, whose middle lat. is 44° 
44' north, is 57,024 Paris toises. 
At Vienna three degrees of the meridian 
were measured ; and the medium for the la- 
titude of 47° 40' north may be taken at 
57,091 Paris toises. See an account of this 
measurement in the Phil. Trans. 1768. 
Finally, in the same volume is an account 
of the measurement of a part of the meri- 
dian in Maryland and Pennsylvania, North 
America, 1766, by messieurs Mason and 
Dixon ; from which it follows that the length 
of a degree whose middle point is 39° 12' 
north, was 363,763 English feet, or 56,9044 
Paris toises. 
Hence from the whole we may collect the 
following table of the principal measures of a 
degree in different parts of the earth, as mea- 
sured by different persons, viz. 
Years of Mea- 
surement. 
1736 and 1737 
1739 and 1740 
1 766 
1739 and 1740 
1760 to 1764 
1752 
1764 to 1 768 
1736 to 1744 
1752 
Names of the 
Measurers. 
Maupertuis, &c. 
( Maupertuis, &c. 
\ and Cassini 
Liesganig 
Cassini 
Beccaria 
( Boscovich and 
l Le Mai re 
Mason & Dixon 
f Bouguer and 
X Condamine 
La Caille 
Length of a 
Degree in 
Paris Toises. 
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Mean Lati- 
■ tude. 
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The method of obtaining the length of a 
degree of the terrestrial meridian, is to mea- 
sure a certain distance upon it by a series of 
triangles, whose angles may be found by ac- 
tual observation, connected with a base 
whose length may be taken by an actual sur- 
vey or otherwise ; and then to observe the 
different altitudes of some star at the two ex- 
tremities of that distance, which gives the 
difference of latitude between them: then 
by proportion, as this difference of latitude is 
to one degree, so is the measured length to 
the length of one degree of the meridian 
sought. This method was first practised by 
Erastosthenes, in Egypt. 
Degree of longitude, is the space be- 
tween two meridians that make an angle of 
1° with each other at the poles ; the quantity 
or length of which is variable, according to the 
latitude, being every where as the cosine of 
the latitude ; viz. as the cosine of one lat. is 
to the cosine of another, so is the length of a 
degree in the former lat. to that in the latter ; 
and from this theorem is computed the fol- 
lowing table of the length of a degree of 
long, in different latitudes, supposing the 
earth to be a globe. 
Note. This table is computed on the sup- 
position, that the degrees of tiie equator 
are equal to those of the meridian at the me- 
dium latitude of 45°, which length is 69^ 
English miles. 
The expressions latitude and longitude are 
borrowed from the antients, who happened to 
be acquainted with a much larger extent of 
earth in the direction east and west than in 
that of north and south ; the former of which 
therefore passed, with them, for the length of 
the earth, or longitude ; and the latter for the 
breadth, or shorter dimension, viz. the lati- 
tude, 
