earth; and therefore, in mye gs noire he- 
nomena, it is not arg to take the volume of the 
globe into the account. In practical geography, how- 
ever, it is frequently an important question to express 
the distance between different points: on the surface of 
the earth, in terms of some known measure, as miles, 
ards, feet, &c.; and as these distances cannot always 
we subjected to actual measurement, it becomes neces- 
sary to determine the dimensions of the globe itself. 
Various attempts have accordingly been made by astro- 
nomers to solve this problem, though it is only from 
the perfection of m instruments, that they have 
been able to accomplish it with any degree of accuracy. 
‘the earth were perfectly spherical, it is obvious that, 
ine its circumference, nothing more would be 
ssary, than to’find the length of a degree of the ter- 
festrial meridian} that is, the distance between two 
lying under the same meridian, but differing 1° 
in latitude, and multiply that distance by 360. It was 
- upon this principle that Eratosthenes, computing the 
the difference of latitude between Alexandria and Syene to 
be 7° 8’ 45”, and estimating the distance between them 
at 5000 stadia, determined the circumference of the 
earth to be about 252,000 stadia. This estimate is va- 
’ Inable, as being the result of the first attempt to ascer- 
tain the dimensions of the globe on‘correct principles. 
In point of acc ; however, as might be expected, 
it is very deficient. Independent of the uncertainty 
with to the length of the stadium which Era- 
tosthenes employed, he committed a considerable error 
in supposing Alexandria and Syene to be under the 
same meridian, praieee et was aa affected b 
an irregularity of which he was not perhaps aware. It 
d has been found, from actual (ieaahteenone that the de- 
la. Ph Seber a on the earth increase in length from 
e equator towards the poles ; that is, if two points be 
taken in a terrestrial meridian, at such a distance from 
each other that perpendiculars at these points, or lines 
in the direction of gravity, when produced tothe heavens, 
include between them 1° of a celestial meridian ; and 
if other two points be taken on the same meridian, but 
nearer the pole, such that perpendiculars from them al- 
so include een them 1° of the celestial meridian, 
then it is found, that the distance between the two first 
points, m on,the surface of the earth, is less than 
the distance between the two last. This difference, in- 
deed, is the necessary consequence of the spheroidal 
Sgure of the earth, which we formerly mentioned ; and 
gh, in geographical ee in general, the irregu- 
larity may be safely neglected, yet it is of importance 
to take it into account, in determining the dimensions 
of the earth. At the equator, a degree of latitude has 
een found to measure 60480.247 fathoms ; at the pa- 
rallel of 45°, 60759.473 ; and in latitude 66° 20’ 10”, 
60952.374, Taking the second of these as nearly a 
mean for all latitudes, and multiplying by 360, we 
have for the whole circumference of the meridian 
21873410.28 fathoms, or 24856.148 English miles. The 
circumference of the equator is found to be 24896.16 
miles, or 40 miles greater than that of the meridian. 
As all the meridians on the globe intersect one ano- 
ther in the poles, the distance between any two of them 
+» dirhinishes as the latitude increases. In many cases, it is 
ade. ~ of importance to know the law of this diminution, that is 
~~ to determine the length of a degree of longitude on any 
parallel of latitude, the d on the equator being gi- 
ven. In order to solve this problem with the greatest 
possible accuracy, it is necessary to make allowance’ for 
the spheroidal figure of the earth, or the difference in 
to « 
5 
GEOGRAPHY. 
151 
the length of degrees of latitude at different distances Mathematé- 
from the equator... But as there are irregularities in Geog 
these differences, that have led to doubt whether the phy. 
earth be a regular spheroid, and as for ordinary purpo- 
ses it is not necessary to aim at a degree of accuracy, 
which is after all perhaps a mere waste of calculation, 
we shall suppose the earth to ‘be a sphere, and on this 
principle exhibit in a Table the diminution of the de- 
grees of longitude for every degree of latitude. In such 
tables, it is usual to express the degree of the equator 
in terms of English miles ; but as the length of this de- 
gree is estimated differently by different writers, we 
shall, in the following Table, assume it equal to unity, 
and exhibit thecorresponding arches of the parallels in 
decimal fractions. ; 
Table of the Diminution of a Degree of Longitude for 
every Degree of Latitude, that of the Equator being 
reckoned Unity. 
Table of 
; Dd of : Degree of : D of Pa 
Latitude. Longita de, | {E*titude] 5 ngitude. Latitude, Longitade. rence 
the Degrees 
1 |. .99985 31 | 85717 61 | 48481 || of Longi- 
2 | .99939 82 | 84805 62 | 46947 | tude. 
3 | 99863 33 | .83867 63 | .45399 
4 | .99756 34 | 82904 64 | .43837 ° 
5 | .99619 35 | .81915 65 | 42262 
6 | 199452 36 | .80902 66 | 40674 
7 | 99255 37 | .79864 67. | .89073 
8 | .99027 38 | .78801 68 | .37461 
9 | .98769 39 | 77715 69 | .85837 
10 | .98481 40 | .76604 70 | .84202 
1l | .98163 41 | .75471 Ti (| 32557 
12 | .97815 42 | .74314 72 | .80902 
13 | .97436 43 | .731385 73 | 29237 
14 .97030 44: -71934 74 27564 
15 | .96593 45 | .70711 75 |. .25882 
16 | .96126 46 | .69466 76 | 24192 
17 | .95630 47 | .68200 77 + «| .22495 
18 | .95106 48 | .66913 78 | .20791 
19 | 94552 49 | .65606 79 | .19081 
20 | .93970 50 | .64279 80 | .17365 
21 | .93358 51 | .62932 81 | .15643 
22 | .92718 52 | .61566 82 | .13917 
23 + .92050. 53 | .60181 83 | .12187 
24 | 91355 54 | .58779 84 | .10453 
25 | 90631 55 | 57358 85 | .08716 
26 | .89879 56 | .55919 86 | .06976 
27 | .89101 57 | 54464 87 | .05234 
28 =| 88295 58. | .52992 88 | .03490 
29 | 87462 59 |, 51504 89 | .01745 
80 | .86603 60 | .50000 90 4 ,00000 
Since the circumferences of circles are to one another Construc- 
as their radii, if the radius of the equator be taken to tion of the 
express a degree of the equator, a degree of any paral- preceding 
Ael will be expressed by the radius of that el, table. 
But the radius e D (Fig. 2.) of any parallel eL, is the 
sine of eN the colatitude, or the cosine of A’ e, the Ja- 
titude of that parallel to the radius AIC. Hence to 
construct the above Table, we have only to take the na~ 
tural cosines of the different parallels to radius 1, or the 
natural numbers corresponding to the logarithmic co- 
sines, removing the decimal point ten places towards 
the left hand in each. “Thus, let it be required to 
