152 GEOGRAPHY. . 
Mathematis find a degree of longitude on the parallel of 25°. “The contained between the parallels of 66° and 57°, that) of ¥ 
cal Geogra- natural cosine of 25° is 90,631 to radius 100,000, and the globe being 1. 4 cal Gi 
phy. making radius 1, the cosine becomes .90631, the length — First, by a Table of natural sines. . ~ <n 
of the degree required. Thus also the logarithmic co- sin. 57° = 83867 
sine of 25° = 9.957276, and the number corresponding sin. 56. = 82904 
to this logarithm is 9,063,100,000, which is the length —- 
of the degree required, that of the equator bemg - 963 
10,000,000,000, or radius of the trigonometrical table. 963 __ : og rS spas ; 
But as it would be inconvenient to operate with these and iy 481.5 is the area required, the radius of the 
numbers, they may both be divided by 10,000,000,000, Table being 100,000, and removin the decimal point 
or the decimal point may be removed ten places to the five places towards the left, the radius becomes 1, and 
left hand in each, which will give 1 for the degree of the area of the zone .004815. j 
the equator, and .90631, as in the preceding Table, for Secondly, by a Table of logarithmic sines. 
that of the parallel of 25°. This number may also be 
found at once from the logarithmic Tables, by subtract- 
r : : MEI cia hs faa ae o ahah ote’ s ihdny SA OLR Sa 
ing 10 from the cosine, and finding the natural number am. “6 o f 
corresponding to the remaining logarithm. Thus the |; Pes —— numbers corresponding to these logas 
cosine of 25° becomes 1.957276, and the number cor- 83867 
responding in the Table of logarithms is .90631. : "32904 
The application of the above Table for finding the K 
length of a degree of longitude under any parallel, con- Difference .00963 
sists in simply multiplying the fraction opposite to the 00963 : 
ven latitude, by the length of a degree of the equator. and —-—= .004815 is the area required. 
hus, to find the length of a degree on the parallel of Be a ; was. oo a 
25°, that of the equator being 60 geographic miles, mul- Upon this principle, the following Table is construct- Table 
tiply -90,631 by 60, and the product 54.3786, or 54.38 ed, exhibiting the area of every zone of 1° from the 7 
nearly, gives the degree required in geographic miles. equator to the pole, that of the globe being unity. © 
If the earth be considered as spherical, a degree of the ips 
equator may be assumed equal to the degree of the me- 
ridian bisected by the parallel of 45°, or 60759.473 fa- 
thoms, which gives for the geographical mile 6075.947 | Q»to 1°|,008725|30°to $19,007520)60° to 61°.004295 
feet. 
: : ; F — 2h —82 |. 
Method of | Before concluding this account of the dimensions of . Eee piles be rane alae 62— 63 |.0040: 
finding the the globe, it may perhaps be of use to some of our rea- | 3 — 4 |.008710/33 4 | 75163—~ 64 ‘Aopen 
area of a dam’ db noimt out a snwel d os hod. of . —34 |.007275)63— .003 
given zone 5 point out a simple an expeditious method, 0} 4 — 5 |,008700/34 —35 |.007195164— 65 |.0037 
of the finding the superficial contents of any given zone of | 5 — 6 |,008685|35 —36 |.00710 ( 
66 |. 
earths the earth. By geometry, the superficies of a sphere, is a 66— 67 |. 
equal to the product of the circumference, multiplied ¥ Bx : peeeds a pith 67— Be ace 
As the sar and vet a apr to the product of | g — g 008630) 38 —39 ; k 
e circymference multiplied by that part of the dia- —10 |. —40 |. 69— 70.1.0 
meter, intercepted between the planes of the two paral- ue ar peak KA —41 rerde 70— oe ae 
lels containing the zone ; that is, the area of the zone ~|jj —12 "008550/41 —42. "006535 71— 72 00277 
is to the area of the whole.sphere, as the perpendicular || 9 13 ‘008520142 —43 ‘00643 79— 73 ‘0026: 
distance of the two parallels of the zone is to the dia- |13 —14 |.008485|43 —44 |00633073— 74 [00248 
meter. But the distance B D (Fig. 2.) between an Ra a 
two parallels fg, ¢ L, is the difference of the sines of "Be i. Bi: peeves A Yeeeah 
and Af, the latitudes of e and f; therefore the area of |g —17 
the zone fe L g : area of the globe: : sin. He—sin. Ef |j7 —18 ; 
: sin. AZ e—sin. 
: diameter : : : — mie i radius. If, therefore, is ee : 
the radius of the sphere be taken to express the whole [20 —21 |. 
area; half the difference of the natural sines, or of the |2! —22 |. 
natural numbers corresponding to the logarithmic sines [22 —25 | 
of any two latitudes, will express the area of the zone 23 —2¢ |. 
included between these latifudes, the radius of the |24 —25 |. 
sphere being equal to the radius of the respective Ta- [25 —26 |. 
bles. Ifthe radius be reduced to unity, the area of the 26. —27 |. 
zone will be a decimal fraction. In the common loga- [27 —28 |.007740/57 —58 .004690/87— 88 |. 
rithmie Tables, this is done by removing the decimal |28 —29 |.007670|58 —59 |.004560'88— 89 |.0002: 
point ten places towards the left hand, or the fraction '29 —30 |.007595|59 —60, .004430,89— 90 |.00007. 
may be found at once, thus: From the trigonometrical 
tables, take the sines of the latitudes, subtract ten from To find from the preceding Table the area of sehih, Ares 
the index of each, and find the numbers corres i : : 
ere 2 - responding Jess than 1° tak portional part of the 20m 
ot ie oe aa logarithms ; half the difference of zone of 1° of which ee ates ie: P i Thas to ™ 
th numbers will express the area of the zone, that of find the area of a zone bet 48°) 43° 35’, take 
e sphere itself being unity. Meet Cae pHa arg! 
; : from the T between 43° 
Example. It is required to find the area of the zone 44°, which iybedi: oy Go"? a? ? wre S- 
4 
Latitude. | Ares. Latitude. | Area] Lativude, | Arem 
