S P H 
S P H 
692 
plane, the section will be a circle; and a 
great circle when the section passer, through 
the centre, otherwise it is a little circle. Hence 
all great circles are equal to each other : and 
the line of section of two great circles of the 
sphere, is a diameter of the sphere : and there- 
fore two great ciicles intersect each other in 
points diametrically opposite ; and make 
equal angles at those points ; and divide each 
other into two equal parts; also any great 
circle divides the whole sphere into two espial 
parts. 
2. If a great circle is perpendicular to any 
other circle, it passes through its poles. And 
if a great circle passes through the pole of any 
other circle, it cuts it at right angles, and 
into two equal parts. 
3. The distance between the poles of two 
circles is equal to the angle of their inclina- 
tion. 
4. Two great circles passing through the 
poles of another great circle, cut all the pa- 
rallels to this latter into similar arcs. Hence, 
an angle made by two great circles of the 
sphere, is equal to the angle of inclination of 
the planes of these great circles. And hence 
also the lengths of those parallels are to one 
another as the sines of their distances from 
their common pole, or as the cosines or their 
distances from their parallel great circle. 
Consequently, as radius is to the cosine of the 
latitude of any point oh the globe, so is the 
length of a degree at the equator, to the 
length of a degree in that latitude. 
3. If a great circle passes through the poles 
of another, this latter also passes through the 
poles of the former ; and the two cut each 
other perpendicularly. 
6. If two or more great circles intersect 
each other in the poles of another great cir- 
cle ; this latter will pass through the poles of 
all the former. 
7. All circles of the sphere that are equally 
distant from the centre, are equal ; and the 
farther they are distant from the centre, the 
less they are. 
8. The shortest distance on the surface of 
a sphere, between any two points on that 
surface, is the arc of a great circle passing 
through those points. And the smaller the 
circle is that passes through the same points, 
the longer is the arc of distance between 
them. Hence the proper measure, or dis- 
tance, of two places on the surface of the 
globe, is an arc of a great circle intercepted 
between the same. See Theodosius, and 
other writers on spherics. 
SPHEROID, a solid body approaching to 
the figure of a sphere, though not exactly 
round, but having one of its diameters longer 
than the other. 
This solkl is usuallyconsidered as generated 
bv the rotation of aii oval plane figure about 
one of its axes. If that is the longer or 
transverse axis, the solid so generated is called 
an oblong spheroid, and sometimes prolate, 
which resembles an egg, or a lemon ; but if 
the oval revolves about its shorter axis, the 
solid will be an oblate spheroid, which re- 
sembles an orange, and in this shape also is 
the figure of the earth, and of the other planets. 
The axis about which the oval revolves, is 
called the fixed axis, and the other is the re- 
volving axis, whichever of them happens to 
he the longer. 
S P H 
When the revolving oval is a perfect el- 
lipse, the solid generated by the revolution is 
properly called an elhpsoid ; as distinguished 
from the spheroid, which is generated from the 
revolution of any oval whatever, whether it is 
an ellipse or not. But generally speaking, 
in common acceptation, the term spheroid is 
used for an ellipsoid; and therefore, in what 
follows, they are considered as one and the 
same thing. 
Any section of a spheroid by a plane, is an 
ellipse (except the sections perpendicular to 
the fixed axis, which are circles) ; and all pa- 
rallel sections are similar ellipses, or having 
their transverse and conjugate axes in the 
same constant ratio ; and the sections parallel 
to the fixed axis are similar to the ellipse from 
which the solid was generated. 
For the surface of the spheroid, whether It is ob- 
long or oblate: 
Let f denote the fixed axis, 
r the revolving axis, 
a = .7854, and q = ^ — j then will 
the surface s be expressed by the following se- 
ries, using the upper signs for the oblong sphe- 
roid, and the under signs for the oblate one ; viz. 
, = 4*r/X(l 
&cc . ; where the signs of the terms, after the first, 
are all negative for the oblong spheroid, but al- 
ternately positive and negative for the oblate 
one. 
H once, because the actor 4 arf is equal to 
4 times the area of the generating ellipse, it 
appears that the surface of the oblong sphe- 
roid is less than 4 times the generating ellipse : 
but the surface of the oblate spheroid is greater 
than 4 times the same; while the suriace of 
the sphere falls in between the two, being just 
equal to 4 times its generating circle. 
Huygens has given two elegant construc- 
tions for describing a circle equal to the super- 
ficies of an oblong and an ovate spheroid, 
which he says he found out towards the latter 
end of the year 1657. 
Of the solidity of a spheroid. Every 
spheroid, whether oblong or oblate, is, like a 
sphere, exactly equal to two-thirds of its cir- 
cumscribing cylinder. So that, if/denotes 
the fixed axis, r the revolving axis, and a — 
7854 ; then j afr 2 denotes the solid content of 
either spheroid. Or, which comes to the 
same thing, if t denotes the transverse, and c 
the conjugate axis of the generating ellipse ; 
then iacH is the content of the oblong sphe- 
roid, 
and | acH is the content of the oblate sphe- 
roid. 
Consequently, the proportiyn of the former 
solid to the latter, is as c to t, or as the less 
axis to the greater. 
Farther, if about the two axes of an ellipse 
are generated two spheres and two spheroids, 
the four solids will be continued proportionals, 
and the common ratio will be that of the two 
axes of the ellipse; that is, as the greater 
sphere, or the sphere upon the greater axis, is 
to the oblate spheroid, so is the oblate sphe- 
roid to the oblong spheroid, and so is the ob- 
long spheroid to the less sphere, and so is the 
transverse axis to the conjugate. 
Spheroid, universal, a name given to 
the solid generated by the rotation of an 
ellipse about some other diameter, which is 
neither the transverse nor conjugate axis. 
SPHEX, a genus of insects of the order | 
hymenoptcra. The generic character is, 
mouth with jaws, without tongue ;• antennas 
of ten joints; wings fiat-incumbent (not j 
pleated) in each sex; sting concealed. As 
the insects of the genus ichneumon deposit J 
their eggs in the bodies of other living insects, J 
so those of the genus sphex deposit theirs in j 
dead ones, in order that the young larva*, 
when hatched, may find' their proper food, j 
I . Thus the sphex figulus ot Linnaeus, having- 
found some convenient cavity for the pur- 
pose, seizes on a spider, and having killed it, 
deposits it at the bottom : then lax ing her egg 
in it, she closes up the orifice of the cavity 
with clay : the larva, which resembles the 
maggot of a bee, having devoured the spider, 
spins itself up in a dusky silken web, and 
changes into a chrysalis, out of which, within 
a certain number of days, proceeds the com- 
plete insect, which is of a black colour, with 
a slightly foot-stalked abdomen, the edges of 
the several segments being of a brighter ap- ; 
pearance than the rest of the body. It should 
be added, that the female of this species pre- 
pares several separate holes or nesis as above 
mentioned, in each of which she places a dead 
insect and an egg : each cell costing her the 
labour of about two days. 
2. The sphex viatica of Linnaeus, which is 
of a black colour and slightly hairy, with, 
brown wings, and the fore part of the abdo- 
men ferruginous with black bands, seizes ca- 
terpillars in a similar manner, burying one in 
every cell, in which she deposits an egg, and 
then closes up the cell. 
3. Sphex sabulosa Lin. is a black and hairy 
species, with the second and third joints of th'e 
' abdomen ferruginous. It inhabits sandy aiul 
gravelly places, in which the female" digs- 
holes with her fore-feet, working in the man- 
ner of a dog, in order to form the cavity, in 
which she places either a spider or a caterpil- 
lar; after which she closes up the cavity, hav- 
ing first laid her egg in the dead insect. 
Linnaeus, in his description of this insect, con- 
tradicts the generic character, since lie ob- 
serves that it has a retractile snout containing ) 
the tongue. 
Many of the extra-European spheges are 
insects of a very considerable size. The 
whole genus is very much allied to those of 
vespa and apis. There are 38 species. Seb’ 
Plate Nat. Hist. fig. 36y. 
SPHINCTER. See Anatomy. 
SPHINX, the hawk moth, a genus of insects 
of the order lepidoptera. The generic cha- 
racter is, antenna; thickest in the middle, sub- 
prismatic, and attenuated at each extrem ity ; 
wings deflected; flight strong, and commonly 
in the evening or morning. The insects 
of this genus have in general a large thorax 
and thick body, commonly tapering towards 
the extremity. The name sphinx is applied 
to the genus on account of the posture as- 
sumed by tiie larvae of several of the larger 
species, which are often seen in an attitude 
much resembling that of the Egyptian sphinx, 
viz. with the tore parts elevated, and the rest 
of the body applied flat to the surface. 
1. One of the most elegant insects of this 
genus is the sphinx ligustri, or privet hawk- 
moth. It is a large insect, measuring nearly 
four inches and a half from wing’s end to wing’s 
end; the upper wings of a brown colour, most 
elegantly varied or shaded with deeper and 
lighter streaks and patches ; the under wings 
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