3 a

a- h

aaa

for the value of a general segment, either greater or less than the semi-spheroid, whose height, taken upon the diameter passing through its vertex and centre of its base, is h= a + x.

When a coincides with f, the above expres3f-h sion becomes pr rhh × for the vaƒƒ lue of a segment whose base is perpendicular to the fixed axis. And here if we put R for the radius of the segment's base, and for rr its value RRff 2fh-hh' PRR hx

the said segment will become

3f-h. 2f-h

T

And when a coincides with r, the general ex3r- - h pression will become pfhh x for the value of the segment whose base is parallel to the fixed axis. And if we put F, R, for the two semi-axes of the elliptic base of this seg ment, respectively corresponding or parallel to f, r, the semi-axes of the generating ellipse, when parallel to the base of the segment, and for f F RR+hh, R

2 h

and r substitute their values and the said frustum will be expressed by p Fhx 3 RR+hh in which the dimensions of itself 2 R only are concerned.

Cor. 3.-A semi-spheroid is equal to of a cylinder, or to double a cone of the same base and height; or they are in proportion as the numbers 3, 2, 1. For the cylinder is 4n frr =nfrr, the semi-spheroid nfrr, and the conen frr.

Cor. 4.-When fr, the spheroid becomes a sphere, and the expression fnrr for the semi-spheroid becomes nr for the semi-sphere. And, in like manner, f and r being supposed equal to each other in the values of the frustums and segments of a spheroid, in the preceding corollaries, will give the values of the like parts of a sphere.

Cor. 5.-All spheres and spheroids are to each other as the fixed axes drawn into the squares of the revolving axes.

Cor. 6.-Any spheroids and spheres, of the same revolving axis, as also their like or corresponding parts cut off by planes perpendicular to the said common axis, are to one another as their other or fixed axes. This follows from the foregoing corollaries.

Cor. 7.-But if their fixed axes be equal, and their revolving axes unequal, the spheroids and spheres, with their like parts terminated by planes perpendicular to the common fixed axis, will be to each other as the squares of their revolving axes.

Cor. 8.-An oblate spheroid is, to an oblong spheroid generated from the same ellipse, as the longer axis of the ellipse is to the shorter. For if T be the transverse axis, and C the conjugate; the oblate spheroid will ben T C, and the oblong}n C2 T; and these quantities are in the ratio of T to C.

Cor. 9.-And if about the two axes of an ellipse be generated two spheres and two spheroids, the four solids will be continual 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 spheroid to the oblong spheroid, so is the oblong spheroid to the less sphere, and so is the transverse axis to the conjugate. For these four bodies will be as T3, T2 C, TC2, C3, where each term is to the consequent one as T to C.

To find the content of a universal spheroid, or a solid conceived to be generated by the revolution of a semi-ellipse about its diameter, whether that diameter be one of the axes of the ellipse or not. 1. Divide the square of the product of the axes of the ellipse by the axis of the solid, or the diameter about which the semiellipse is conceived to revolve; multiply the quotient by 5236, and the product will be the content required. That is, X 5236 = the content; T and C being the transverse and d conjugate axes of the ellipse, and d the axis of the solid.

T C

Or, 2. The continual product of 5236, the diameter about which the revolution is made, the square of its conjugate diameter, and the square of the sine of the angle made by those diameters, the radius being 1, will be the content. That is, de css x 5236 the content; c being the conjugate diameter to d, and s the sine of the angle made by the diameters. For the demonstration of this rule see Hutton, ubi infra. Hence, if d=T, the rule becomes p T C for the oblong spheroid: and, if d= C, it will be p C T for the oblate spheroid: and if T, C, and d, be all equal, the rule will be pd3 for the sphere. See Hutton's Mensuration.

Dr. Halley has shown, that in a sphere, Mercator's nautical meridian line is a scale of logarithmic tangents of the half complements of the latitudes. But, as the earth has been found to be a spheroid, this figure will make some alteration in the numbers resulting from Dr. Halley's theorem. Mr. Maclaurin has therefore given us a rule, by which the meridional parts to any spheroid may be found with the same exactness as in a sphere.

SPHERUS, a Greek philosopher, a disciple of Zeno of Cyprus, who flourished about A.A.C. 243. He came to Sparta in the reign of Agis III. and Cleomenes III., and opened a school for philosophy.-Plut. Diod.

SPHEX, ichneumon wasp, or savage, a genus of insects belonging to the order of hymenoptera. See ENTOMOLOGY. The mouth is armed with entire jaws, but contains no tongue; the mandibles are horny, crooked, dentated; the lip horny, the apex membranaceous. The palpi or feelers are four. The antennæ have from ten to sixteen joints. The wings of both sexes are extended without folds, and laid horizontally on the back. The sting is sharp, and concealed within the abdomen. There are ninety-seven species. The manner of living is different in the various species, and so is the general form of the body and their haunts; but though the

method of life be utterly different, yet the same manners appear innate and inherent in all. They agree in being the fiercest of all flies: they will attack insects much larger than themselves, and this whether they be defenceless or armed, as they are provided with a sting. The strength in all this savage kind is great; their jaws are hard and sharp, and in their sting lies a poison suddenly fatal to the creatures with whom they, engage. The savage seizes hardily on the animal he attacks, and gives a stroke of amazing force; after which he falls down as if himself were killed, but it is to rest from his fatigue, and enjoy his victory. He keeps a steady eye on the creature he has struck till it dies, which happens in a few minutes, and then drags it to the nest to feed the young. The number of other insects they destroy is scarcely to be conceived; the mouth of their cave is like that of a giant in the days of yore, strewed with the remains of prey. The eyes, the filament that serves as a brain, and a small part of the contents of the body, are all the savage eats, and he will kill fifty for a meal. Of this numerous genus only two are natives of Britain and Ireland, viz. 1. S. cribraria is black, with yellow ringlets on the abdomen; the antennæ are short, and turned backwards; the fore legs are broad, with an appendix like a shield. 2. S. viatica is black; the antennæ are short and thick; the first three segments of the abdomen red brown; the pedicle is short; the length half an inch.

SPHINCTER, in anatomy, a term applied to a kind of circular muscles, or muscles in form of rings, which serve to close and draw up several orifices of the body, and prevent the excretion of the contents. See ANATOMY.

SPHINX, n. s. Gr. opty. Defined below. The sphinx was a famous monster in Egypt, that remained by conjoined Nilus, having the face of a virgin, and the body of a lion.

Peacham on Drawing. SPHINX, OF SPHYNX, in the mythology, a monster which had the head and breasts of a woman, the body of a dog, the tail of a serpent, the wings of a bird, the paws of a lion, and a human voice. It sprang from the union of Orthos with the Chimera, or of Typhon with Echidna. The sphinx had been sent into the neighbourhood of Thebes by Juno, who wished to punish the family of Cadmus, which she persecuted with immortal hatred; and it laid this part of Boeotia under continual alarms, by proposing enigmas, and devouring the inhabitants if unable to explain them. In the midst of their consternation, the Thebans were told by the oracle that the sphinx would destroy herself as soon as one of the enigmas she proposed was explained. In this enigma she wished to know what animal walked on four legs in the morning, two at noon, and three in the evening. Upon this Creon king of Thebes promised his crown and his sister Jocasta, the widow of king Laius, in marriage to him who could deliver his country from the monster by a successful explanation of the enigma. It was at last explained by Edipus, who observed that man walked on his hands and feet in the morning of life, at the noon of life he walked erect, and in the evening of his days he supported his infir

mities upon a stick. See JOCASTA and OEDIPUS. The sphinx, upon this explanation, dashed her head against a rock, and expired. Among the Egyptians the sphinx was the symbol of religion, by reason of the obscurity of its mysteries; and on the same account the Romans placed a sphinx in the pronaos or porch of their temples. Sphinxes were used by the Egyptians to show the beginning of the water's rising in the Nile; with this view, as it had the head of a woman and body of a lion, it signified that the Nile began to swell in July and August, when the sun passes through the signs of Leo and Virgo. There are several of these still to be seen; one in particular, near the pyramids, much spoken of by the ancients, being of a prodigious size, and cut out of the rock; the head and neck appear only at present, the rest of the body being hid in the sand. This, according to Thevenot, is twenty-six feet high, and fifteen feet from the ear to the chin; but Pliny assures us, the head was no less that 102 feet in circumference, and sixty-two feet high from the belly, and that the body was 143 feet long, and was thought to be the sepulchre of king Amasis. See PYRAMIDS. The learned Mr. Bryant (in his Ancient Mythol. vol. iii. p. 532), observes that the sphinx seems to have been originally a vast rock of different strata; which, from a shapeless mass, the Egyptians fashioned into an object of beauty and veneration. The Egyptians used this figure in their buildings; from them the Greeks derived it, and afterwards improved it into an elegant ornament. It is also frequently used in modern architecture. The sphinx of the Egyptians is said in the Asiatic Researches, vol. ii. p. 334, to have been found in India. Colonel Pearce was told by Murari Pandit, a man of learning among the Hindoos, that the sphinx, there called singh, is to appear at the end of the world, and as soon as he is born will prey on an elephant he is therefore figured seizing an elephant in his claws; and the elephant is made small, to show that the singh, even a moment after his birth. will be very large in proportion to it. But in opposition to this account, given by Murari Pandit, the late Sir William Jones, the learned and illustrious president of the Asiatic Society, was assured by several Brahmins that the figure taken for a sphinx was a representation of a lion seizing a young elephant.

SPHINX, in entomology, hawk-moth; a genus of insects belonging to the order of lepidoptera. The antennæ are shaped somewhat like a prism, and are more slender at each end than at the middle. The tongue is generally thrust out: the two palpi are bent back, and the wings deflexed. The name sphinx is given to this genus on account of the singular attitudes of their caterpillars, who apply the hinder part of their body to a branch of a tree, holding the rest of it erect, like the fabulous sphinx. Most of them spin their cod under ground, making them up with small parcels of earth and grains of corn interwoven with threads. The sphinxes fly either early in the morning or after sunset in the evening. They fly heavily and sluggishly, often emitting a kind of sound. There are about 165 species already discovered, of which ten are found in Great Britain and Ireland: viz.

1. S. atropos, jessamine hawk-moth. The wings are entire; the trunk long, spiral. Above, first wings brown, clouded with gray and yellow, and a yellowish spot in the centre; second, yellow, with two waved transverse stripes. The abdomen is yellow, with seven black brown belts. The thorax marked like a Death's head, whence the name, from Atropos, the third and last of the Fatal Sisters, who cuts the thread of life. The length is two inches. Caterpillar very large, yellow, with six green and orange oblique belts, and a posterior horn.

2. S. convolvuli, unicorn, or bindweed hawkmoth. The antennæ are long and thick; the trunk very long and spiral. Above, body marked with black and red belts; wings entire, browngray, with black zig zag transverse lines. The breadth three inches. Caterpillar smooth, green, with a posterior horn.

3. S. elpenor, elephant moth. The wings are angular, entire. Above, first wings striped transversely with red and green: second, black at the base, and red outwards. The body red and green. Caterpillar smooth, brown and yellow, with a posterior horn, and a snout like a hog. It lives on vines, convolvulus, &c.

4. S. filipendulæ, burnet moth. The antennæ, legs, and body, are black. Second wings red, with a greenish border. First wings bluish-green, with six red spots, in pairs. Length eight lines. Caterpillar yellow, with black spots. It lives on

grass.

The an

5. S. ligustri, privet hawk-moth. tennæ are long, thick, and brown. Trunk long, spiral. First wings two inches long, narrow, entire, brown; second, short, red, with black bars. The abdomen is red, with black rings. Caterpillar smooth, yellow-green, with a posterior horn.

6. S. ocellata, eyed willow hawk-moth. There is no trunk; the wings are indented. Above, first wings dark and light brown, marbled; second, red, with a large yellow black eye. Beneath, a large red triangle from the base of the first wings. The breadth one inch and a half. Caterpillar smooth, green, with oblique white lines on the sides, and a posterior horn. The eggs are green; it lives on willows.

7. S. populi, poplar hawk-moth. The wings are scalloped, bluish-gray, and waved with dark lines. On the first wings a long white spot, and the base of the second red brown. Wings reversed. Length one inch. A long spiral trunk caterpillar, green, smooth, with oblique white spots, and a posterior horn. It lives on poplars and willows.

8. S. stellatarum, large bee-moth. The antennæ are thick, towards the ends brown. The trunk is spiral; the wings are short and entire; the body is thick, brown, and hairy. First wings are brown, waved; second, red brown. It resembles a large bee. Caterpillar smooth, with a posterior blue horn, tipt with red. It lives on gallium

9. S. tiliæ, lime hawk-moth. No trunk; the wings are scalloped; the antennæ are white on the upper side, yellow on the under. Above, first wings gray-brown, with two irregular large green spots; second wings orange. Beneath, greenish

gray. Caterpillar green, shagreened, with a posterior horn.

10. S. tipuliformis, small bee-moth. The thorax is yellow beneath; the wings are short, with black veins. The abdomen black, bearded, yellow at the extremity. Caterpillar on the lonicera.

SPHINX, in zoology. See SIMIA.

SPHORULITE, in mineralogy. Colors brown and gray. In imbedded roundish balls and grains. Glimmering. Fracture even, splintery. Opaque. Scratches quartz with difficulty. Brittle. Specific gravity 24 to 25. Nearly infusible. It occurs in pearlstone and pitchstone porphyries, in the vicinity of Glasshutte near Schemnitz; and in the pitchstone of Meissen.

SPHONDYLIUM, in anatomy, one of the vertebræ of the back.

SPHRAGIDIUM, a famous cave of Boeotia, in Mount Citheron.—Paus. ix. c. 3. SPI'AL, n. s. Fr. espial. A spy; scout; a watcher. Obsolete.

His ears be as spials, alarum to crie.

Tusser's Husbandry.

He privy spials placed in all his way, To weet what course he takes, and how he fares. Spenser. Their trust towards them hath rather been as to good spials and good whisperers, than good magistrates and officers.

For he by faithful spial was assured
That Egypt's king was forward on his way.

Bacon.

Fairfax.

SPICA, in botany. See BOTANY.
SPICE, n. s. & v. a.) Fr. espices; Italian
SPICER, n. s.
specei, of Lat. speci.
SPICERY.
SA vegetable produc-

tion, fragrant to the smell, and of pungent taste;
an aromatic substance used in sauces: to season
with spice: a spicer is a dealer in spice: spicery
is the commodity or depository of spices.
Dangerous rocks,
Which, touching but by gentle vessel's side,
Would scatter all the spices on the stream.

Shakspeare. Is not manhood, learning, gentleness, and virtue, the spice and salt that seasons a man?

Id. Troilus and Cressida.

His mother was a vot'ress of my order, And in the spiced Indian air by night Full often she hath gossip'd by my side.

Shakspeare.
Their camels were loaden with spicery, and balm,
and myrrh.
Raleigh's History of the World.
Names have been derived from occupations, as
Salter and Spicer.
Camden.

She in whose body
The western treasure, eastern spicery,
Europe and Africk, and the unknown rest,
Were easily found.

Donne.

These hymns may work on future wits, and so
May great-grandchildren of thy praises grow;
And so, though not revive, embalm and spice
The world, which else would putrify with vice. Id.
With a festivall

She'll first receive thee; but will spice thy bread
With flowrie poysons.

So in the wicked there's no vice,
Of which the saints have not a spice.

Chapman.

Hudibras.

What though some have a fraught Of cloves and nutmegs, and in cinnamon sail,

Herbert.

If thou hast wherewithal to spice a draught,

When griefs prevail?

Off at sea north-east winds blow

Sabæan odour, from the spicy shore

Of Araby the blest; with such delay

Well pleased they slack their course; and many a league,

Cheered with the grateful smell, old ocean smiles.

Milton. High sauces and rich spices are fetched from the Indies. Baker. It containeth singular relations, not without some spice or sprinkling of all learning.

Browne's Vulgar Errours. Garlick, the northern spice, is 'in mighty request among the Indians. Temple.

Dryden.

For them the Idumæan balm did sweat, And in hot Ceilon spicy forests grew. The spicery, the cellar and its furniture, are too well known to be here insisted upon. Addison on Italy.

The regimen in this disease ought to be of spicy and cephalick vegetables, to dispel the viscosity. Arbuthnot on Diet.

Under southern skies exalt their sails, Led by new stars, and borne by spicy gales! Pope. SPICK AND SPAN. Span-new is used by Chaucer, and is supposed to come from Saxon rpannan to stretch; Lat. expandere: whence span. There is also a Swedish sping span, meaning every bit. Span-new is therefore originally used of cloth new extended or dressed at the clothiers, and spick and span is newly extended on the spikes or tenters; it is, however, a low word. Quite new; now first used.

While the honour thou hast got Is spick and span new, piping hot, Strike her up bravely.

Butler.

They would have these reduced to nothing, and then others created spick and span new out of nothing.

I keep no antiquated stuff;

Burnet.

Swift.

But spick and span I have enough. SPICKNEL, OF SPIGNEL. See ATHAMANTA. SPICULA. See BOTANY. SPIDER, n. s. softened from spinder, or spinner, from spin. Junius, with his usual felicity, dreams that it comes from Gr. omilav, to extend; for the spider extends his web. Perhaps it comes from Dutch spieden, Dan. speyden, to spy, to lie upon the catch. Sax. don, dona, is a beetle, or properly an humble bee, or stingless bee. May not spider be spy dor, the insect that watches the dor? Johnson. Sax. rpin atteɲ.-Thomson. From spin, and atter, venom. The animal that spins

Skinner thinks this word

a web for flies.

The spider's touch how exquisitely fine! Feels at each thread, and lives along the line. Pope.

SPIDER, in entomology. See ARANEA and ENTOMOLOGY.

SPIDER, SHEPHERD. See PHALANGIUM. SPIDERWORT, GREAT SAVOY, a species o. HEMEROCALLIS.

SPIERINGS (H.), an eminent landscape painter, born at Antwerp, about 1633. His manner of designing was agreeable, his touch delicate, and his coloring natural.

SPIERS (Albert Van), an historical painter, born at Amsterdam in 1666. After studying in Italy he returned to his native city, where he acquired great fame. He died in 1718.

SPIGELIA, worm grass, in botany, a genus of plants belonging to the class of pentandria, and order of monogynia; natural order fortyseventh, stellata: COR. funnel-shaped: CAPS. didymous, bilocular, and polyspermous. There are two species; 1. S. anthelmia, has a herbaceous stem, and its highest leaves are fourfold. The effects of this medicine,' says Dr. Browne, are these :-It first procures sleep, almost as certainly, and in an equal degree, with opium: the eyes seem to be distended, and sparkle as it were before the eruption of the small-pox or measles, which may be easily observed after the sleep is over; the pulse grows regular and rises, the fever cools, the symptoms appear more favorable, and the worms are generally discharged by the use of the subsequent purgative (if not before) in great quantities, often above 100 at a time; but when a few only come away, which is seldom, and these alive, the same doses are again repeated, which seldom or never fail. I never saw this medicine fail when there was the least probability of success; nay, often prove successful when there was not the least reason to expect it. I have been, however, cautious in ordering it for children; for though I never knew it at all hurtful, its effect upon the eyes has often deterred me from ordering it to children, whose fibres are weak and relaxed, and in whom the fevers from this source are seldom so vehement as to hinder the administration of other medicines, likely as effectual in other cases of this nature. This plant is generally had in low dry lands, after they have been turned up some months, and after great rains; its taste is herbaceous, and somewhat clammy; its growth is soft and sudden; its stalk hollow, smooth, and roundish. Its herbaceous taste and sudden growth would alone make me think it capable of little or no action, had not hundreds of careful observations satisfied me to the contrary.'

2. S. Marilandica, perennial worm-grass, or Indian pink. The best description of this plant which we have seen is given by Dr. Woodville in his Medical Botany; a work which exhibits a complete systematic view of the medicinal effects of vegetables. Its stem is four cornered; all the leaves opposite Dr. Garden, in a letter to the late Dr. Hope, professor of botany in the university of Edinburgh, dated 1763, gives the following account of the virtues of this plant:- About forty years ago the anthelmintic virtues of the root of this plant were discovered by the Indians;

since which time it has been much used here by physicians, practitioners, and planters; yet its true dose is not generally ascertained. I have given it in hundreds of cases, and have been very attentive to its effects. I never found it do much service, except when it proved gently purgative. Its purgative quality naturally led me to give it in febrile diseases which seemed to arise from viscidity in the primæ viæ; and, in these cases, it succeeded to admiration, even when the sick did not void worms. I have of late, previous to the use of the Indian pink, given a vomit, when the circumstances of the case permitted it; and I have found this method to answer so well that I think a vomit should never be omitted. I have known half a drachm of this root purge as briskly as the same quantity of rhubarb; at other times I have known it, though given in large quantities, produce no effect upon the belly: in such cases it becomes necessary to add a grain or two of sweet mercury, or some grains of rhubarb; but the same happy effects did not follow its use in this way, as when it was purgative without addition. The addition, however, of the purgative renders its use safe, and removes all danger of convulsions of the eyes, although neither ol. rutæ sabinæ, nor any other nervous substance, is given along with it. It is, in general, safer to give it in large doses than in small; for from the latter more frequently the giddiness, dimness of the sight, and convulsions, &c., follow: whereas from large doses I have not known any other effect than its proving emetic or violently cathartic. To a child of two years of age, who had been taking ten grains of the root twice a-day, without having any other effect than making her dull and giddy, I prescribed twenty-two grains morning and evening, which purged her briskly and brought away five large worms. After some months an increased dose had the same good effect. I prefer the root to the other parts of the plant; of which, when properly dried, I gave from twelve to sixty or seventy grains in substance. In fusion it may be given to the quantity of two, three, or four drachms, twice a day. I have found that, by keeping, the plant loses its virtue in part; for forty grains of the root which has not been gathered about two months will operate as strongly as sixty which has been kept for fifteen months.' In Dr. Garden's subsequent letters, addressed to Dr. Hope, in 1764 and 1766, the efficacy of this root in worm cases is further confirmed; and he observes that the root keeps better than he at first thought (having lately used it several years old with great success). In what he calls continued or remitting low worm fevers, he found its efficacy promoted by the addition of rad. sepentar. virg.

SPIGELIUS (Adrian), an eminent anatomist, surgeon, and botanist, born at Brussels in 1578. He became professor of anatomy and surgery at Padua. The senate of Venice honored him with the order of St. Mark. He died 1625. His works on these branches of science were printed at Amsterdam, in 3 vols. folio, 1645.

SPIGNA, or SPIGNO, a town and castle, and ci-devant marquisate of Italy, in the late duchy of Montferrat; now annexed to France, and included in the department of Marengo; seated

Bacon.

Drawn up in ranks and files, the bearded spikes Guard it from birds, as with a stand of pikes. Denham.

Suffering not the yellow beards to rear, He tramples down the spikes, and intercepts the year. Dryden. them down fast. Lay long planks upon them, spiking or pinning Mortimer's Husbandry. Lay long planks upon them, pinned or spiked down to the pieces of oak on which they lie.

Moxon's Mechanical Exercises.

He wears on his head the corona radiata, another type of his divinity: the spikes that shoot out represent the rays of the sun. Addison.

A youth, leaping over the spiked pales, was suddenly frighted down, and in his falling he was catched by those spikes. The gleaners,

Spike after spike, their sparing harvest pick.

Wiseman.

Thomson The oil of spike is much used by our artificers in their varnishes, but it is generally adulterated

Hill's Materia Medica.

SPIKE, OIL OF, an essential oil distilled from lavender, and much used by the varnish makers and the painters in enamel.

SPIKE'NARD, n. s. Lat. spica nardi. A plant, and the oil or balsam produced from the plant.

A woman, having an alabaster box of ointment of spikenard, brake and poured it on his head. Mark xiv. 3.

He cast into the pile bundles of myrrh, and sheaves of spikenard, enriching it with every spicy shrub. Spectator.

It grows plentifully in Java. It has been known to the medical writers of all ages.

Hill's Materia Medica. SPIKENARD. See NARDUS. SPIKENARD, CELTIC, a species of valeriana. SPIKENARD, FALSE, a species of lavandula. SPIKENARD, INDIAN, or TRUE. See NARDUS. The Indian or True Spikenard was discovered in 1786, and announced in the Philosophical Transactions for 1790: yet Mr. Lee, in his Introduction to Botany, p. 330, published in 1794, says it is still 'unknown.'

SPIKENARD, PLOUGHMAN'S. See BACCHARIS. It is also the name of a species of Conyza.

SPIKENARD, WILD, a species of Asarum. SPIKE-ROLLER, in agriculture, a useful implement of the roller kind, introduced by Mr. Randall of York. It has been found of much advantage in bringing stiff cloddy lands into a