of the convention that for u =∞, the difference u is to be
understood to stand for u. This being so, a single valued function
of u,...u, without essential singularities for infinite or finite values
of the variables can be shown, by induction, to be, as in the case of
necessarily a rational function of the variables. A function
having no singularities for finite values of all the variables is as before
called an integral function; it is expressible by a power series
converging for all finite values of the variables; a single valued
function having for finite values of the variables no singularities
other than poles or polar points of indetermination is called a
meromorphic function; as for p=1 such a function can be expressed
as a quotient of two integral functions having no common zero
point other than the points of indetermination of the function;
but the proof of this theorem is difficult.
The single valued functions which occur, as explained above, in
the inversion of algebraic integrals of the first kind, for >1, are
meromorphic. They must also be periodic, unaffected that is when
the variables u1, ...up are simultaneously increased each by a
proper constant, these being the additive constants of indeterminate-
ness for the p integrals (R,(x,y)dx arising when (x,y) makes a closed
circuit, the same for each integral. The theory of such single valued
meromorphic periodic functions is simpler than that of meromorphic
functions of several variables in general, as it is sufficient to consider
only finite values of the variables; it is the natural extension of
the theory of doubly periodic functions previously discussed. It
can be shown to reduce, though the proof of this requires considerable
developments of which we cannot speak, to the theory of a single
integral function of u1, . . . up, called the Theta Function. This is
expressible as a series of positive and negative integral powers of
quantities exp (cu1), exp (c2u2), ... exp (Cpup). wherein c1,... cp are
proper constants; for p=1 this theta function is essentially the
same as that above given under a different form (see § 14, Doubly
Periodic Functions), the function (u). In the case of p1, all
meromorphic functions periodic with the same two periods have
been shown to be rational functions of two of them connected by a
single algebraic equation; in the same way all meromorphic functions
of p variables, periodic with the same sets of simultaneous periods,
2p sets in all, can be shown to be expressible rationally in terms of
+1 such periodic functions connected by a single algebraic equation.
Let x.... x, y denote p+1 such functions; then each of the partial
derivatives dx/ou, will equally be a meromorphic function of the
same periods, and so expressible rationally in terms of x1, ... Xp,Y;
thus there will exist p equations of the form

dx, R1du1+...+Ridup,

and hence p equations of the form

du1 = H1,dx1 + ... + H.pdxp. wherein H1, are rational functions of x,... x, y, these being connected by a fundamental algebraic (rational) equation, sayf(x,... Xpy) =0. This then is the generalized form of the corresponding equation for p=1.

algebraic constructs of any number of dimensions. The number of linearly independent surfaces of order n-4, possessing the requisite particularity in regard to the singular lines and points of the surface, is thus a number invariant by birational transformation, and the equality of these numbers for two surfaces is a necessary condition of their being capable of such transformation. The number of surfaces of order m having the assigned particularity in regard to the singular points and lines of the fundamental surface can be given by a formula for a surface of given singularity; but the value of this formula for m=n-4 is not in all cases equal to the actual number of surfaces of order n-4 with the assigned particularity, and for a cone (or ruled surface) is in fact negative, being the negative of the deficiency of the plane section of the cone. Nevertheless this number for m=n-4 is also found to be invariant for birational transformation. This number, now denoted by pa, is then a second invariant of birational transformation. The former number, of actual surfaces of order #-4 with the assigned particularity in regard to the singularities of the surface, is now denoted by P. The difference P-Pa, which is never negative, is a most important characteristic of a surface. When it is zero, as in the case of the general surface of order x, and in a vast number of other ordinary cases, the surface is called regular.

On a plane algebraical curve we may consider linear series of sets of points, obtained by the intersection with it of curves +1 + ...o, wherein A, A, . . . are variable coefficients; such a series consists of the sets of points where a rational function of given poles, belonging to the construct f(x,y) =o, has constant values. And we may consider series of sets of points determined by variable curves whose coefficients are algebraical functions, not necessarily rational functions, of parameters. Similarly on a surface we may consider linear systems of curves, obtained by the intersection with the given surface of variable surfaces +λ12+...=0, and may consider algebraic systems, of which the individual curve is given by variable surfaces whose coefficients are algebraical, not necessarily rational, functions of parameters. Of a linear series upon a plane curve there are two numbers manifestly invariant in birational transformation, the order, which is the number of points forming a set of the series, and the dimension, which is the number of parameters A2/A, entering linearly in the equation of the series. The series is complete when it is not contained in a series of the same order but of higher dimension. So for a linear system of curves upon a surface, we have three invariants for birational transformation; the order, being in the number of variable intersections of two curves of the system, the dimension, being the number of linear parameters λι/λ, λε/λ, . . . in the equation for the system, and the deficiency of the individual curves of the system. Upon any curve of the linear system the other curves of the system define a linear series, called the characteristic series; but even when the linear system is complete, that is, not contained in another linear system of the same order and higher dimension, it does not follow that the characteristic series is complete; it may be contained in a series whose dimension is greater by Pe-pa than its own dimension. When this is so it can be shown that the lincar system of curves is contained in an algebraic system whose dimension is greater by P.-pathan the The extra p-po-Pa variable para. dimension of the linear system. meters so entering may be regarded as the independent co-ordinates of an algebraic construct fly,x1,.. Xp)=0; this construct has the property that its co-ordinates are single valued meromorphic functions of variables, which are periodic, possessing 2p systems of periods; the p variables are expressible in the forms

u1 =ƒR1(x,y)dx1t.... +Rp(x,y)dx,,

wherein R,(x,y) denotes a rational function of x1, x, and y. The original surface has correspondingly p integrals of the form (Rdx+Sdy), wherein R, S are rational in x, y, z, which are every From this point of view, then, the number p, Po-Pa is, for a surface, analogous to the deficiency of a plane curve; another analogy arises in the comparison of the theorems: for a plane curve of zero deficiency there exists no algebraic series of sets of points which does not consist of sets belonging to a linear series; for a surface for which Pepa o there exists no algebraic system of curves not contained in a linear system.

§ 26. Multiply-Periodic Functions and the Theory of Surfaces.The theory of algebraic integrals fR(x,y)dx, wherein x,y are connected by a rational equation f(x,y) =o, has developed concurrently with the theory of algebraic curves; in particular the existence of the number p invariant by all birational transformations is one result of an extensive theory in which curves capable of birational correspondence are regarded as equivalent; this point of view has made possible a general theory of what might otherwise have remained a collection of isolated theorems. In recent years developments have been made which point to a similar unity of conception as possible for surfaces, or indeed for algebraic constructs of any number of dimensions. These develop-where finite; and it can be shown that it has no other such integrals. ments have been in two directions, at first followed independently. but now happily brought into the most intimate connexion. On the analytical side, E. Picard has considered the possibility of classifying integrals of the form f(Rds+Sdy), belonging to a surface f(x,y,z) =0, wherein R and S are rational functions of x, y, z, according as they are (1) everywhere finite, (2) have poles, which then lie along curves upon the surface, or (3) have logarithmic infinities, also then lying along curves, and has brought the theory to a high degree of perfection. On the geometrical side A. Clebsch and M Noether, and more recently the Italian school, have considered the geometrical characteristics of a surface which are unaltered by bi-co-ordinates of the points are rational functions of two parameters; rational transformation. It was first remarked that for surfaces of order there are associated surfaces of order n-4, having properties in relation thereto analogous to those of curves of order n-3 for a plane curve of order n, if such a surface f(x,y) =o have a double curve with triple points triple also for the surface, and (x,y,z) =o be a surface of order n-4 passing through the double curve, the double integral

dx dy

SSoddy

is everywhere finite; and, the most general everywhere finite integral of this form remains invariant in a birational transformation of the surface f. the theorem being capable of generalization to

of the points of the curve are rational functions of a single parameter, But whereas for a plane curve of deficiency zero, the co-ordinates it is not necessarily the case that for a surface having P-P=o the it is necessary that P.-P. o, but this is not sufficient. For surfaces, beside the p linearly independent surfaces of order n-4 having a definite particularity at the singularities of the surface, it is useful to consider surfaces of order k(n-4), also having each a definite particularity at the singularities, the number of these, not containing the original surface as component, which are linearly independent, is denoted by P. It can then be stated that a sufficient condition for a surface to be rational consists of the two conditions Pa=0, P=0. More generally it becomes a problem to classify surfaces according to the values of the various numbers which are invariant under birational transformation, and to determine for each the simplest form of surface to which it is birationally equivalent. Thus, for example, the hyperelliptic surface discussed by Humbert,

receiving the waters of the St Croix river and forming part of the boundary between New Brunswick and the state of Maine The Bay of Fundy is remarkable for the great rise and fall of the tide, which at the head of the bay has been known to reach 62 ft. In Passamaquoddy Bay the rise and fall is about 25 ft., which gradually increases toward the narrow upper reaches. At spring tides the water in the Bay of Fundy is 19 ft. higher than it is in Bay Verte, in Northumberland Strait, only 15 m. distant. Though the bay is deep, navigation is rendered dangerous by the violence and rapidity of the tide, and in summer by frequent fogs. At low tide, at such points as Moncton or Amherst, only an expanse of red mud can be seen, and the tide rushes in a bore or crest from 3 to 6 ft. in height. Large areas of fertile marshes are situated at the head of the bay, and the remains of a submerged forest show that the land has subsided in the latest geological period at least 40 ft. The bay receives the waters of the St Croix and St John rivers, and has numerous harbours, of which the chief are St Andrews (on Passamaquoddy Bay) and St John in New Brunswick, and Digby and Annapolis (on an inlet known as Annapolis Basin) in Nova Scotia. It was first explored by the Sieur de Monts (d. c. 1628) in 1604 and named by him La Baye Française.

FUNERAL RITES, the ceremonies associated with different methods of disposing of the dead. (See also BURIAL AND BURIAL ACTS; CEMETERY; and CREMATION.) In general we have little record, except in their tombs, of races which, in a past measured not merely by hundreds but by thousands of years, occupied the earth; and exploration of these often furnishes our only clue to the religions, opinions, customs, institutions and arts of long vanished societies. In the case of the great culture folks of antiquity, the Babylonians, Egyptians, Hindus, Persians, Greeks and Romans, we have, besides their monuments, the evidence of their literatures, and so can know nearly as much of their rites as we do of our own. The rites of modern savages not only help us to interpret prehistoric monuments, but explain peculiarities in our own rituals and in those of the culture folks of the past of which the significance was lost or buried under etiological myths. We must not then confine ourselves to the rites of a few leading races, neglecting their less fortunate brethren who have never achieved civilization. It is better to try to classify the rites of all races alike according as they embody certain leading conceptions of death, certain fears, hopes, beliefs entertained about the dead, about their future, and their relations with the living.

of which the co-ordinates are meromorphic functions of two variables of the simplest kind, with four sets of periods, is characterized by Po = 1, P2 = -1; or again, any surface possessing a linear system of curves of which the order exceeds twice the deficiency of the individual curves diminished by two, is reducible by birational transformation to a ruled surface or is a rational surface. But beyond the general statement that much progress has already been made in this direction, of great interest to the student of the theory of functions, nothing further can be added here. BIBLIOGRAPHY.-The learner will find a lucid introduction to the theory in E. Goursat, Cours d'analyse mathématique, t. ii. (Paris, 1905), or, with much greater detail, in A. R. Forsyth, Theory of Functions of a Complex Variable (2nd ed., Cambridge, 1900); for logical rigour in the more difficult theorems, he should consult W. F. Osgood, Lehrbuch der Functionentheorie, Bd. i. (Leipzig, 19061907); for greater precision in regard to the necessary quasigeometrical axioms, beside the indications attempted here, he should consult W. H. Young, The Theory of Sets of Points (Cambridge, 1906), chs. viii.-xiii., and C. Jordan, Cours d'analyse, t. i. (Paris, 1893), chs. i., ii.; a comprehensive account of the Theory of Functions of Real Variables is by E. W. Hobson (Cambridge, 1907). Of the theory regarded as based after Weierstrass upon the theory of power series, there is J. Harkness and F. Morley, Introduction to the Theory of Analytic Functions (London, 1898), an elementary treatise; for the theory of the convergence of series there is also T. J. I'A. Bromwich, An Introduction to the Theory of Infinite Series (London, 1908); but the student should consult the collected works of Weierstrass (Berlin, 1894 ff.), and the writings of Mittag-Leffler in the early volumes of the Acta mathematica; carlier expositions of the theory of functions on the basis of power series are in C. Méray, Leçons nouvelles sur l'analyse infinitésimale (Paris, 1894), and in Lagrange's books on the Theory of Functions. An account of the theory of potential in its applications to the present theory is found in most treatises; in particular consult E. Picard, Traité d'analyse, t. ii. (Paris, 1893). For elliptic functions there is an introductory book, P. Appell and E. Lacour, Principes de la théorie des fonctions elliptiques et applications (Paris, 1897), beside the treatises of G. H. Halphen, Trailé des fonctions elliptiques et de leurs applications (three parts, Paris, 1886 ff.), and J. Tannery et J. Molk, Eléments de la théorie des fonctions elliptiques (Paris, 1893 ff.); a book, A. G. Greenhill, The Applications of Elliptic Functions (London, 1892), shows how the functions enter in problems of many kinds. For modular functions there is an extensive treatise, F. Klein and R. Fricke, Theorie der elliptischen Modulfunctionen (Leipzig, 1890); see also the most interesting smaller volume, F. Klein, Uber das Ikosaeder (Leipzig, 1884) (also obtainable in English). For the theory of Riemann's surface, and algebraic integrals, an interesting introduction is P. Appeil and E. Coursat, Théorie des fonctions algébriques et de leurs intégrales; for Abelian functions see also H. Stahl, Theorie der Abel'schen Functionen (Leipzig, 1896), and H. F. Baker, An Introduction to the Theory of Multiply Periodic Functions (Cambridge, 1907), and H. F. Baker, Abel's Theorem and the Allied Theory, in cluding the Theory of the Theta Functions (Cambridge, 1897): for theta functions of one variable a standard work is C. G. Jacobi, Fundamenta nova, &c. (Konigsberg, 1828); for the general theory of theta functions, consult W. Wirtinger, Untersuchungen uber ThetaFunctionen (Leipzig, 1895). For a history of the theory of algebraic functions consult A. Brill and M. Noether, Die Entwicklung der Theorie der algebraischen Functionen in allerer und neuerer Zeit, Bericht der deutschen Mathematiker-Vereinigung (1894); and for a special theory of algebraic functions, K. Hensel and G. Landsberg, Theorie der algebräischen Function u.s.w. (Leipzig, 1902). The student will, of course, consult also Riemann's and Weierstrass's Ges. Werke. For the applications to geometry in general an important contribution, of permanent value, is E. Picard and G. Simart, Théorie des fonctions_algébriques de deux variables indépendantes (Paris, 1897-1906). This work contains, as Note v. t. ii. p. 485, a valuable summary by MM. Castelnuovo and Enriques, Sur quelques 1. A dead body is unclean, and the uncleanness extends résultats nouveaux dans la théorie des surfaces algébriques, containing many references to the numerous memoirs to be found, for the most to things and persons which touch it. Hence the Jewish law in the transactions of scientific societies and the mathematical (Num. v. 2) enacted that whoever is unclean by the dead part. journals of Italy. shall be put outside the camp, that they defile not the camp Beside the books above enumerated there exists an unlimited in the midst whereof the Lord dwells." Such persons were number of individual memoirs, often of permanent importance unclean until the even, and might not eat of the holy things and only imperfectly, or too elaborately, reproduced in the pages of the volumes in which the student will find references to them. unless they bathed their flesh in water. A high priest might on The German Encyclopaedia of Mathematics, and the Royal Society's no account "go in to any dead body" (Lev. xxi. 11). Why Reference Catalogue of Current Scientific Literature, Pure Mathematics, a corpse is so widely tabooed is not certain; but it is natural to published yearly, should also be consulted. (H. F. BA.) see one reason in the corruption which in warm climates soon FUNDY, BAY OF, an inlet of the North Atlantic, separating sets in. The common experience that where one has died New Brunswick from Nova Scotia. It is 145 m. long and 48 m. another is likely to do so may also have contributed, though, of wide at the mouth, but gradually narrows towards the head, course, there was no scientific idea of infection. The old Persian where it divides into Chignecto Bay to the north, which sub-scriptures are full of this taboo. He who has touched a corpse is divides into Shepody Bay and Cumberland Basin (the French powerless in mind, tongue and hand" (Zend Avesta in Sacred Beaubassin), and Minas Channel, leading into Minas Basin, to Books of the East, pt. i. p. 120), and the paralysis is inflicted by the east and south. Off its western shore opens Passamaquoddy the innumerable drugs or evil spirits which invest a corpse, 3ay, a magnificent sheet of deep water with good anchorage, | Fire and earth, being alike creations of the good and pure god

The main ideas, then, underlying funeral rites may roughly be enumerated as follows:

1. The pollution or taboo attaching to a corpse.
2. Mourning.

3. The continued life of the dead as evinced in the housing and equipment of the dead, in the furnishing of food for them, and in the orientation and posture assigned to the body.

4. Communion with the dead in a funeraf feast and otherwise.
5. Sacrifice for the dead and expiation of their sins.
6. Death witchery.

7. Protection of the dead from ghouls.
8. Fear of ghosts.

330

or

Ahuramazda, a body must not be burned or buried; and so the
ancient Persians and their descendants the Parsees build Dakmas
"towers of silence" on hill-tops far from human habitations.
Inside these the corpses are laid on a flagged terrace which
drains into a central pit. Twice a year the bones, picked clean
by dogs and birds of prey, are collected in the pit, and when it
is full another tower is built. In ancient times perhaps the
bodies of the magi or priests alone were exposed at such expense;
the common folk were covered with wax and laid in the earth,
the wax saving the earth from pollution. In Rome and Greece
the corpse was buried by night, lest it should pollute the sunlight;
and a trough of water was set at the door of the house of death
that men might purify themselves when they came out, before
mixing in general society. Priests and magistrates in Rome
might not meet or look on a corpse, for they were thereby
rendered unclean and incapable of fulfilling their official duties
without undergoing troublesome rites of purification. At a
Roman funeral, when the remains had been laid in the tomb,
all present were sprinkled with lustral water from a branch of
olive or laurel called aspergillum; and when they had gone
home they were asperged afresh and stepped over a fire. The
house was also swept out with a broom, probably lest the ghost
of the dead should be lying about the floor. Many races, to
avoid pollution, destroy the house and property of the deceased.
Thus the Navahos pull down the hut in which he died, leaving its
ruins on the ground; but if it be an expensive hut, a shanty
is extemporized alongside, into which the dying man is trans-
ferred before death. No one will use the timbers of a hut so
ruined. A burial custom of the Solomon Islands, noted by
R. H. Codrington (The Melanesians, p. 255), may be dictated
by the same scruple. There" the mourners having hung up a
dead man's arms on his house make great lamentations; all
remains afterwards untouched, the house goes to ruin, mantled,
as time goes on, with the vines of the growing yams, a picturesque
and indeed, perhaps, a touching sight; for these things are not
set up that they may in a ghostly manner accompany their
former owner." H. Oldenberg (Religion des Veda, p. 426) describes
how Hindus shave themselves and cut off their nails after a
death, at the same time that they wash, renew the hearth fire,
and furnish themselves with new vessels. For the hair and
nails may harbour pollution, just as the medieval Greeks believed
that evil spirits could lurk in a man's beard (Leo Allatius, De
opinionibus quorundam Graecorum). The dead man's body
is shorn and the nails cut for a kindred reason; for it must be
purified as much as can be before it is burned as an offering on
the pyre and before he enters on a new sphere of existence.

and he would then sit or kneel down, and, with his hands carefully
held behind his back, would gnaw at it as best he could." Often
a degraded outcast was kept in a village to feed mourners. Such
a taboo is strictly similar to those which surround a sacred chief
or his property, a menstruous woman or a homicide, rendering
them dangerous to themselves and to all who approach them.
3. Primitive folk cannot conceive of a man's soul surviving
apart from his body, nor of another life as differing from this,
and the dead must continue to enjoy what they had here.
Accordingly the Patagonians kill horses at the grave that the
dead may ride to Alhucmapu; or country of the dead. After a
year they collect a chief's bones, arrange them, tie them together
and dress them in his best garments with beads and feathers.
Then they lay him with his weapons in a square pit, round
which dead horses are placed set upright on their feet by stakes.
As late as 1781 in Poland F. Casimir's horse was slain and buried
with him. In the Caucasus a Christian lady's jewels are buried
with her. The Hindus used to burn a man's widow on his pyre,
because he could not do without her; and St Boniface commends
the self-sacrifice of the Wend widows who in his day burned
themselves alive on their husbands' pyres.

The tumuli met with all over the north of Europe (in the
Orkneys alone 2000 remain) are regular houses of the dead,
models of those they occupied in life. The greater the dignity
of the deceased, the loftier was his barrow. Silbury hill is
170 ft. high; the tomb of Alyattes, father of Crocsus, was a
fourth of a league round; the Pyramids are still the largest
buildings in existence; at Oberea in Tahiti is a barrow 267 ft.
long, 87 wide and 44 high. Some Eskimo just leave a dead
man's body in his house, and shut it up, often leaving by his
side a dog's head to guide him on his last journey, along with
was laid
his tools and kayak. The Sea Dyaks set a chief adrift in his war
canoe with his weapons. So in Norse story Hake
wounded on a ship with the dead men and arms; the ship was
taken out to sea and set on fire." The Viking was regularly
buried in his ship or boat under a great mound. He sailed
after death to Valhalla. In the ship was laid a stone as anchor
and the tools, clothes, weapons and treasures of the dead. The
Egyptians, whose land was the gift of the river Nile, equally
believed that the dead crossed over water, and fashioned the
hearse in the form of a boat. Hence perhaps was derived the
Greek myth of Charon and the Styx, and the custom, which still
survives in parts of Europe, of placing a coin in the mouth of the
dead with which to pay the ferryman. The Egyptians placed
in the tomb books of a kind to guide the dead to the next world.
The Copts in a later age did the same, and to this custom we owe
the recovery in Egypt of much ancient literature. The Armenians
till lately buried with a priest his missal or gospel.

2. We are accustomed to regard mourning costume as primarily an outward sign of our grief. Originally, however, the special In Egyptian entombments of the XIIth to the XIVth dynasties garb seems to have been intended to warn the general public were added above the sepulchres what Professor Petrie terms soul. that persons so attired were unclean. In ancient Rome mourners stayed at home and avoided all feasts and amusements; laying houses, viz, small models of houses furnished with couch and aside gold, purple and jewels, they wore black dresses called table, &c., for the use of the ka or double whenever it might wish to come above ground and partake of meats and drinks. They lugubria or even skins. They cut neither hair nor beard, nor lighted fire. Under the emperors women began to wear white. recall, in point of size, the hut-urns of the Etruscans, but the On the west coast of Africa negroes wear white, on the Gold latter had another use, for they contain incinerated remains. Etruscan tombs, like those of Egypt and Asia Minor, were made Coast red. The Chinese wear hemp, which is cheap, for mourning to resemble the dwelling-houses of the living, and furnished with dress must as a rule be destroyed when the season of grief is past to get rid of the taboo. Among the Aruntas of Australia coffered ceilings, panelled walls, couches, stools, easy chairs with p. lxx.). the wives of a dead man smear themselves with white pipe-clay footstools attached, all hewn out of the living rock (Dennis, until the last ceremonies are finished, sometimes adding ashes-Cities and Cemeteries of Etruria,.vol this not to conceal themselves from the ghost (which may partly be the aim of some mourning costumes), but to show the ghost that they are duly sorrowing for their loss. These widows must "Among the not talk except on their hands for a whole year. Maoris," says Frazer (Golden Bough, i. 323), “anyone who had handled a corpse, helped to convey it to the grave, or touched a dead man's bones, was cut off from all intercourse and almost all communication with mankind. He could not enter any house, or come into contact with any person or thing, without utterly bedevilling them. He might not even touch food with his hands, which had become so frightfully tabooed or unclean as to be quite useless. Food would be set for him on the ground,

Of the old Peruvian mummies in the Kircherian Museum at Rome, several are of women with babies in their arms, whence it is evident that a mother had her suckling buried with her; it would console her in the next world and could hardly survive her in this. The practice of burying ornaments, tools and weapons with the dead characterizes the inhumations of the Quaternary epoch, as if in that dim and remote age death was already regarded as the portal of another life closely resembling this. The cups, tools, weapons, ornaments and other articles deposited with the dead are often carefully broken or turned upside down and inside out; for the soul or manes of objects liberated by such fracture or inversion and so passes into the

dead man's use and possession. For the same reason where the dead are burned, their properties are committed to the flames. The ghost of the warrior has a ghostly sword and buckler to fight with and a ghostly cup to drink from, and he is also nourished by the impalpable odour and reek of the animal victims sacrificed over his grave. Instead of valuable objects cheap images and models are often substituted; and why not, if the mere ghosts of the things are all that the wraith can enjoy? Thus Marco Polo (ii. 76) describes how in the land of Kinsay (Hang-chau) "the friends and relations make a great mourning for the deceased, and clothe themselves in hempen garments, and follow the corpse, playing on a variety of instruments and singing hymns to their idols. And when they come to the burning place they take representations of things cut out of parchment, such as caparisoned horses, male and female slaves, camels, armour, suits of cloth of gold (and money), in great quantities, and these things they put on the fire along with the corpse so that they are all burned with it. And they tell you that the dead man shall have all these slaves and animals of which the effigies are burned, alive in flesh and blood, and the money in gold, at his disposal in the next world; and that the instruments which they have caused to be played at his funeral, and the idol hymns that have been chaunted shall also be produced again to welcome him in the next world." The manufacture of such paper simulacra for consumption at funerals is still an important industry in Chinese cities. The ancient Egyptians, assured that a man's ka or double shall revivify his body, took pains to guard the flesh from corruption, steeping the corpse in natron and stuffing it with spices. A body so prepared is called a mummy (q.v.), and the custom was already of a hoary antiquity in 3200 B.C., when the oldest dated mummy we have was made. The bowels, removed in the process, were placed in jars over the corpse in the tomb, together with writing tablets, books, musical instruments, &c., of the dead. Cemeteries also remain full of mummies of crocodiles, cats, fish, cows and other sacred animals. The Greeks settled in Egypt learned to mummify their dead, but the custom was abhorrent to the Jews, although the Christian belief in the resurrection of the flesh must have been formed to a large extent under Egyptian influence. Half the superiority of the Jewish to other ancient religions lay in this, that it prescribed no funeral rites other than the simplest inhumation.

The dead all over the world and from remote antiquity have been laid not anyhow in the earth, but with the feet and face towards the region in which their future will be spent; the Samoans and Fijians towards the far west whither their souls have preceded them; the Guarayos with head turned eastwards because their god Tamoi has in that quarter" his happy hunting grounds where the dead will meet again" (Tylor, Prim. Cult. ii. 422). The legend is that Christ was buried with His head to the west, and the church follows the custom, more ancient than itself, of laying the dead looking to the East, because that is the attitude of prayer, and because at the last trump they will hurry eastwards. So in Eusebius (Hist. Eccl. 430. 19) a martyr explains to his pagan judge that the heavenly Jerusalem, the fatherland of the pious, lay exactly in the east at the rising place of the sun. Where the body is laid out straight it is difficult to discern the presence of any other idea than that it is at rest. In Scandinavian barrows, e.g. in the one opened at Goldhavn in 1830, the skeletons have been found seated on a low stone bench round the wall of the grave chamber facing its opening, which always looks south or east, never north. Here the dead were continuing the drinking bouts they enjoyed on earth.

The Peruvians mummified their dead and placed them jointed and huddled up with knees to chin, looking toward the sunset, with the hands held before the face. In the oldest prehistoric tombs along the Nile the bodies are doubled up in the same position. It would seem as if in these and numerous other similar cases the dead were deliberately given in their graves the attitude of a foetus in the womb, and, as Dr Budge remarks (Egyptian Ideas of the Future Life, London, 1899, p. 162), may perhaps be justified in seeing in this custom the symbol of a hope that, as the child is born from this position into the

we

world, so might the deceased be born into the life beyond the
grave." The late Quaternary skeletons of the Mentone cave
were laid in a layer of ferrugineous earth specially laid down for
them, and have contracted a red colour therefrom. Many other
prehistoric skeletons found in Italy have a reddish colour, perhaps
for the same reason, or because, as often to-day, the bones were
stripped of flesh and painted. Ambrose relates that the skeletons
of the martyrs Gervasius and Protasius, which he found and
deposited A.D. 386 under the altar of his new basilica in Milan,
were mirae magnitudinis ut prisca aclas ferebat, and were also
coloured red. He imagined the red to be the remains of the
martyrs' blood! Hic sanguis clamat coloris indicio. Salomon
Reinach has rightly divined that what Ambrose really hit upon
was a prehistoric tomb. Red earth was probably chosen as a
medium in which to lay a corpse because demons flee from red.
Sacred trees and stones are painted red, and for the most solemn
a favourite taboo colour.
of their rites savages bedaub themselves with red clay. It is

4. A feast is an essential feature of every primitive funeral,
it still survives. A dead man's soul
and in the Irish "wake
or double has to be fed at the tomb itself, perhaps to keep it
from prowling about the homes of the survivors in search of
victuals; and such food must also be supplied to the dead at
stated intervals for months or years. Many races leave a
narrow passage or tube open down to the cavity in which the
corpse lies, and through it pour down drinks for the dead.
Traces of such tubes are visible in the prehistoric tombs of the
British Isles. However, such provision of food is not properly
a funeral feast unless the survivors participate. In the Eastern
"Ye appease the shades
churches and in Russia the departed are thus fed on the ninth,
twelfth and fortieth days from death.
of the dead with wine and meals," was the charge levelled at
the Catholics by the 4th-century Manichaeans, and it has hardly
ceased to be true even now after the lapse of sixteen centuries.
The funeral feast proper, however, is either a meal of communion
with or in the dead, which accompanies interment, or a banquet
off the flesh of victims slain in atonement of the dead man's
sins. Some anthropologists see in the common meal held at the
grave" the pledge and witness of the unity of the kin, the chief
means, if not of making, at least of repairing and renewing it."
The flesh provided at these banquets is occasionally that of the
dead man himself; Herodotus and Strabo in antiquity relate
this of several half-civilized races in the East and West, and a
similar story is told by Marco Polo of certain Tatars. Nor
among modern savages are funeral feasts off the flesh of the dead
unknown, and they seem to be intended to effect and renew a
sacramental union or kinship of the living with the dead. The
Uaupes in the Amazons incinerate a corpse a month after death,
pound up the ashes, and mix them with their fermented drink.
They believe that the virtues of the dead will thus be passed on
to his survivors. The life of the tribe is kept inside the tribe
and not lost. Such cannibal sacraments, however, are rare, and,
except in a very few cases, the evidence for them weak. The
slaying and eating of animal victims, however, at the tomb is uni-
versal and bears several meanings, separately or all at once.
animals may be slain in order that their ghosts may accompany
the deceased in his new life. This significance we have already
dwelt upon. Or it is believed that the shade feeds upon them,
as the shades came up from Hades and lapped up out of a trench
the blood of the animals slain by Ulysses. The survivors by
eating the flesh of a victim, whose blood and soul the dead thus
consume, sacramentally confirm the mystic tie of blood kinship
with the dead. Or lastly, the victim may be offered for the sins
Such expiatory sacrifices of animals
of the dead. His sins are even supposed to be transferred into
it and eaten by the priest
for the dead survive in the Christian churches of Armenia, Syria
and of the East generally. Their vicarious character is emphasized
in the prayers which accompany them, but the popular under-
standing of them probably combines all the meanings above
enumerated. It has been suggested by Robertson Smith
E. S. Hartland, Legend of Perseus (1895), ii. 278.
(Religion of the Semites, 336) that the world-wide customs of

The