ages in its influence upon human progress, as well as the most widely distributed in the human family. This gave, also, the Turanian system of relationship.

8. Marriage between Single Pairs. Instances of marriage between single pairs may have, and probably did, occur in all periods of man's history; but they must have been exceptional, from the necessity of the case, in the primitive ages. After the tribal organization came into existence, and the cohabitation of brothers and sisters was broken up, as well as all intermarriage in the tribe, there must have been a very great curtailment of the license of barbarism. Women for wives became objects of negotiation out of the tribe, of barter, and of capture by force. The prevalence of these practices throughout Asia and America is well established. Wives thus gained by personal effort, and by purchase, would not be readily shared with others. In its general tendency it would lead to individual contracts to procure a single wife for a single husband, and thus tend directly to inaugurate marriage between single pairs. The immense influence of the tribal organization upon human progress toward the true family state cannot be overestimated.

9. The Barbarian Family. In the early ages this stage of the family could scarcely be distinguished from the communal.

10. Polygamy.-In its relation to pre-existing customs and institutions polygamy is essentially modern. It presupposes a very great advance of society from its primitive condition, with settled governments, with stability of such kinds of property as existed, and with enlargement of the amount, as well as permanence, of subsistence. It seems to spring out of antecedent customs, akin to the Hawaiian, by natural suggestion. If this be so, then polygamy must be regarded as having been a reformatory institution. Considered from this standpoint, instead of a retrograde movement, it was a powerful advance in the direction of the true family.

11. The Patriarchal Family. - Polygamy resulted in the establishment of the patriarchal family, or the family in its third stage. A family with a single male head was an immense advance upon the communal. It necessitated, to some extent, a privileged class in society, before one person would be able to support several sets of children by several different mothers. Polygamy in its higher forms belongs to the dawning ages of civilization.

12. Polyandria. - This custom requires no further notice.

13. Property. Considered as an Institution. It is impossible to overestimate the influence of property upon the civilization of mankind. It was the germ, and is still the evidence, of his progress from barbarism. The master passion of the civilized mind is for its acquisition and enjoyment. Governments, institutions, and laws, all resolve themselves into so many agencies designed for the creation and protection of property. But, above all, the desire of parents to transmit it to their children was the great turning-point between barbarism and civilization. When this desire, which arose with the development of property, was consummated by the introduction of lineal succession to estates, it revolutionized all the social ideas of barbarous society. Marriage between single pairs became the first condition to certainty of parentage; and thus, in course of time, became the rule, rather than the exception; the interests of property required individual ownership to stimulate personal exertion; and the protection of the state became necessary to render it stable. With the rise of property, considered as an institution, with the settlement of its rights, and, above all, with the established certainty of its transmission to lineal descendants, came the first possibility among mankind of the true family in its modern acceptation. All previous family states were but a feeble approximation.

14. The Family. As now constituted, the family is founded upon marriage between one man and one woman. A certain parentage was substituted for a doubtful one; and the family became organized and individualized by property rights and privileges. The establishment of lineal succession to property as an incident of descent overthrew, among civilized nations, every vestige of pre-existing customs and institutions inconsistent with this form of marriage. The persistency with which the classificatory system has followed down the families of mankind to the dawn of civilization furnishes evidence conclusive that property alone was capable of furnishing an.adequate motive for the overthrow of this system and the substitution of the descriptive. There are strong reasons for believing that the remote ancestors of the Aryan, Semitic, and Uralian families possessed the classificatory system, and broke it up when they reached the family state in its present sense.

Upon this family, as now constituted, modern civilized society is organized and reposes. The whole previous experience and progress of mankind culminated and crystallized in this one great institution.

It was of slow growth, planting its roots far back in the ages of barbarism, a final result, to which the experience of the ages had steadily tended. The family, which in this view of the case is essentially modern, is the offspring of this vast and varied experience of the ages of barbarism.

Since the family was reached, it has also had its stages of progress, and a number of them. The rise of family names, as distinguished from the single personal name common in barbarous nations, is comparatively modern in the Aryan family. The Roman GENS is one of the earliest illustrations. This people produced the triple formula to indicate the name of the individual, of the Gens or great family, and of the particular family within the Gens. Out of this arose, in due time, the doctrine of agnation, to distinguish the relationship of the males, who bore the family name, from that of the females of the same family. Agnatic relationship was made superior to cognatic, since the females were transferred, by marriage, to the families of their husbands. This overthrew the last vestige of tribalism, and gave to the family its complete individuality.

15. The Overthrow of the Classificatory System of Relationship and the Substitution of the Descriptive. Without attempting to discuss the fragments of evidence tending to show that the Aryan, Semitic, and Uralian families once possessed the classificatory system, it will be sufficient to remark, that, if such were the fact, the rights of property and the succession to estates would have insured its overthrow. These are the only conceivable agencies sufficiently potent to accomplish so great a change. Without such a change the family, as now constituted, would have remained impossible.

In conclusion I may remark, that the probable truth of this solution cannot be fully appreciated from the limited presentation of the facts contained in this article. At most it will but serve to invite attention to the great sequence of customs and institutions which seem to mark the successive stages of man's progress through the periods of barbarism, and to indicate the intimate relations which this remarkable system of consanguinity appears to sustain to the condition, experience, and advancement of mankind during the primitive ages. The manuscript containing the body of the evidence is now in course of publication by the Smithsonian Institution.

Five hundred and ninety-second Meeting.

March 10, 1868.

ADJOURNED STATUTE MEETING.

The PRESIDENT in the chair.

The President called the attention of the Academy to the recent decease of Sir David Brewster of the Foreign Honorary Members, and of Hon. Daniel Lord, of New York, of the As sociate Fellows.

Five hundred and ninety-third Meeting.

April 14, 1868. MONTHLY MEETING.

The PRESIDENT in the chair.

The President called the attention of the Academy to the recent decease of Dr. Samuel L. Dana, of the Resident Fellows, and of Professor William Smyth, of the Associate Fellows.

The following paper was presented :

-

Dispersion of a Ray of Light refracted at any number of Plane Surfaces.* By EDWARD C. PICKERING.

LET α a ag, &c., be the angles included between the surfaces, n, në ng their indices of refraction, i, i, i, the angles of incidence, r1 r r the angle of refraction; sin i = n1 sin r1 and in general

As the dispersion of any portion of the spectrum is always proportional to the angular divergence of two rays of nearly equal refrangibility, if we vary n1 ng, &c., drm will measure the dispersion. Differentiating (1)

cos im dimrm cos rm drm + sin rm dnm

* Since presenting this communication to the Academy, I have learned that a portion of this subject was studied by Sir David Brewster in 1812. I have, therefore, modified my paper, omitting what was not new, except when necessary to preserve the context.

if n1 ng ng are all functions of N, making the latter the independent variable and dividing by dN, we have

also the dispersion of a ray after passing m surfaces, or

and (3) becomes

drm

dN

Im = am lm-1 — bm

(4)

This formula by successive substitutions may be applied to any case. For a single surface

which equals unity when tang r1 = n1 or at the angle of total polarization. That is, the unit of dispersion is that produced by a single surface when the ray is in the position of total polarization. For two surfaces (4) becomes

a being the angle of the prism. For minimum deviation