Long after the appearance of these long-heads arrived several varieties of broad-heads, among them Mongoloid, Ugro-Finnish, and Turanian types. Dr. Krause arrives at the following résumé, that the Cannstadt skull represents the Germanic or better the Aryan type. "This race lived in Middle Europe in the oldest times to which prehistoric investigation descends and has not immigrated from Asia since the great ice-era. This conclusion has been adopted by the most prominent anthropologists, in France by Hamy, Topinard, Quatrefages, in England by Beddoe, Flower, Thurnam, in Germany by Ecker, Lindenschmit, Hölder, Virchow, and others."

Dr. Krause adds: "Virchow however takes in this question of the characteristic features of the Aryan race a strange and isolated position, in so far as he believes that from the beginning there had been and are still broad-heads as well as long-heads among the Germanic races." With respect to the conflict between Virchow and Dr. Krause, we should prefer to call the old and original races by new names, as Quatrefages did; we should speak of them as the Cannstadt type, the Cro-Magnon type, etc. When we speak of Aryans, or Saxons, or Germanic nations, we should know that they are no longer the pure Cannstadt type, but a mixture, and this mixture has not even to-day become sufficiently fixed to produce one uniform race. There are certain features predominant in certain nations, and certainly the blond long-heads are purest in the Teutonic nations; nevertheless, it is not an uncommon occurrence that in one and the same family both types are distinctly represented. Johannes Ranke on the strength of this fact has no faith in the constancy of the skull and does not regard it as a fit method of settling any race problem.

The Aryans, i. e. the tall, blond broad-heads of the Cannstadt type are distinguished by strength and by power of will. They were hunters, fishermen, sea-faring people, and warriors. They loved the sea, they loved rivers and lakes. They appear repeatedly in history as conquerors. The arts and industries, however, the use of metals, the invention of pottery, do not seem to have originated among them.

It seems to us that Dr. Krause exhibits an excusable partiality for the blond tall Aryas in comparison with the dark South-European long-heads as well as the broad-heads. The Aryans were chiefly the rulers, except in Palestine, where the tall blond Amorites had been conquered by Semites. It appears that the conquest of a country by the Aryas for instance in India, in Persia, in Greece, gave a start to civilisation, as the Ostro-Goths restored peace and reawakened the arts in Italy. But at the same time we notice that the Aryas were most likely more savage than their broad-headed fellowmen. The present Teutonic population represents so little the pure type of the old tall long-heads that Professor Virchow refuses to recognise long-headedness as a race symptom at all. We find long-heads and broad-heads in the same family. Both long-headed parents may have broad-headed children and vice versa. This need not prove the correctness of Professor Virchow's position, but it may very well prove that the present nations, the Teutonic race not excluded, are the product of a mixture. As the most important feature of Aryan character Dr. Krause considers their religion, and we are inclined to accept Dr. Krause's opinion as thoroughly sound. The Aryan religion, he says, is the cult of light in opposition to the southern cult of darkness. The original Semites worshipped the earth, the moon, the night; the Aryan, worshipped the sun, the sky, the day, the former bowed before womanhood and sentimentality; the latter represented manhood and will-power. (The Jews are not pure Semites, they show a constant proportion in the north of a little over 14/100 and in the south of a little over 13/100 of tall, blond long-heads. These blond Jews, are according to Virchow, the Amorites with which the Israelites mixed after the conquest of Palestine. The religion of the Jews also shows very strong Aryan influences especially since their contact with the Persians.)

The Aryan religions as a rule begin the world with male motherless Gods; while the Semitic religions begin with female mother-gods without fathers. There is the giant Ymir or in Alfadur, here the goddess Kybele, Isis, Rhea, or Demeter. This difference is founded on a social difference which again depends upon climatic conditions. In the south we find in the beginning a state of matriarchy. There was no great difficulty in bringing up large families and the assistance of the father was not needed. In consequence thereof the father was and remained a stranger, an occasional visitor. There were no lasting family ties between himself and the mother of his children, the sexual relations remained free, and the right of heredity recognised the mother only. How different was it in the north! Without their father a family had to perish. The severe struggle for life created the family and eventually the monogamic family, it made the men strong, active, liberty-loving. There was undoubtedly much rudeness among the northern nations; they were savages in many respects, but wherever they appeared as conquerors they introduced their religion of light, activity, and submission to moral laws. The conquered tribes contributed undoubtedly many most valuable qualities to the mixture from which the future races arose, qualities which the Aryans would perhaps never have been able to evolve out of themselves alone. Nevertheless the Aryans gave character to the nations, impressed upon them their speech, their thought, their world-conception and their morality.

Dr. Krause's treatment of comparative mythology with reference to the physical and geographical conditions under which myths originate, is very suggestive, and we wish he had also taken into consideration the parallelism of the northern Sun-myths with Christianity. Dr. Krause mentions that the idea of immortality is an Aryan thought, he might have added that the idea of a dying God who will again rise from the dead can only have originated in the home of the Baldur myth.

Dr. Krause's work contains in 624 pages an almost inexhaustible store of investigations. It is one of the most interesting books we have ever seen. We mention here only the chapters on the Megalithian Monuments, on Orion, on the northern animals of Apollo, on little Red Ridinghood, on the Wagon in the Skies and Tom Thumb, on Helen and her northern representatives, and on the history of the Odyssee. The book would be more valuable to the reader if it possessed an index.

κρς.

DIE MATHEMATIK DIE FACKELTRAEGERIN EINER NEUEN ZEIT. By C. Dillmann.
Stuttgart: W. Kohlhammer, 1889.

The importance of this little book does not lie so much in the theories as in the practical aims of the author. Oberstudienrath Dillmann is a reformer in the system of higher education; he is not a mere theorist, but a man of experience who has now been for years the principal of a school like that which he advocates. Mr. Dillmann's idea is very simple and obviously correct. He claims that the old so-called classical method, where the teaching of dead languages is made the basis of education, no longer meets the needs of our time; that there is however another discipline, which for its universality and its fundamental importance in every branch of knowledge should be made the corner-stone of education, and that is mathematics. So he proposes to have our boys educated in mathematical high schools.