AG2 SECTIONAL TRANSACTIONS.—H. 
amount of commercial communication spread over large areas. Some of the 
old trade routes are known, but it would be of the greatest interest to trace 
others; they might serve to explain many problems which have baffled 
ethnologists. 
4, Mr. W. Bonser.—The Magic Practices of the Finns in Relation 
to those of other Arctic Peoples. 
Primitive Arctic culture survived owing to its isolation, but was modified 
and complicated in Finland owing to its contact there with Christianity. The 
Shaman derived his powers from the supreme god, who was himself, therefore, 
the greatest sorcerer. The powers, together with the familiars, were heredi- 
tary. The Lapps, being the original inhabitants, were reputed greater magicians 
than the Finns. The sorcerer was baptised, usually by his mother, both for 
initiatory and protective purposes. It was usual to remove the clothing for 
practising magic, but to put on extra clothing as a protection against the 
magic of others. The efficacy of magic was increased by the neighbourhood 
of rocks and stones, especially those of a variegated nature. The dead Shaman 
was more potent than the living one: wherefore the underworld was a store- 
house of Shamanic wisdom. 
5. Prof. C. A. Broprs Brockweiu.—The Evolution of Arithmetic 
as Exemplified in Plato’s Millennium Cycle, erroneously styled 
his Geometrical Number. 
Ancient statements show that pre-Christian Mediterraneans used arithmetical 
processes without analogy in modern arithmetic. Western treatises on arithmetic 
of the fifteenth and sixteenth centuries show that our arithmetic tables had not 
been invented at the beginning of the sixteenth century. Modern scholars, 
through ignorance of these things, have misinterpreted almost all ancient 
numbers, have obscured the meaning of most ancient time-determinations, have 
failed to discriminate between cause and effect, and so to unfold the evolution 
of ancient Mediterranean social and cultural institutions. 
Plato’s dynastic abacus is a typical exemplification of Mediterranean arith- 
metic worked by processes belonging to different stages of social evolution. The 
apparent contradictions of ancient dates and longevity numbers, &c., have arisen 
from the custom of transmitting one and the same date, or number, in the styles 
of different stages of arithmetical evolution. 
6. Mrs. Scoressy Rovurtepar. — Mangarevan Folk-lore: Some 
Results of an Expedition to the Austral Islands and Mangareva. 
While there exist numerous megalithic remains in the Austral Islands, and 
interesting maraes on even the neighbouring island of Temoe, there have never 
been on Mangareva any stoneworks of importance. 
Mangareva is, however, rich in folk-lore, and is possibly unique among 
Pacific islands in possessing written history in the native tongue. This dates 
from about the middle of last century, the work being instigated by the early 
R.C. missionaries; it appears to be a genuine record of events for about the — 
two hundred years preceding, und comprises yet earlier legends. Interesting 
additions to the written histcries are still recounted verbally. 
A large number of folk-tales, more purely domestic or mythical in character, — 
have been transmitted orally and are well known. 
The number of songs is enormous. A large collection has been made in 
writing by a Mangarevan recently deceased. They refer frequently to the folk- 
tales, but many cannot be explained. There are interesting points of contact 
with the Easter Island script. 
The general knowledge of folk-lore has been kept alive through dances or 
dramatic representations, when the best-known stories are depicted with stage 
properties and accompanied by songs. 
7. Capt. A. G. Parz.—lIs there a New Race Type? 
