December 20, 1912] 



SCIENCE 



863 



Space-time Manifold of Eelativity. The 

 J^on-Euelidean Geometry of Mechanics and 

 Electromagnetics." The paper contains an 

 elementary account of the non-Euclidean 

 geometry which lies at the basis of any real 

 treatment of relativity free from imaginaries. 

 The vector analysis germane to this geometry 

 is developed from the start, and is not only in- 

 teresting for its applications to the subject at 

 hand, but instructive as an example of non- 

 Euclidean vector analysis. A place of funda- 

 mental importance is given to the singular or 

 minimal elements of the space, that is, to lines 

 of zero length, planes of zero area, and so on. 

 By this means radiant energy and momentum 

 may be treated with great simplicity and 

 power. ■ In particular the questions of the con- 

 tinuous and discontinuous in physics may be 

 discussed from an illuminating point of view. 

 The methods adopted make it possible to de- 

 velop the formulas connected with the elec- 

 tron, whether considered as a point charge or 

 as continuously distributed, without any ap- 

 proximations, in particular without the com- 

 mon concept of " quasi-stationary " motion. 

 Like all the papers appearing in the Proceed- 

 ings of the Academy this memoir is published 

 separately in paper covers and may be pur- 

 chased separately directly from the American 

 Academy, 28 Newbury Street, Boston. 



The high commissioner for Australia has, 

 as we learn from Nature, received official in- 

 formation of the arrangements that are being 

 made for the visit of the British Association 

 to Australia in 1914. A federal council has 

 been formed, under the patronage of the gov- 

 ernor-general, with the prime minister as 

 chairman. The members of the association 

 will arrive at Fremantle on August 4, Ade- 

 laide August 8, Melbourne August 13, Sydney 

 August 20 and Brisbane August 27, and those 

 returning home by the shortest route will reach 

 London on October 11. The Commonwealth 

 has granted £15,000 to be handed to the Brit- 

 ish Association to cover the passages of not 

 fewer than 150 official representatives, includ-: 

 ing selected Dominion and foreign men of 

 science. Dr. Eivett has been appointed or- 

 ganizing secretary, and will visit London next 



year. The governments of the several states 

 offer special facilities for prolonged visits of 

 men of science interested in special problems 

 in Australia. 



Anthracite coal was at one time an impor- 

 tant factor in blast-furnace practise, but its 

 use in that line of industry has now almost 

 entirely ceased, according to E. W. Parker, 

 of the United States Geological Survey, as it 

 has been supplanted by coke made from bitu- 

 minous coal. The principal demand for an- 

 thracite will be in the future, as it has been 

 in the more recent past, restricted largely to 

 domestic trade, for which such sizes as fur- 

 nace, egg, stove and chestnut are required. 

 The breaking down of the lump coal, which 

 was formerly a marketable product, for the 

 preparation of the domestic sizes results in a 

 much larger proportion of the small or unde- 

 sirable sizes, all of which are sold at less than 

 the cost of production. All the profits on the 

 mining operations must be obtained from the 

 prepared domestic sizes, for the revenue ob- 

 tained from the smaller sizes, which are sold 

 largely in competition with bituminous coal 

 for steaming purposes, serves only to reduce 

 the cost of the domestic sizes. The conditions 

 under which the anthracite mines are oper- 

 ated, the greater depths to which the workings 

 are carried, the consequent increased expense 

 of mining and the increasing cost of labor all 

 contribute to make anthracite fuel more and 

 more a luxury. During recent years the 

 anthracite operators have adopted the policy of 

 making an allowance of 50 cents per ton from 

 circular prices for domestic coal purchased in 

 April of each year, with an advance of ten 

 cents per ton for each succeeding month until 

 the schedule prices are restored in September. 

 This has had a more salutary effect in steady- 

 ing the anthracite trade than any other action 

 taken by those controlling the anthracite in- 

 dustry. Its purpose is to encourage the pur- 

 chase of coal in the spring and early summer, 

 making the cellars of the consumers the 

 storage places for the following winter, and 

 at the same time to cause the mines to be 

 operated more regularly, thus giving steadier 

 employment to employees throughout the year. 



