DISCOVERY 



303 



persist for ever, since there are certain forms of num- 

 bers which cannot be expressed in less. 



The third problem is : Is 2'^' — i a prime number, 

 that is to say a number without factors other than 

 unity and itself ? Part of the interest of this still 

 unsolved problem lies in the fact that a certain mathe- 

 matician, Mersenne, asserted in 1644 that the only 

 values of the index n up to the number 257 for which 

 2" — I is prime are 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 

 and 257. This assertion was believed to be true for 

 many years, because there was no evidence to the 

 contrary, and mathematicians wondered how Mer- 

 senne had arrived at this result. Had he discovered 

 some formula which he kept to himself, and which 

 later mathematicians had failed to rediscover ? It 

 was believed so, and an enormous amount of labour 

 and of paper was expended in trying to verify this 

 assertion. It has now been established that part of 

 it is probably mere guesswork based on inadequate 

 evidence and is wrong. 67 should have been left 

 out ; 61, 89, and 107 included. Mersenne may also 

 have been wrong in omitting 137. It is now the least 

 value of n. for which the answer is still in doubt. 

 \\"hen written out 2"' — i is a number of forty-two 

 digits, so a computer setting out to verify if it be a 

 prime number has a considefable task before him ! 



THE ORIGIN OF COAL SEAMS 



The purport of Professor Kendall's presidential 

 address to the Geology Section was to show that coal 

 seams are the result of growth and accumulation of 

 peat, on the spot, and that all the phenomena of the 

 British coal measures can be explained upon this 

 hypothesis. True, coal seams are characterised by 

 certain definite facts. They are of wide extent, 

 show uniformity of thickness and character over 

 extensive areas, are very free from admixture with 

 the accumulated matter resulting from the disintegra- 

 tion of rocks, and show no signs of aquatic animals 

 within the seam. The inference is that in the main 

 they are formed from old beds of peat in a lowland 

 area which has undergone, in the course of geological 

 time, intermittent depression such as would bring in 

 at one time the muds and sands from flowing water 

 and at another time even the sea. It is of interest 

 to note that near at hand there is at the present day 

 an area which corresponds closely to the areas in 

 past ages from which the coal measures have been 

 formed. This is the North Sea. At some period 

 subsequent to the last ice age the whole of the British 

 Isles appears to have stood relatively to the sea 

 about 80 ft. above its present level. The North Sea 

 was then a vast plain, so nearly at the sea level that 

 it became a morass. Round its margins were forests 

 of oak, pine, and birch, and the greater part of the 



area furnished the conditions for a great peat swamp. 

 At the present day it is a huge bed of peat, throughout 

 its length and breadth, as trawlers testify, and at its 

 edges on the coasts of Holland and of England, as 

 observations at favourable conditions of the tide 

 show. 



BREATHING AT HIGH ALTITUDES 

 Mr. J. Barcroft, F.R.S., an authority on respiration, 

 and the leader of an expedition which has recently 

 been out to the Andes to study the effect of the lack 

 of oxygen on the human system, gave an account of 

 his observations to the Physiological Section. His 

 party made their observations in a mining village in 

 Peru, 14,200 ft. above sea-level. At that altitude 

 they were slightly out of breath, even when sitting 

 ilown, and exertion like walking up hill made them 

 pant. They found their brains worked much more 

 slowly than at lower altitudes. The people who 

 lived at these extreme altitudes, and consequently 

 were acclimatised, were very short of stature, but had 

 the chests of men of 5 ft. 11 in. Cows, they found, 

 could give milk when living at 12,000 ft., but not at 

 13,000 ft. At 14.000 ft. they gradually died of lack 

 of oxj'gen. At this elevation dogs, ponies, and sheep 

 could live, but dogs not very happily. These experi- 

 ments, like those conducted at other places of high 

 elevation, such as in Tibet and on Pike's Peak, are 

 throwing a flood of light on the subject of respiration 

 which is of great practical interest to all those who 

 venture to high elevations, whether on the ground or 



in the air. 



A. S. Russell. 



Reviews of Books 



COUNTRIES AND CLIMATES 



The Climate of the Continents. By W. G. Kendrew, 

 M.A. (Oxford : Clarendon Press, 21s.) 



Mr. Kendrew differs from most of us in speaking and 

 writing of the weather in no mean or narrow sense. We 

 are dwellers in small places ; Mr. Kendrew is a citizen of 

 the terrestrial sphere. Our interest in cHmate is mainly 

 personal, confined to the present or recent past, and to 

 our immediate neighbourhood, and useful as an opening 

 in polite conversation ; Mr. Kendrew's is deep and 

 abiding, not confined to country-side or country, but con- 

 tent with embracing nothing less important than what 

 O. Henry called the terrestrial, globular, planetary hunk 

 of matter, slightly flattened at the poles, known as the 

 Earth. 



Yet the subject is, or can be made, very interesting, 

 because it touches us at many points, and its study need 

 not prostrate us. We cannot always understand the 



