FEBRUARY 28, 1907 | 
NATURE 
415 
lateral occipital protuberances, 140; height from basion to 
top of occipital crest, 137; least breadth maxillary zygo- 
matic process, 70; breadth across sockets of canines, 70; 
breadth across tips of canines, 290; length of palate, 270; 
least palatal breadth, between m*, 40; basal diameter of 
canine, 40; lower jaw, length, bone only, 325; breadth 
across symphysis at base of canines, 130; least breadth 
across diastema, 105; height at diastema, 55; tip to tip 
of canines, 22¢: basal diameter, outer face of canines, 22, 
inner face, 24, posterior face, 16; horizontal length of 
p', 15, of m', 19, of m?, 26-5, of m*, 45. 
Dental formula : 7c. p.7.{7.3. 
As I have said, this cranium is massive, the bones 
rugose on their outer surface, the nasals mostly fused 
together, and the frontal depression strongly marked. 
Henry H. Giciiort. 
Florence, Royal Zoological Museum, February 17. 
Gambling and Mathematics. 
Your reviewer ‘‘G. H. B.”’ suggested in Nature of 
January 31 (p. 318) that every schoolboy should know 
something about choice and chance in order that he may 
not develop into a gambler. I agree with him. But one 
may suspect that gamblers are either those who have not 
had the advantages of a mathematical education or those 
who belong to ‘‘ slow dull’’ grade and are unable to 
appreciate those advantages; and yet one may be quite 
unable to prove that this is really the case. 
Can any of your correspondents bring forward evidence 
to show that mathematicians gamble less than other men, 
or that gamblers really are mathematically defective ? 
The matter is important as indicating the point at which 
the efforts of an anti-gambling league should be most 
usefully applied. Is it in the intelligent teaching of mathe- 
matics? And are we right in distrusting the methods of 
exhortation when the methods of algebra will suffice ? 
Bootham School, York. HuGuH RICHARDSON. 
Tue subject of Mr. Richardson’s letter raises a wide 
field of discussion, of which the few words in my notice 
convey a very imperfect idea. I should like to see the 
matter discussed in a suitable quarter when such can be 
found, but I believe it is a question for psychologists as 
well as mathematicians. 
I take it that the ordinary gambler speculates in order 
to win, and that the prospect of winning is the incentive 
which does the greatest harm. 
When a man speculates by staking, say, 11. on the 
chance of winning rool., the notion of winning rool, makes 
a big impression on his mind, and means something more 
real to him than the idea that the odds are 200 to 1 
against him (say). He forms a clear mental picture of the 
prize, and the odds do not present the same picture to 
his mind. Consequently, he exaggerates his prospects. 
What I meant to imply is that schoolboys ought to learn 
to calculate probabilities, so that when they grow up they 
should think as clearly and form as strong mental pictures 
of the odds against them in a game of chance as they 
do of the value of the prizes, and that they should learn 
to calculate expectations and to think of these rather than 
of the prizes. 
But when Mr. Richardson uses the word ‘‘ algebra ”’ 
he implies something different from what I mean, which 
is more correctly described as arithmetic. What I should 
like would be to see a chapter on probabilities treated in 
an elementary course of arithmetic, and boys familiarised 
with the idea of probability calculations, the representation 
of probabilities by fractions, and the calculation of expect- 
ations, without any algebra being put in to puzzle them. 
Quite simple questions, in fact. I will not say that every- 
one who had studied probabilities would not indulge in a 
game of chance now and then, but they would go in with 
the expectation of losing rather than winning, and they 
would know it was no use to try to make up a loss by 
making false estimates of the probability of the luck turn- 
ing. If nobody gambled except for the amusement, and if 
everybody before doing so made a calculation beforehand as 
to how much they were prepared to pay for that amuse- 
ment, realising that their expectation in every case was a 
No. 1948 VOL. 75] 
loss (if playing against a bank), the worst evil of gambling 
would be eliminated. The only difficulty would be the 
psychological one of preventing a man from being carried 
away by his excitement. 
What people should know is that to speculate against 
a bank or syndicate is a bad investment, and that even 
to speculate where all profits are distributed between 
players is not a paying investment, but is really also a 
bad investment even if the expectation equals the man’s 
stake, on the ground that a bird in the hand is worth 
two in the bush. The loss of the bird in the hand means 
a definite loss of income; the expectation cannot be re- 
garded as income. Gaara B: 
Some New Methods in Meteorology. 
Since the appearance in Nature of December 20, 1906, 
of my review of Prof. Bigelow’s ‘‘ Studies’’ under the 
above title, I have had some correspondence with Prof. 
Willis L. Moore, chief of the U.S. Weather Bureau. 1 
am glad, with Prof. Willis Moore’s sanction, to quote part 
of his letters to me, which will, I hope, allay any appre- 
hensions which may have been aroused as to the methods 
of research likely to be adopted at the new Mount Weather 
Observatory. Prof. Moore writes :—* . Since June, 
1905, Prof. William J. Humphreys, of Johns Hopkins 
University, and formerly Professor of Physics at the Uni- 
versity of Virginia, has been Supervising Director at our 
institution at Mt. Weather. We wish to ascertain facts 
by experimentation, rather than to exploit theories, how- 
ever beautiful they may be. We consider Prof. Bigelow’s 
numerous papers as expressing simply his own views. . . . 
Neither myself nor any member of my staff desires to be 
considered responsible for any theories that may be 
advanced in the publications of the Bureau, except he be 
the author.’’ 
Prof. Willis Moore’s explanation, and his recognition 
of experiment as the necessary and ultimate criterion, 
justify the expectation that, backed as it is by the re- 
sources of the U.S. Weather Bureau, the new research 
observatory at Mount Weather will prove a most useful 
institution for the advancement of scientific meteorology. 
CHARLES CHREE. 
ae scope of this work, which runs to nearly 
1600 pages. is defined in the preface, where it 
is stated to be “‘ essentially a compilation from many 
sources,’’ but differing from most books of that 
kind, “‘ first, in being based to a very large extent on 
materials hitherto unpublished, and accessible only 
through private channels of information, and 
secondly in having been constructed with special 
knowledge of the subject and in a critical spirit.”’ 
Accurate though these statements be, they offer but 
slight indication of how thoroughly the book is in- 
spired with the experience and critical knowledge of 
the authors, and how well the subjects dealt with 
have been unified in their hands, a task the difficulty 
of which may be judged in part by a consideration of 
the unsatisfactory nature of much that has been 
written as well as by the length of the bibliography 
which follows the preface. The authors explain that 
the several parts of the book dealing with the 
physical and cultural characteristics of the tribes had 
been originally arranged under subject headings, and 
that the book was then re-written upon “a phylo- 
genetic system, so as to throw into relief the differ- 
ences which separate one race from another,’’ a plan 
which no one will doubt has added immensely to the 
clarity of the work. Although the title-page bears 
the name of both authors, the greater part of the 
work has been written by Mr. Skeat, Mr. Blagden 
By W. W. Skeat and C. O. 
1 “ Pagan Races of the Malay Peninsula.” 
(London: Mac- 
Blagden. Vol. i., pp. xl+724; vol. ii., pp. xi+855. 
millan and Co., Ltd., 19c6.) Price 42s. net. 
