APRIL: 22, 1915] 
NATURE 
219 

education authorities in establishing and administer- 
ing schemes for the advancement of apprentices. 
Perhaps the most important feature of the Memor- 
andum is the distinction which it draws between the 
major and the minor course. Industrial training has 
suffered hitherto from a lack of proper appreciation 
of the differences between the training required by 
the future artisan (or ‘‘tradesman”’) on the one hand, 
and the future ‘‘technical’’ man (whether designer, 
manager, or commercial representative) on the other. 
The distinction now drawn does not, liowever, go deep 
enough. The Memorandum does not sufficiently dis- 
courage the prevailing notion that the ideal evening 
student first enters evening classes at fourteen, and 
continues to attend such classes for seven years. Thus, 
instead of insisting that the technical student should 
remain at a secondary school until he is at least 
sixteen, and then, perhaps, enter his major (senior) 
course when he enters works, the Memorandum con- 
templates that the technical student and the trade 
student shall both follow the same junior (evening) 
course from fourteen to sixteen. It would surely 
be better that the trade student’s own minor course 
should begin at fourteen instead of at sixteen, and 
attract him, by its special adaptation to the circum- 
stances of his particular trade, from the moment when 
he leaves his day school. Moreover, since the trade 
student will as a rule have less opportunity for general 
reading in later life, his minor course might well 
include some ‘‘citizenship’’ subjects, such as indus- 
trial history considered at first from the point of view 
of his particular trade. 
More than half of the Memorandum is devoted to 
“outlines of work ’’ for various recommended courses. 
This portion is full of most useful suggestions. Some, 
however, are open to objection, or, at least, to criti- 
cism. Thus there is a curious confusion between 
weight and mass on page 20 (‘‘ g x force=mass x linear 
acceleration,’ which would make g a pure number, 
independent of the system of units employed). It is 
also doubtful whether the conception of “work” is 
really so difficult as to justify the suggested postpone- 
ment of its introduction until the second year of the 
senior course. Again, the four years’ (major) course in 
mathematics outlined in the Memorandum might with 
advantage be less ‘* practical’’ in its first two years, 
during which some time might well be found for 
geometry. 
ENGLISH MATHEMATICS. 
“| te Mathematical Gazette has recently published a 
translation of an address delivered by Prof. Gino 
Loria to the International Congress of Historical 
Studies. This is a well-proportioned and detached 
estimate of the main contributions of England to the 
body of mathematical science, from the earliest avail- 
able records to the present time. An important sug- 
gestion is made that it may be possible to find in 
some of our libraries manuscript works by some of 
those early writers who, unlike ourselves, did not 
hasten to publish their discoveries, and were often 
surprised by death. In this connection the names 
of Bradwardine, Richard of Wallingford, John 
Maudith, and Tonstall are mentioned. Another note 
is that James Gregory made lengthy stays in Italy, 
and was therefore probably acquainted with the work 
of Galileo;.so the question arises how far Newton 
may have been influenced by the achievements of the 
great Italian philosopher. Prof. Loria suggests in- 
quiry about this as an important piece of research. 
Prof. Loria emphasises, with justice, the fact that 
the renascence of English mathematics in the nine- 
teenth century coincided with a better knowledge and 
NO. 2373, VOL. 95] 


appreciation of work being done abroad. . The great- 
ness of Newton, like that of Euclid and Archimedes, 
had a sort of benumbing effect upon his successors, 
and even contemporaries; although, of course, there 
are exceptions, like Maclaurin and Brook Taylor and 
Waring. It is also pointed out that even now there 
are certain branches of mathematics which Englishmen 
persistently ignore, or else treat by obsolete and 
clumsy methods. The example given is descriptive 
‘geometry ; and it is noted that Brook Taylor laid down 
the principles of this subject in a way perfectly 
analogous to that adopted long afterwards, and in- 
dependently, by Fiedler. It is not stated by Prof. 
Loria, but it is a fact that most of our text-books on 
descriptive geometry are simply contemptible, from a 
scientific point of view, and not to be compared with 
Fiedler’s treatise, or the classic work of Monge, which 
does in the main follow the lines of what we call 
descriptive geometry, in the restricted sense of ortho- 
gonal projection. 
Even able students who use these books, and attain 
great practical efficiency, have no conception at all of 
the subject as a whole, and are baffled by the simplest 
problems about traces of lines and planes. So far as 
we know, there is only one good treatise on descrip- 
tive geometry in the English language, and that is in 
the ‘‘Penny Cyclopedia,” where so many other 
treasures have been buried and forgotten. This leads 
to the remark that Prof. Loria has a proper appre- 
ciation of the works of De Morgan, and laments that 
they are so inaccessible; with this sentiment we 
cordially agree. 
An Italian is as likely as anyone to sympathise with 
English modes of thought; so any conclusion drawn 
from this address is likely to be flattering rather than 
the reverse. We must remember, too, that, when we 
speak of English mathematicians, we are pt to in- 
clude such men as Maclaurin, Rowan Hamilton, and 
Sylvester, who were not Englishmen at all. But even 
in this inclusive sense of the term ‘“‘ English” one 
cannot but feel that Continental opinion about English 
mathematics is almost bound to be analogous to that 
about English literature in general. Newton is Eng- 
lish, and, like Shakespeare, ar Dante, or Goethe, incom- 
parable; but we have lesser men, of a more distinctly 
national type, who may, perhaps, be more justly appre- 
ciated at home than abroad. As an example, we may 
instance W. H. Fox Talbot, now only vaguely remem- 
bered in connection with photography. As a mathe- 
matician he is, of course, not to be compared with 
Abel; nevertheless he did investigate some cases of 
Abel’s theorem in a very instructive and fundamental 
way, implicitly showing that the theorem is really a 
deduction from the known facts about symmetric 
functions of the roots of an equation, and the elemen- 
tary theory of partial fractions. We are inclined to 
believe that the simplest proof of Abel’s theorem will 
ultimately follow the lines that Talbot has indicated. 
‘There are many points in the address to which we 
cannot refer; but one that deserves mention is that 
Newton is reported to have said that the style of the 
ancient geometers is the only one appropriate to any 
mathematical treatise worthy of the name. Judging 
by the ‘Principia,’ it is probable that this storv is 
authentic. Gabe: 

PUBLIC HEALTH. 
HE Medical Officer’s Supplement to the forty- 
third Annual Report of the Local Government 
Board for 1913-14 (Cd. 7612, price 1s. 11d.), while it 
deals mainly with matters primarily. of medical. in- 
terest, of necessity includes within its: scope much that 
is of value to all scientific minds. 
The question of infant mortality occupies a pro. 
