Dec. 28, 1882] 
to the same binary quantic, “provided that the Editor shall 
not himself have previously discovered the same, and 
given public notice thereof.” The truth of this proposition 
has been assumed as a fundamental postulate in the cal- 
culation of ground forms, and its importance cannot 
be over-estimated. It is, however, somewhat of an 
anachronism to draw attention to it by the offer of a 
prize. Such prizes exist in Universities and in the older 
academies, but by many they are not regarded with much 
favour. It seems unlikely that any competent person 
would be tempted to investigate the subject by hope of 
the reward. Pure mathematics offers no mercenary in- 
ducements to its followers, who are attracted to it by the 
importance and beauty of the truths it contains; and the 
complete absence of any material advantage to be gained 
by means of it, adds perhaps even another charm to its 
study. 
The late Prof. Benjamin Peirce denoted the base of the 
Napierian logarithms and the ratio of the circumference to 
the diameter of a circle by two special symbols turned oppo- 
site ways, somewhat resembling a 6and a6 reversed. The 
forms of these symbols would seem to imply that 2°71828... 
and 3'14159... were regarded as allied to one another, and 
in some reciprocal or inverse manner too, though it is not 
easy to see what the author’s point of view was. Two 
writers in the American Journal use Prof. Peirce’s 
symbols in place of 7 and ¢, and this is to be regretted, as 
any departure from the recognised notation in elementary 
matters is always unfortunate. Even if the symbols 
were happily chosen, which does not appear to be the 
case, they would require the cutting of new type, and it is 
absolutely certain that there is not the least chance of 
their general adoption. If now used by a few prominent 
writers in America, they may spread to such an ex- 
tent as to make it very difficult for their successors to 
get rid of them. The preservation of the international 
character of mathematical notation is of paramount im- 
portance, and the existence of local notations, especially 
when they find their way into text-books, is a calamity. 
In England the Cambridge notations, sin-*+, due we 
believe to Herschel and Babbage, and the factorial nota- 
tion due to the late Prof. Jarrett, are still retained by 
many English writers, although it has long been evident 
that there is no chance of their adoption by continental 
mathematicians. It is always desirable to adhere to an 
established notation, if it is generally understood and 
accepted, even if it is unsatisfactory, rather than attempt 
to replace it bya better one, unless there seems very 
good reason to suppose that the attempt will be suc- 
cessful. 
In the previous article in NATURE reference was made 
to the services which Dr. J. E. Hendricks, of Des Moines, 
Iowa, has rendered to mathematics in America by the 
publication of the Azalyst, which jhe established in 1874, 
and has continued to the present time. This journal is 
published every two months, and has now completed 
its ninth volume. In spite of typographical and other 
difficulties the editor has published it regularly, and it 
shows no signs of diminished vitality or interest on his 
| part. It has been self-supporting, and its success is due 
to the genuine love of their subject felt by the editor and 
the contributors. A great part of each number is unfor- 
| tunately devoted to problems—the lowest form of mathe- | 
} 
NATURE 
195 
matics—and the space available for more valuable matter 
is thus considerably diminished. One also is tempted to 
wish that the editor would show greater strictness in cur- 
tailing or excluding the writings of certain contributors, 
but nevertheless the Avadys¢ contains not a few useful 
papers. It is easy to see the blemishes in such a journal 
by merely turning over the pages, but it is not so easy to 
estimate the services which it confers upon science by 
inducing teachers to look beyond the text-books and 
interest themselves in a subject for which a genuine 
taste can only be acquired by attempting to do work for 
oneself. The large quarto page of the American Journal 
and the elaborate nature of some of its papers render it 
unsuitable for the short notes and the more unpretentious 
class of papers in which the author lays but little claim to 
originality. For these the Avalyst is available ; but, 
after all, the chief value of such a publication consists in 
the interest in mathematics it excites and fosters in those 
who could be reached in no other way, and the induce- 
ment it affords for those who are unable to devote their 
whole time to the subject to nevertheless undertake useful 
and profitable work. No previous American mathe- 
matical journal has ever been published regularly for nine 
years, and Dr. Hendrick has reason to feel proud of the 
success of his efforts. 
In 1877 Mr. Artemas Martin, of Erie, Pennsylvania, 
issued the first number of the Zathematical Visitor, a quarto 
journal which was published annually until Jan., 1880, and 
since then has appeared semi-annually. The first volume 
ended with the number published in January, 1881. The 
journal consists entirely of problems and solutions, there 
being a senior and a junior department. Several of the 
problems relate to probability questions and involve very 
complicated and elaborate integrations. As the solution 
of a prize question, Mr. E. B. Seitz gives, in the number 
for January, 1879, the values of the coefficients obtained 
by reverting a general series proceeding by ascending 
powers of the variable, as far as the sixteenth order. 
The journal is beautifully printed, and is set up by the 
editor himself. In the number for January, 1880, he 
says: “This number of the Vzsfor has been delayed 
some months. in consequence of the sickness of the 
editor, who has done all the type-setting with his own 
hands. He is not a practical printer, and never had set 
up a stickful of type till last May or June.” 
At the beginning of the present year Mr. Martin issued, 
besides the Vzsttor, a new publication, entitled Zhe 
Mathematical Magazine: a Journal of Elementary 
Mathematics, of which four numbers have now appeared. 
It is of large quarto size, and, like the Vzsztor, is printed 
by the editor’s own hands. No mathematical journal, if 
it is to contain anything of real value, can be elementary. 
Mathematics is an old science, and the really elementary 
parts of it must be acquired from text-books and by 
means of the examples which the student works out for 
himself as exercises. Elementary mathematics is a sub- 
ject for the school-room, but is unsuitable for a journal, 
and such a publication as Mr. Martin’s, if it continues 
elementary, is educational rather than scientific. In 
no instance, we believe, has it been found possible to 
restrict a mathematical journal really to the elements of 
the subject alone, though ‘of course elementary articles, 
and articles which are of interest to junior readers, form 
