100 
the well-known pug mill. By the use of this machine the 
mixture is rendered very uniform. 
Of all the methods used for making the bricks, the 
best seems to be that of moulding the clay when in stiff 
condition. The clays in the stiff mud machines are tem- 
pered toa plastic state; when freshly made these bricks 
will retain their shape under considerable weight. 
The machine most generally used is the Auzer machine, 
consisting of a revolving screw which carries the clay 
forward and forces it out of the die. It combines 
economy of handling with a saving of steam power. The 
great objection is a tendency of the machine to build the 
bar of clay out of concentric layers, especially in a very 
plastic clay. By the use of shales, this difficulty has been 
partially removed. 
Automatic cut-off tables have been devised which 
dispense with the slow method of hand cutting. Ina 
recent test 250 bricks per minute were cut and removed. 
Re-pressing the bricks, which was once in great favor, 
is found to add nothing to their value, though the method 
is still used. 
The bricks must be carefully dried to rid them of the 
large amount of water used in mixing the clays. They 
must finally be burned so as to possess the qualities of 
toughness, vitrification, and uniformity. 
The cost of manufacture, including loss in burning, 
averages about seven dollars per thousand. The cost to 
cities averages fourteen dollars, which will probably be 
greatly reduced under better financial management. 
There are at present in Ohio forty-four manufactories, 
with 357 kilns, making annually 292,000,000 bricks. 
A PLEA FOR THE STUDY OF THE PHILOS- 
OPHY OF MATHEMATICS. 
BY FRANKLIN A. BECHER, MILWAUKEE, WIS. 
In early times mathematics and philosophy were 
kindred sciences. Mathematics was the essential study 
required to a preparatory entrance into the higher and 
more advanced branches of human knowledge. They 
were the complements of one another. Both set out with 
definite ends in view, yet the methods pursued were in 
some respects quite different. While the one assumed 
certain postulates to be true for the purpose of developing 
the science, the other was endeavoring to establish a 
principle upon which everything extant rested. ‘The 
methods pursued were almost diametrically opposite. 
Mathematics developed in the direction from the par- 
ticular to the general. It was not until the introduction 
of the idea of the function, by Euler, into mathematical 
reasoning that a more general method was possible. <A 
philosophy of any science cannot be established until 
some well-defined general conceptions are developed. 
The philosophy of mathematics is no exception to this 
rule. Through the development of a more general 
method, the conceptions extended and became more 
universal; that which gave impetus to this was the intro- 
duction of the idea of the function. It was not long 
before the method of inquiry changed in this respect. 
Formerly higher algebra sought mainly to. determine 
those values of functions for which they vanished, while 
modern algebra has for its problem to discover the 
peculiarity or nature of the function, regarding only 
incidentally the numeric value. The masters of modern 
higher algebra have gained thereby an opportunity to 
SCIIBINICIE, 
Vol. XXIII. No. 577 
discover new thought-forms, which differ essentially from 
the old ones. These new thought-forms have aided much 
in suggesting many beautiful theorems and problems 
which again have led up to new discoveries. The pro- 
gress made has been with giant strides, so that many 
fundamental conceptions and propositions are fast losing 
their validity. It is but within recent times that the 
conception manifoldness was introduced into mathematical 
reasoning by Riemann, This conception sheds light over 
the whole field of mathematics, and therefore has aided 
in establishing a foundation for a philosophy of mathe- 
matics. The essentials to a philosophy of the science 
are well stated by Grassmann, who says: ‘‘Since both 
mathematics and philosophy are sciences in the strictest 
sense of the terms, the methods employed in each must 
accordingly have something in common, which gives them 
their peculiar scientific character. Now, we give a 
scientific character to a method of treatment when the 
student, on the one hand, is of necessity led by it to the 
recognition of every single truth, and on the other hand 
is placed in a position wherefrom he is enabled, at every 
point in the development, to survey the course of further 
progress.”” Here we have the importance shown of 
having some central conception or conceptions, from 
which we can view the whole field. The men and their 
works that have contributed to establishing these general 
methods and conceptions, thereby laying a foundation 
for a philosophy of. mathematics, are: Grassmann, in his 
‘“Ausdehnungslehre’”’ (Hyde’s Directional Calculus); 
Hamilton, in his ‘‘ Quarternions’”’; Pierce, in his ‘‘ Linear 
, 
-Associative Algebra,” and Cantor, in his ‘‘ Mannigfaltig- 
” 
keitsrechung,”’ the most important work from a philo- 
sophical standpoint. 
Few, if any, of our universities seem to devote any 
time to the study of the philosophy of mathematics, and 
there are only a small number that embody any of the 
above named subjects in their curricula. In fact, it is 
only very recently that our modern text-book writers 
have deviated from the trodden path and introduced some 
of the more advanced notions in their works. It is only 
within a few months that a new and excellent treatise, the 
first in this country, on the ‘‘ Theory of Functions,” by 
Harkness and Morley, has appeared. Why most of our 
mathematical text-book writers, like lawyers, have a 
strong inclination to adhere to old musty forms and ways 
of presentation is difficult to perceive. 
The importance of the study of the philosophy of 
mathematics is beyond all question. A knowledge merely 
of the objective side of any subject is not only detrimental 
to its presentation, but a thorough knowledge of the 
subject can never be obtained. It is like the bones and 
muscles to the human body without the nerves. Again, 
if these subjects are not taught which lead up to the 
philosophy of mathematics, so that a consistent, true and 
proper view can be had of the entire field of this know- 
ledge, a teaching of this branch is fruitless. The study 
of all the fundamental principles of these subjects and 
the study of the philosophy of mathematics ought to be 
thoroughly mastered by every one who aspires to have an 
accurate knowledge of the subject and wishes to become 
a mathematician. 
—J. B. Lippincott Company announce as an addition 
to their extensive list of medical books a new volume 
entitled ‘‘ Pain,” by J. Leonard Corning, A.M., M.D. 
The author has made a specialty of the study of this 
important subject, and holds that there is no department 
of neurology a knowledge of which is so essential to the 
physician. 
