
NOTICES AND ABSTRACTS 
OF 
MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 
MATHEMATICS AND PHYSICS. 
Tue President, Professor MacCullagh, on taking the Chair, remarked on the con- 
nexion between pure mathematics and the physical sciences, and the reasons which 
had induced the Association to class them together as objects of the same Section. 
The geometer may pursue his speculations to an indefinite extent, without any refer- 
ence to the external world; but he finds the best and most useful applications of them in 
the field of physical research,—in the study of those material laws, the knowledge of 
which is an essential element in the progress of the human race. Independently of 
their utility, the minds feels a natural—almost an irresistible—tendency to such ap- 
plications. Even the great geometer of antiquity (Archimedes), who thought his 
science degraded the moment it became conversant about material objects, and was 
made subservient to merely useful purposes, was yet compelled, by the strong impulse 
of a natural curiosity, to deviate from the proud but narrow rule which he had pre- 
scribed to himself; and then the same splendid genius which had enabled him to find 
the proportions of the cylinder and sphere, and to approximate to some of the most 
refined methods of the modern geometry, led him to lay the foundation of Ra- 
tional Mechanics—of that science which has since grown to such a wonderful ex- 
tent, and has contributed so powerfully to the advancement of civilization. The 
laws of the visible universe are written in the diagrams of geometry and in the 
symbols of analysis; and this remarkable correspondence, established by the will 
of the Creator, between the mathematical conceptions of the human mind and the 
phznomena of the external world, was perceived by the philosophers of remote an-~ 
v tiquity as clearly, and recognized as fully, as it is by those of the present day. 
~ 
ow 
_ It was the perception of this truth which caused Pythagoras to say that numbers are 
_ the principles of all things, and Plato to affirm that geometry is employed in the con- 
struction of the world. So great, indeed, was the predilection of Plato for geometry, 
_ that he required a previous acquaintance with it from all those who wished to become 
_ students of his philosophy ; but while we agree with him as to the great importance 
_ of that science, more especially as an introduction to the study of physics, we shall not 
follow his example so far as to inscribe over the door of our Section-room, ‘“ Let no 
one who is not versed in geometry enter here ;” for then we should exclude that large 
and important class of physical inquirers whose object is merely the discovery of new 
facts, and of elementary laws, which are the expressions of such facts. For in this way 
much may be done, and much has been done, by men slightly or not at all acquainted 
with mathematics, in which category will be found some of the most eminent names 
of modern science. But beyond such elementary laws it is impossible to proceed (as 
many an inventive mind has found when it was too late) without the help of mathe- 
matical science, which alone is competent to grasp the higher generalizations, and to 
discover those remoter laws which link together the more complicated phenomena, 
and enable us to predict them in all possible cases. 

1843. B 
