500 
The British Association . 
[October, 
rational and practical ; and since artizans often work inac- 
curately, it came to pass that mechanics and geometry were 
distinguished in this way, that everything accurate was re- 
ferred to geometry, and everything inaccurate to mechanics. 
But the inaccuracies appertain to the artizan and not to 
the art, and geometry itself has its foundation in mechanical 
practice, and is in fa<5t nothing else than that part of uni- 
versal mechanics which accurately lays down and demon- 
strates the art of measuring.” He next explains that 
rational mechanics is the science of motion resulting from 
forces, and adds, — “ The whole difficulty of philosophy 
seems to me to lie in investigating the forces of nature from 
the phenomena of motion, and in demonstrating that from 
these forces other phenomena will ensue.” Then, after 
stating the problems of which he has treated in the work 
itself, he says — “ I would that all other natural phenomena 
might similarly be deduced from mechanical principles. 
For many things move me to suspeCt that everything de- 
pends upon certain forces in virtue of which the particles of 
bodies, through forces not yet understood, are either impelled 
together so as to cohere in regular figures, or are repelled 
and recede from one another.” 
Every subject, whether in its usual acceptation scientific 
or otherwise, may have a mathematical aspect ; as soon, in 
fa6t, as it becomes a matter of strict measurement, or of 
numerical statement, so soon does it enter upon a mathe- 
matical phase. It is not so much elaborate calculations or 
abstruse processes which characterise this phase as the 
principles of precision, of exactness, and of proportion. 
These are principles with which no true knowledge can en- 
tirely dispense. If it be the general scientific spirit which 
at the outset moves upon the face of the waters, and out of 
the unknown depth brings forth light and living forms, it is 
no less the mathematical spirit which breathes the breath 
of life into what would otherwise have ever remained mere 
dry bones of faCt, which reunites the scattered limbs and 
re-creates from them a new and organic whole. 
Taking precision and exactness as the characteristics which 
distinguish the mathematical phase of a subject, we are 
naturally led to expeCt that the approach to such a phase 
will be indicated by increasing application of the principle 
of measurement, and by the importance which is attached 
to numerical results. And this very necessary condition 
for progress may be fairly described as one of the main 
features of scientific advance in the present day. 
If* continued the President, it were my purpose, by 
