MATHEMATICAL SECTION. 119 
and certainly there would be a clearness and meaning that are so. 
often wanting. Thus, if any one asserts that when a planet comes 
to its perihelion it ought to fall into the sun, the law of gravitation 
being true, he is not worth listening to unless he will put his asser- 
tion into a formula; and when he is able to do this he will probably 
find out his own error. There will be so much gain by simply re- 
ducing the problem to its elements and giving it a correct form. 
Again, where scientific statements may be true, there will be a gain 
in giving them, when possible, a mathematical expression. Thus, 
when we are told that the fixed star 1830 Groombridge is running 
away, disobedient to the law of gravitation, how much better it 
would be if we could see on the blackboard the mathematical proof 
of this assertion, so that we could judge for ourselves on what 
assumption it is based. The subject of impulsive forces is one that 
we hear disputes about in our own society, and it seems to be a fair 
field for a mathematical exposition. How often do we see such 
phrases as “energy,” “potential energy,” “kinetic energy,” “ con- 
servation of energy,” “work,” “ virial,” &c. Could not some one 
of our members give us a clear account of these terms, show us how 
they are connected with the general equations of mechanics, what 
new ideas they contain, and on what limitations they may be based ? 
As the application of mathematics is extended, sounding phrases 
are sure to come into use, and it is well to test them and know what 
they mean. 
In the discussions of this Section, while all are invited to be 
critical, I trust that we shall all be kind and good tempered. We 
come together for discussion and mutual improvement, and while 
error is not to be spared we must be charitable to each other’s faults. 
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