ur in dreaming, and slaying an imaginary enemy with
envenomed words and frequent dabs of ink. If I cannot concentrate my
mind more on these mathematical researches, I fear a dreadful 'plough'
will harrow my feelings at the end of my sojourn in these halls of
learning.

Concentration! How many of our words and ideas and thoughts are derived
from that primal fount of all arts and sciences--mathematics! Here is
one which owes its origin to the mathematically trained mind of some
early philological professor, who had learnt to apply his scientific
knowledge to the enrichment of his native tongue. He quoted to himself
the words of the Roman poet:

'Ego cur, acquirere pauca
Si possum, invideor, cum lingua Catonis et Enni
Sermonem patrium ditaverit, et nova rerum
Nomina protulerit? Licuit, semperque licebit.'

His mind conceived endless figures of circles and ellipses scattered
promiscuously over the page, defying the attempts of the student to
reduce them to order. What must he do before he can apply his formulae
and equations, determine their areas, or describe their eccentric
motion? He must reduce them to a common centre, and then he can proceed
to calculate the abstruse problems in connection with the figures
described. They may be the complex motions of double-star orbits, or the
results of the impact of various projectiles on the tranquil surface of
a pool. It matters not--the principle is the same; he must concentrate,
and reduce to a common centre.

This is the great defect of those who have no accurate mathematical
knowledge; they cannot concentrate their minds with the same degree of
intensity upon the work which lies before them. Their thoughts fly off
at a tangent, as mine do very often; but then I have not been classed
yet in the Tripos; and, O male poetical sycophant, you may be right
after all when you say:

'O woman! in our hours of ease
Uncertain, coy and hard to please,
As variable as the noon-day shade.'

Yes, as variable as the most variable quantities _x_, _y_, _z_. I, a
student of Girtham College, blush to own that my thoughts very often fly
off at a tangent.

'Fly off at a tangent!' All hail to thee, most noble mathematical
phrase! Here is another fine mathematical expression, plainly
exemplifying the action of centrifugal force. The faster the wheel
turns, the greater is the velocity of the discarded particles which fly
off along the line, perpendicular to