e needed to indicate subsequent writing.

Another and a larger portion of the work consists of discussion of matters
of contemporary interest, for the Budget was in some degree a receptacle
for the author's thoughts on any literary, scientific, or social question.
Having grown thus gradually to its present size, the book as it was left
was not quite in a fit condition for publication, but the alterations which
have been made are slight and few, being in most cases verbal, and such as
the sense absolutely required, or transpositions of sentences to secure
coherence with the rest, in places where the author, in his more recent
insertion of them, had overlooked the connection in which they stood. In no
case has the meaning been in any degree modified or interfered with.

One rather large omission must be mentioned here. It is an account of the
quarrel between Sir James South and Mr. Troughton on the mounting, etc. of
the equatorial telescope at Campden Hill. At some future time when the
affair has passed entirely out of the memory of living Astronomers, the
appreciative sketch, which is omitted in this edition of the Budget, will
be an interesting piece of history and study of character.[1]

A very small portion of Mr. James Smith's circle-squaring has been left
out, with a still smaller portion of Mr. De Morgan's answers to that
Cyclometrical Paradoxer.

In more than one place repetitions, which would have disappeared under the
author's revision, have been allowed to remain, because they could not have
been taken away without leaving a hiatus, not easy to fill up without
damage to the author's meaning.

I give these explanations in obedience to the rules laid down for the
guidance of editors at page 15.[2] If any apology for the fragmentary
character of the book be thought necessary, it may be found in the author's
own words at page 281 of the second volume.[3]

The publication of the Budget could not have been delayed without lessening
the interest attaching to the writer's thoughts upon questions of our own
day. I trust that, incomplete as the work is compared with what it might
have been, I shall not be held mistaken in giving it to the world. Rather
let me hope that it will be welcomed as an old friend returning under great
disadvantages, but bringing a pleasant remembrance of the amusement which
its weekly appearance in the _Athenaeum_ gave to both writer and reader.

The Paradoxes are dealt with in chronologica