iscellaneous nature.
Some of them at least would be of the highest interest to us now.

In the _Philosophical Transactions_ for 1789, p. 220, HERSCHEL tells us
that he communicated to that Society "certain mathematical papers"
relating to central forces other than the force of gravity, which are or
may be concerned in the construction of the sidereal heavens. This early
idea was still entertained by HERSCHEL in 1789, and the mathematical
papers referred to must be contained in the _Minutes_ of the Society,
which on its dissolution were torn from the Minute-book and returned to
the writers.

The earliest published writing of HERSCHEL is the answer to the prize
question in the "Ladies' Diary" for 1779, proposed by the celebrated
LANDEN, namely:

"The length, tension, and weight of a musical string being given,
it is required to find how many vibrations it will make in a given
time, when a small given weight is fastened to its middle and
vibrates with it."

In the _Philosophical Transactions_ of the Royal Society for 1780, are
two papers of his. The title of the first is, _Astronomical Observations
on the Periodical Star in Collo Ceti_, by Mr. WILLIAM HERSCHEL, of Bath.
This was communicated to the Society by Dr. WILLIAM WATSON, Jr., and
was read May 11, 1780, at the same time as the other paper on the
mountains of the moon. It is to be noted that HERSCHEL was at this time
plain "Mr. WILLIAM HERSCHEL, of Bath." It was only in 1786 that he
became "Dr. HERSCHEL," through the Oxford degree of LL.D.

Neither of these two papers is specially remarkable on its purely
astronomical side. The problems examined were such as lay open before
all, and the treatment of them was such as would naturally be suggested.

The second of these two contained, however, a short description of his
Newtonian telescope, and he speaks of it with a just pride: "I believe
that for distinctness of vision this instrument is perhaps equal to any
that was ever made." He was, at least, certain of having obtained
excellence in the making of his instruments.

In his next paper, however, read January 11, 1781, a subject is
approached which shows a different kind of thought. It is the first
obvious proof of the truth of the statement which he made long
afterwards (1811), when he said: "A knowledge of the construction of
the heavens has always been the ultimate object of my observations."

The title of this paper was _Astronomical Observa