BY ELIAS LOOMIS, LL.D.,

PROFESSOR OF NATURAL PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE,
AND AUTHOR OF A COURSE OF MATHEMATICS."

NEW YORK:

HARPER & BROTHERS, PUBLISHERS,

827 TO 335 PEARL STREET.

1871.

Entered, according to Act of Congress, in the year 1869, by
HARPER & BROTHERS,

In the Clerk's Office of the District Court of the United States for the
Southern District of New York.

TO THE

HON THEODORE FRELINGHUYSEN, LLD

CHANCELLOR OF THE UNIVERSITY OF THE CITY OF NEW YORZ.

THE FRIEND OF EDUCATION, THE PATRIOT STATESMAN,

AND THE CHRISTIAN PHILANTHROPIST,

This Work

IS RESPECTFULLY DEDICATED

BY

THE AUTHOR