THE

QUADRATURE OF THE CIRCLE.

INTRODUCTION.

"No amount of attestation of innumerable and honest witnesses, would ever convince any one versed in mathematical and mechanical science, that a person had squared the circle, or discovered perpetual motion.”—Baden Powell, in Essays and Reviews, 8th Ed., page 141.

"THE Quadrature of the Circle" is a problem which it has long been pronounced an impossibility to solve, on the authority of names, of such high standing in the scientific world both in ancient and modern times, that latterly, every man who has entertained the idea of attempting its solution has been regarded as a wild enthusiast. "You may as well attempt to square the circle," has passed into a proverb, which is as familiar to the peasant as to the philosopher, and the former, would probably with just as little hesitation as the latter, arrive

at the conclusion, that the man who could imagine he had discovered its solution, was in a state of mind which hardly fitted him to be entrusted with the care of his own person. And yet, the solution of the problem is extremely simple after all. It would almost appear as if its very simplicity had been the grand obstacle which had hitherto stood in the way of its discovery.

"The British Association for the Advancement of Science" may assume infallibility, and authoritatively proclaim that the solution of the problem is impossible; and may consequently decline to permit the consideration of the subject to be introduced into their deliberations. Other learned Associations may add the weight of their authority by endorsing such a course of procedure. The Astronomer Royal of England may make a display of his contempt for any one who should venture to address him as an "authority" on the question. And yet, they must all ultimately succumb to the force of truth, however humiliating it may be to their pride to submit to the infliction.

The following correspondence arose out of a pamphlet (see Appendix A.) which I published about the period of the last meeting of the British Association at Oxford. At that meeting I distributed about 500 copies of the pamphlet among the Savans there assembled, and at the same time, I forwarded a copy to each member of the two Houses of Parliament. In this way I distributed