Miscellanea Mathematica Volume 6; Consisting of a Large Collection of Curious Mathematical Problems, and Their Solutions. Together with Many Other Important Disquisitions in Various Branches of the Mathematics. Being the Literary Correspondence of Severa (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1775 Excerpt: ...and Ladies'" Miscellany. S I R, IMust again beg the indulgence of a page or tw- in your Miscellany, in answer to Mr. Wildbore's reply in No. V.--Had the subject, concerning which we differ, been in itself intricate, or one that had required. great depth of mathematical knowledge to explain and illustrate, I should have entered very unwillingly into a dispute with this gentleman. But as I cannot see.it-in that light, and think every one who has been a little accustomed to exercise his thoughts on things of this nature, must be properly qualified to. judge of its me-rits, I venture what follows in farther support of what 1 have advanced in my other letters.--I own-1 cannot discover any arguments in favour of my opinion more direli or conclusive than those I have already given, but as placing the affair in a different point of view, may perhaps be thought by some to add strength to them, I shall without farther preface subjoin what more occurs to me as illustrative ef the subject. Let us suppose then, in the first place, two eqoal and similar cylindric vessejs, full of water, to be moved upwards with an equal and given velocity, the one in a vacuum, the, other, in the air. At the instant the motion Here Ibeg.it may be observed and remembered, that there is no greater force or pressure-on the surface of the vessel in the air, than against its bottom, for, as is proved by the writers on mechanics, it requires no greater force to raise this vessel than the, other in vacuo. Note also, that the resistance of the medium, and the relative weight cf a body in it, are not concerned in the present dispute. motion commences, suppose also a hole to be opened in the bottom of each. In this cafe Mr. Wildbore must allow that the water will flow from the vessel in va...