Angles, to the Diameter of the Circle: These three sorts of infinite Quantity are analogous to a Line, Surface and Solid, and after the same manner cannot be compared, or have any proportion the one to the other. Besides these, there are several other Species of infinite Quantity, arising from the Contemplation of Curves, and their Asymptotes; which, by reason of the difficulty of the Subject, cannot be made so plain to most Readers: But what has been already said, may be sufficient to evince what we undertook to explain. _An Account of Dr. _Robert Hook_'s Invention of the Marine Barometer, with its Description and Uses; published by order of the Royal Society, by _E. Halley_, R. S. S._ Since it was found that the _Torricellian Tube_, commonly call'd the _Mercurial Barometer_, by the rising and falling of the _Quick-silver_ therein, doth presage the Changes of the Air, in relation to fair and foul Weather; upon several Years Observation of it, it has been proved and adjusted for that purpose by Dr. _Robert Hook_; and there have been by him many attempts to improve the Instrument, and render the Minute Divisions on the Scale thereof more sensible. He also judging that it might be of great use at Sea, contrived several ways to make it serviceable on Board of Ship; one of which he explain'd to the _Royal Society_ at their Weekly Meeting in _Gresham College_, _January 2. 1667/8_. Since which time he hath further cultivated the Invention, and some Years ago produced before the said _Society_, the Instrument I am now to describe, which for its subtilty and usefulness, seemeth to surpass all other performances of the like Nature. 'Till such time as the Author's present Indisposition will give him leave to bestow freely his Thoughts on this Subject upon the Publick, it is the Opinion of the Society, that such an Account be given of this Contrivance, as may render it known, and recommend it to the Mariners use, for which it was principally intended. The _Mercurial Barometer_ requiring a perpendicular Posture, and the _Quick-silver_ vibrating therein with great Violence upon any Agitation, is therefore uncapable of being used at Sea (tho' it hath lately been contrived to be made portable), so it remain'd to find out some other Principle, wherein the Position of the Instrument was not so indispensably necessary: For this, all those that use the Sea are obliged to the great facility Dr. _Hook_ has always shewn, in applying Philosophical Experiments to their proper uses.