[13] The Dwarf Apple and Pear trees have succeeded better. And indeed in Trees of the same kind, those that keep closest to the Earth always produce the most and best Fruit. For which Reason 'tis that the Gardiners check and restrain the Growth of better Fruit-trees, and prevent their running up to too great a Height.
An Account of the Measure of the thickness of Gold upon Gilt Wire; together with Demonstration of the exceeding Minuteness of the Atoms or constituent Particles of Gold; as it was read before the Royal Society, by E. Halley.
WHAT are the constituent Parts of Matter, and how there comes to be so great a diversity in the weight of Bodies, to all appearance equally solid and dense, such as are Gold and Glass, (whose specifick Gravities are nearly as 7 to 1) seems a very hard Question to those that shall rightly consider it: For from undoubted Experiment, Gravity is in all Bodies proportionable to the Quantity of Matter in each; and there is no such thing as a Propension of some more, others less, towards the Earth's Center; since the Impediment of the Air being removed, all Bodies descend, be they never so loose or compact in Texture, with equal Velocity. It follows therefore, That there is 7 times as much Matter in Gold, as in a piece of Glass of the same Magnitude; and consequently, that at least six parts of seven in the Bulk of Glass, must be Pore or Vacuity: This some Favourers of the Atomical Philosophy have endeavoured to solve, by supposing the primary or constituent Atoms of Gold to be much larger than those of other Bodies, and consequently the Pores fewer; whereas in other Bodies, the great multitude of the interspersed Vacuities does diminish their Weights.
Being desirous to examine this Notion of the Magnitude of Atoms of Gold, I bethought my self of the extreme Ductility of that Metal, which is seen in the beating of it into Leaf, and above all in the drawing fine Gilt-wire, by means whereof, I believed I might most exactly obtain the true thickness of the Coat of Gold, that appears, even with the Microscope, so well to represent Gold it self, that not the least point of Silver appears through it. In order to this, I inform'd my self among the Wire-drawers, what Gold they us'd to their Silver; and they told me, That the very best double Gilt Wire was made out of Cylindrick Ingots, 4 Inches in Circumference, and 28 Inches long, which weigh 16 Pounds Troy; on these they bestow 4 Ounces of Gold, that is, to every 48 Ounces of Silver one of Gold; and that two Yards of the super-fine Wire weighs a Grain. Hence at first sight it appear'd, that the length of 98 Yards is in weight 49 Grains, and that a single Grain of Gold covers the said 98 Yards, and that the 10000th part of a Grain is above ⅓ of an Inch long; which yet may be actually divided into 10, and so the 100000th part of a Grain of Gold be visible without a Microscope. But being desirous to compute the thickness of the Skin of Gold, by means of the specifick Gravities of the Metals, viz. Silver 10⅓, and Gold 18⅔, I found the Diameter of such Wire the 1⁄386 part of an Inch, and its Circumference the 1⁄123 part; but the Gold in thickness not to exceed the 1⁄134500 part of an Inch; whence it may be concluded, that the Cube of the hundredth part of an Inch would contain above 2433000000, (or the Cube of 1345) of such Atoms. And it may likewise be marvelled at, that Gold being stretcht to so great a degree, as is here demonstrated, should yet shew it self of so even and united a Texture, as not to let the white Colour of the Silver under it appear through any the least Pores; which argues, that even in this exceeding thinness very many of those Atoms may still lie one over the other: Which is a Consideration may merit the Thoughts of this Honourable Society, as tending to examine that renowned Atomical Doctrine, which has of late much obtain'd among the Learned.
An Account of the several Species of Infinite Quantity, and of the Proportions they bear one to the other; as it was read before the Royal Society, by E. Halley.
THAT all Magnitudes infinitely great, or such as exceed any assignable Quantity, are equal among themselves, though it be vulgarly received for a Maxim, is not yet so common as it is erroneous; and the Reason of the mistake seems to be, That the Mind of Man, coming to contemplate the Extensions of what exceeds the bounds of its Capacity, and of which the very Idea does include a Negation of Limits; it comes to pass that we acquiesce generally, and it suffices to say such a Quantity is infinite.
But if we come more nearly to examine this Notion, we shall find, that there are really besides infinite Length and infinite Area, no less than three several sorts of infinite Solidity; all of which are Quantitates sui generis, having no more relation or proportion the one to the other, than a Line to a Plane, or a Plane to a Solid, or a Finite to an Infinite. But that among themselves, each of those Species of Infinites are in given Proportions, is what I now intend to make plain, if possible.
But first, infinite Length, or a Line infinitely long, is to be considered either as beginning at a Point, and so infinitely extended one way, or else both ways from the same Point; in which case the one, which is a beginning infinity, is the one half of the whole, which is the Summ of the beginning and ceasing Infinity; or, as I may say, of Infinity, à parte ante, and à parte post: Which is analogous to Eternity in Time or Duration, in which there is always as much to follow as is past, from any point or moment of Time: Nor doth the Addition or Subduction of finite Length or Space of time alter the case either in Infinity or Eternity, since both the one or the other cannot be any part of the whole.