Now fince OE is fuppos'd to confift of 100 Animalcula-Spaces, the Number of Light-Particles in the fame will likewise be 10.

XV. From whence it therefore follows, that the Number of Light-Particles in the Length OE, fuppofing there be one in each AnimalculaSpace, Is to the Number of the fame, fuppofing likewise, that they increase according to the Rule Num. X. As 10, or fo many Units as are contain'd in the Lines A G, Br, Cs, Dt, &c. Are to the Produce of all the Numbers that compose the Perpendicular Lines Aa, Bb, Cc, Dd, &c.

XVI. It is not necessary to prove that the Numbers of all these Perpendiculars Aa, Bb, Cc, Dd, c. do contain fo great a Quantity.

20

Since the first and greatest A a being 1020. The Second Bb will amount to 104, or 250. The Third Cc 102.

The Fourth Dd 10%.

20

And fo forth; each of these Lines equal to the Line Aa or 100 divided by the Squares of their Distances from O; all which amounting to the Number of 10; fo as the laft FE, by an Unit, will produce a great Sum, which to compute here would be a very great Trouble, and require too much Time and Room.

XVII. That we may not therefore be deceiv'd in our Calculation, we fhall make choice of a much fmaller Sum than we need do, and therefore only retain the Number 1020, that alone being the greateft quantity of Light-Particles in the Space of one of the Animalcula, or the Line A a; and we will throw away the reft Bc, Cc, Dd, &c. which would likewife amount to a vast Sum.

And having done fo, it will eafily follow; that the increased Light-Particles 1020, or A a (Num. XVI.) Are to the Number of Light-Particles in OE, As one in the Space of each Animaculum, or VOL. III. Ggg 2

to

to 10° (Num. XIV.) As 10 to 1. Or that (if we admit the Increase Num. X.) the Animalcula in OE are 10 times more, than if we were to fuppofe but one in each of the Spaces between O and E, QRSE. This is applicable to all the Rays like OE thro' the enlighten'd Globe, and confequently to the faid whole Globe.

XVIII. Before I proceed, I beg leave to obviate the Opinions that fome People may entertain of these Matters:

Namely, That fince the Curve-Line a, b, c, &c. F which connects all the Tops, a, b, c, &c. of the Perpendicular Lines A a, Bb, C, &c. which are here drawn so close to each other, is of a known Property; which, if we call each of the Lines or Distances OA, OB, OC, &c. x, and the refpe&ive Perpendiculars Aa, Bb, Cc, &c. each y, and the Line O E, a, and EF, b, and exprefs the fame by the followng Algebraic Equation, xxy

ab. A Mathematician will wonder, perhaps, why I did not find the Area of the Magnitude of the Mixtilineum A a FE by Approximation, or even after the Method of Mercator, Wallis, and other great Mathematicians; to the end, that after having compared the fame with the Greatness of the Rectangle AGFE, to find the Proportion from thence of the increas'd Number of Particles of Light in OE to the Number of the fame OE, if there were but one Particle in the Space of each Animalculum: which has been done, it may be, by others on the like Occafion.

But they must be pleas'd to observe; First, That I have omitted thefe Methods, because all of 'em suppose, that the Line OE is to be divided into infinite fmall Parts, as OA, AB, BC, &c. whereas we have only adapted our Divifions to fuch Parts as are equal to the Space fill'd by each of thofe Animalcula that are vifible thro' a Micro

scope,

fcope, which is yet bigger an infinite Number of times than one of the infinite Parts.

Secondly, We have given one Reafon in Numb. XVII. which will make our Conclufions much more acceptable, because we choofe fo much fmaller a Number.

Thirdly, What we here write is not fo much for great Mathematicians, as for others that are of a good natural Understanding, tho' not thoroughly vers'd in Lines and Figures; wherefore, when we can use other Methods of Proving, we avoid as much as poffible thofe of the Mathematicians; my chief End being to render my felf intelligible even to the meaneft Capacity, rather than to please the Learned, provided I can make the Truth appear in fuch a manner.

XIX. To draw therefore thofe Conclufions which we have in View from thefe and the foregoing Principles; let us fuppofe, (1.) with Leuwenhoek, that 1,000.000,000 of thofe Animalcula which are visible thro' a Microscope, do make up one Grain of Sand, Sect. X. (2) That 1 000,000 of Sands are equal to a Cubical Inch, Sect. X. according to which 10 of thefe Animalcula are equal to a Cubical Inch, allowing but 10 Inches to a Foot in length.

Now according to Num. V. the Globe QRSE contains 418660 of fuch Inches, and confequently 418660 of the faid Animalcula.

XX. Let us fuppofe further, that in every one of the Spaces fill'd by each Animalculum, there is but one Light-Particle thro' the whole Globe.

XXI. If now the Velocity of Light be fo great as to enlighten this Globe in one Second, (See Num. VI. and VIII.) and a Candle of Six to the Pound will burn 5 Hours, there will be part of a Grain of Tallow spent in each Second. Confequently there will proceed from Ggg 3

of a Grain

of

of Tallow 41866026 Particles of Light, and 14 times fo many, or 5161240 from a whole Grain.

460

XXII. But one Grain is Part of an Inch of 10 to the Foot, Num. VII. there proceeds there< fore from one Inch of Candle-Tallow 460 times 53612402; or in one Number 2696170402 Particles of Light.

XXIII. But fuppofing with Mr. Leuwenhoek, 1000 Diameters or Lengths of one of these Animalcula equal to one Grain of Sand; and 100 Diameters of one Sand, to be the Length of an Inch, and 10 Inches the Length of one Foot.

Then 10 Diameters of the Animalcula make the Length of one Foot, and 10 of the fame, the Length of OE, or 10,000 Feet.

XXIV. Now we have fhown, Num. XVII. that altho' we throw away many Thousands of Millions of Light-Particles in the Globe QRSE, there be really 100 more Light-Particles, than when as above in Num. XX, we fuppofe but one fingle Particle in the fpace of each Animalculum. So that there proceeds from of a Grain of Tallow, 10 times more Particles than are fuppofed Num. XXI; and confequently from one Inch of Tallow, 10 more than in Num. XXII; that is, from one Inch of Tallow there will proceed 26961704022 fuch Particles.

XXV. And all this is true: Firft, Altho' we fhould fuppofe that there is but one Light-Particle in the Space of one Animalculum, at the extreme Part of the illuminated Globe, or at V E, which every Body fees is too little, confidering the gradual Increase of Light, as we come nearer to the Candle O. And Secondly, although the faid Globe fhould be enlighten'd but once in one Second, or that the Light paffes from O to E in that time.

But

But forafmuch as according to Num. VIII, the Light runs 1000 times fwifter, and does not only run once, but 1000 times the Length of OE on all Sides, there being 1000 of fuch Globes fill'd with Light by Part of a Grain of Tallow in one Second.

It plainly follows, that the Number found by Num. XXIV, must be multiply'd by 1000; and that one Inch of the Tallow burning in fuch a Candle does emit 269617040 Particles of Light, whereby the most astonishing Smallness and Number thereof is plainly Demonftrated.

40

SECT. XVI. How many Particles of Light fly out of a burning Candle in a Second.

To know then how many Particles of Light fly from a burning Candle in the Second of a Minute; it has been Demonftrated from the foregoing Confiderations, that of a Grain of Tallow is confumed in the Second of a Minute, or, which is the fame thing, one whole Grain in 14 Seconds. Now an Inch of Tallow contains 460 Grains, fo that an Inch of Wax or Candle-Tallow is burnt in 460 times 14, that is, in 6440 Seconds; in which time if there proceeds 2696170400 Particles of Light from an Inch of Tallow, there will fly out of a burning Candle in the Second of a Minute, the Number of 418660 Particles.

SECT. XVII. The Particles of Light compared with the Sand of the whole Earth.

AND fince according to the most exact Meafure of the French Aftronomers, the Diameter of the Earth amounts to39.231,564 Paris Feet, reckoning 10 Inches to one Foot, and that 100 Sands are equal to one Inch; the Number to be taken Ggg 4

for