Then letting down the Tube again, I opened the top, and then thrust down the small Tube, till I perceived the Quicksilver to rise within it to a mark that I had plac’d just an inch from the top; and immediately clapping on a small piece of cement that I had kept warm, I with a hot Iron seal’d up the top very fast, then letting it cool (that both the cement might grow hard, and more especially, that the Air might come to its temper, natural for the Day I try’d the Experiment in) I observ’d diligently, and found the included Air to be exactly an Inch.

Here you are to take notice, that after the Air is seal’d up, the top of the Tube is not to be elevated above the superficies of the Quicksilver in the box, till the surface of that within the Tube be equal to it, for the Quicksilver (as I have elsewhere prov’d) being more heterogeneous to the Glass then the Air, will not naturally rise up so high within the small Pipe, as the superficies of the Mercury in the box, and therefore you are to observe, how much below the outward superficies of the Mercury in the box, that of the same in the Tube does stand, when the top being open, free ingress is admitted to the outward Air.

Having thus done, I permitted the Cylinder, or small Pipe, to rise out of the box, till I found the surface of the Quicksilver in the Pipe to be two inches above that in the box, and found the Air to have expanded it self but one sixteenth part of an inch; then drawing up the small pipe, till I found the height of the Quicksilver within to be four inches above that without, I observed the Air to be expanded only ⅐ of an inch more then it was at first, and to take up the room of 1⅐ inch: then I raised the Tube till the Cylinder was six inches high, and found the Air to take up 1²⁄₉ inches of room in the Pipe; then to 8, 10, 12. &c. the expansion of the Air that I found to each of which Cylinders are set down in the following Table; where the first row signifies the height of the Mercurial Cylinder; the next, the expansion of the Air; the third, the pressure of the Atmosphere, or the highest Cylinder of Mercury, which was then neer thirty inches: The last signifies the force of the Air so expanded, which is found by substracting the first row of numbers out of the third; for having found, that the outward Air would then keep up the Quicksilver to thirty inches, look whatever of that height is wanting must be attributed to the Elater of the Air depressing. And therefore having the Expansion in the second row, and the height of the subjacent Cylinder of Mercury in the first, and the greatest height of the Cylinder of Mercury, which of it self counterballances the whole pressure of the Atmosphere; by substracting the numbers of the first row out of the numbers of the third, you will have the measure of the Cylinders so deprest, and consequently the force of the Air, in the several Expansions, registred.

The height of the Cylinder of Mercury, that, together with the Elater of the included Air, ballanced the pressure of the Atmosphere. The Expansion of the Air. The height of the Mercury that counter-ballanc’d the Atmosphere.The strength of the Elater of the expanded Air.
00 01 30 30
02 01¹⁄₁₆ 30 28
04 01⅐ 30 26
06 01²⁄₉ 30 24
08 01⅓ 30 22
10 01½ 30 20
12 01⅔ 30 18
14 01⅚ 30 16
16 02²⁄₂₇ 30 14
18 02⁴⁄₉ 30 12
20 03 30 10
22 03⁷⁄₉ 30 8
24 05⁷⁄₁₈ 30 6
25 06⅔ 30 5
26 08½ 30 4
26¼ 09½ 30 3¾
26½ 10¾ 30 3½
26¾ 13 30 3¼
27 15½ 30 3

I had several other Tables of my Observations, and Calculations, which I then made; but it being above a twelve month since I made them; and by that means having forgot many circumstances and particulars, I was resolved to make them over once again, which I did August the second 1661. with the very same Tube which I used the year before, when I first made the Experiment (for it being a very good one, I had carefully preserv’d it:) And after having tryed it over and over again; and being not well satisfied of some particulars, I, at last, having put all things in very good order, and being as attentive, and observant, as possibly I could, of every circumstance requisite to be taken notice of, did register my several Observations in this following Table. In the making of which, I did not exactly follow the method that I had used at first; but, having lately heard of Mr. Townly’s Hypothesis, I shap’d my course in such sort, as would be most convenient for the examination of that Hypothesis; the event of which you have in the latter part of the last Table.

The other Experiment was, to find what degrees of force were requisite to compress, or condense, the Air into such or such a bulk.

The manner of proceeding therein was this: I took a Tube about five foot long, one of whose ends was sealed up, and bended in the form of a [Schem. 37.]
Fig. 4. Syphon, much like that represented in the fourth Figure of the 37. Scheme, one side whereof AD, that was open at A, was about fifty inches long, the other side BC, shut at B, was not much above seven inches long, then placing it exactly perpendicular, I pour’d in a little Quicksilver, and found that the Air BC was 6⅞ inches, or very near to seven; then pouring in Quicksilver at the longer Tube, I continued filling of it till the Air in the shorter part of it was contracted into half the former dimensions, and found the height exactly nine and twenty inches; and by making several other tryals, in several other degrees of condensation of the Air, I found them exactly answer the former Hypothesis.

But having (by reason it was a good while since I first made) forgotten many particulars, and being much unsatisfied in others, I made the Experiment over again, and, from the several tryals, collected the former part of the following Table: Where in the row next the left hand 24. signifies the dimensions of the Air, sustaining only the pressure of the Atmosphere, which at that time was equal to a Cylinder of Mercury of nine and twenty inches: The next Figure above it (20) was the dimensions of the Air induring the first compression, made by a Cylinder of Mercury 5³⁄₁₆ high, to which the pressure of the Atmosphere nine and twenty inches being added, the elastick strength of the Air so comprest will be found 34³⁄₁₆, &c.

A Table of the Elastick power of the Air, both Experimentally and Hypothetically calculated, according to its various Dimensions.

The dimensions of the included Air.The height of the Mercurial Cylinder counter-pois’d by the Atmosphere.The Mercurial Cylinder added, or taken from the former.The sum or difference of these two Cylinders.What they ought to be according to the Hypothesis.
---------- ----------------- -------- ----------
12 29 + 29 = 58 58
13 29 + 24¹¹⁄₁₆ = 53¹¹⁄₁₆ 53⁷⁄₁₃
14 29 + 20³⁄₁₆ = 49³⁄₁₆ 49⁵⁄₇
16 29 + 14 = 43 43½
18 29 + 9⅛ =38⅛38⅔
20 29 + 5³⁄₁₆ = 34³⁄₁₆ 34⅘
24 29 0 = 29 29
48 29 − 14⅝ =14⅜14½
96 29 − 22⅛ = 6⅞ 7²⁄₈
192 29 − 25⅝ = 3⅜ 3⅝
384 29 − 27²⁄₈ = 1⁶⁄₈ 1⁷⁄₁₆
576 29 − 27⅞ = 1⅛ 1⁵⁄₂₄
768 29 − 28⅛ = 0⅞ 0[7¼]⁄₈
960 29 − 28⅜ = 0⅝ 0[5⅘]⁄₈
1152 29 − 28⁷⁄₁₆ = 0⁹⁄₁₆ 0¹⁰⁄₁₆