Supposing therefore that the Portion of the Tube containing Air, was one Foot in Length of Height, divided also into a thousand Parts; one Degree of Heat would encrease or expand it two Parts and four Tenths more than the thousand Parts into which the Foot was divided. CAUTION. _The fourth Table properly consists of only nine horizontal Columns of thousands, in Breadth; which Columns are extended in Length to one hundred Lines, corresponding to 100 Degrees of Heat._ _The Table is here divided, in order that it may conform to the Size of the Pages: by which Means the Formation of each vertical Number by the following Rule, (which renders the Table_ self-evident_) might without this Caution, have been attended with some Difficulty._ The vertical Columns _below_ the Figures expressing each thousand, shew the Expansion of Air _on_ each respective thousand, _with_ the corresponding Degrees of Temperature indicated by the Thermometer in the vertical Column to the left Hand. Example the first: to find the Expansion of Air _on_ one thousand Feet, _with_ one Degree of Temperature; the Answer in the Table is 2.4, or 2.43: i.e. 2 Feet and 4 Tenths of a Foot, rejecting the 2d Decimal as too minute. Example the second: to find the Expansion _on_ 8 thousand Feet, _with_ 99 Degrees of Heat: the Answer is 1924.56: and so of the Rest. Thus _any_ of the _vertical Numbers_ shewing the Expansion, may be readily _formed_, by _doubling_, _first_, the Number immediately under each thousand in the horizontal Line, for the nine first thousands, (of which the Breadth of the Table properly consists, exclusive of the thermometric Column) for the Expansion below it: and, _afterwards_, for each Expansion immediately below the former, by adding, to the Expansion _last_ found, the Number immediately under its respective thousand. First Example: to find the vertical Number for the Expansion under the first thousand, viz. 1000, _with_ 2 Degrees of Heat: the Number under 1000 is 2.43: double this: and the Answer is 4.86. Second Example: suppose the Expansion _last_ found be that _on_ one thousand Feet _with_ 24 Degrees of Heat; viz. 58.32: and the Expansion _on_ the same thousand, _with_ one Degree of Heat more, viz. on 25 Degrees, be required; add the Expansion _on_ one thousand Feet, _with_ 24 Degrees, viz. 58.32 to the Expansion _on_ the same 1000, _with_ 1 Degree, viz. 2.43 ————— and the Answer is, by Addition, 60.75 Third Example: supposing the Expansion _last_ found to be the Expansion _on_ 9000 Feet _with_ 99 Degrees of Heat, which in the Table is 2165.1. It is required to find the Expansion _on_ the same 9000 Feet, with 100 Degrees of Heat; add to the Expansion last found,