This Table is calculated from Briggs’s Logarithms: each Number, in the second Column, being nothing more than the Logarithm—corresponding to the Point, (in the first Column,) at which the Quicksilver stands in the barometric Tube,—subtracted from the Logarithm of 32 Inches multiplied by 6.

Construction of the second Table.

This Table consists of three vertical Columns only: tho’ here tripled, for the greater Convenience of Inspection.

The first or left Hand Column shews, in Inches and Tenths (from ten Inches) the Gradations of the Quicksilver in the barometric Tube, beginning as low as one Inch above the Surface in the Cistern, and proceeding throu’ all the intermediate Points, to the unusual Extent of 32 Inches:[121] supposing likewise that the Tube is elevated in the Atmosphere, so that the contained Quicksilver, when exposed to the Temperature of 31°.24 of Farenheit, rests at each Point in the Table.

The second vertical Column gives the different Heights in Feet and Tenths, to which the barometric Tube must be raised above its Level at 32 Inches, in order that the contained Quicksilver, if exposed to the Temperature of 31°.24 of Farenheit, may stand at each Point indicated in the first Column.

The third vertical Column, gives, likewise in Feet and Tenths, the difference between each two adjoining Heights in the second Column, corresponding to a single Tenth (of Quicksilver): which single Tenth is the Difference between each two adjoining Tenths of an Inch in the first Column.

For Example: Suppose the Quicksilver in the barometric Tube, in the first Column, stands at

Inches

16.1

 answering to

19570.4

 Height in Feet in the Atmosphere.
And again at

16.2

 answering to

19398.4

———
Difference of .1 in Feet: remaining

= 172.0

which sixteen Inches two Tenths, is a single Tenth more than sixteen Inches one Tenth, and will therefore answer to a less Height in the Atmosphere by that single Tenth; considering that the lower the Quicksilver falls in the Tube, the higher must the Barometer itself be raised in the Atmosphere, in order that the Quicksilver may rest at the lower Points of the Tube. If therefore a less Height in the Atmosphere be required which shall answer to one Tenth more than 16 Inches two Tenths; subtract the Height answering to 16.2 from the Height answering to 16.1, i. e. subtract the less Height from the greater, and the Remainder gives that less Height in the third Column, answering to the Height of one Tenth more than 16 Inches 2 Tenths, of the Barometer.

[121] The Barometer, (to which the Scale of Heights is applied, in the 2d Column of the 2d Table) is supposed to be sunk within the Surface of the Earth, till the Quicksilver rests at 32 Inches, as appears from the last Article in the table, viz. 32 Inches, 0.00 Feet. 32 Inches is therefore the Foundation of the Table, and corresponds, according to Shuckburgh, to 1647 Feet, under the Surface of the Sea, at low Water.