395. To find the Expansion of .6 above 4° on .178 above 24 Inches. The Expansion _with_ 4° _on_ .178 is already found to be .0000712: divide it by 4, and the Answer is .0000178, viz. the Expansion _with_ 1° _on_ .178 above 24 Inches: And, for the Expansion with .1 Tenth; the Answer, with the Addition of a Cypher and decimal Point to the left, becomes .00000178. Lastly, for the Expansion with .6, say, If .1 : .00000178 :: .6? Multiply the 2d and 3d Terms, and divide by first: .00000178 .6 —————————— .000001068. The Answer is a Decimal less, viz. .00001068; i.e. the Decimal of an Inch, to which .6 Tenths of a Degree above 4 Degrees of Heat, on .178 Tenths of an Inch above 24 Inches, raises the Barometer: which, after all, is so inconsiderable, that it may be fairly rejected. Yet the Rules by which these Deductions are made, may be useful in other Cases. Prepare for Addition, as before. The Decimals, in the Answers, may be omitted, when they exceed four Places. [Sidenote: 5th Step.] 396. 5th Step. To proceed with the second Example. Place the different Expansions now found, above each other, Units, Tens, &c. under Units, Tens, &c. preparatory to Addition, thus; For the Expansion _with_ 4°, .6 _on_ 24, .178: 1st. _with_ 4°, _on_ 24, .0097 2d. _with_ .6 _on_ 24, .00144 3d. _with_ 4°, _on_ .178 .0000712 4th. _with_ .6 _on_ .178 .00001068 ————————— The Expansions with 4°,.6 added = .01122188 To the Sum add the Height of the _colder_ Barometer 24.178 ——————————— 24.1892| The Answer is Height of the _colder_ Barometer, now equal in Temperature to the _warmer_: (rejecting all but the four first Decimals.) [Sidenote: 6th Step.] 397. 6th Step. Place the Barometers _now_ of the same Temperature, i.e. _equal_ to the warmer, in one View, thus: 1st. the _upper_ Barometer, 24.1892 2d. the _lower_ Barometer, 28.1328 END OF THE FIRST STAGE. _The 7th Step applied in the second Example._ [Sidenote: _7th Step._] 398. Find the Height, in Feet, in the 2d Column of the 2d Table, corresponding to Inches and Tenths of the _upper_ barometric Tube, in the 1st. Column of the same Table, thus: (Sect. 371.) The Barometer standing at 24.1892; it must be considered where, in the 2d Column of the 2d Table, a Height corresponding to _such_ Inches and Tenths can lie: and the Answer is, somewhere _above_ 24 Inches .1 Tenth, but not so high as 24 Inches .2 Tenths: 24 Inches .1892 Tenths, being _more_ than 24 Inches .1 Tenth, but _less_ than 24 Inches .2 Tenths. First then, look in the 1st Column for Inches 24, .1 Tenth; and the corresponding Height in Feet is 7388.0: but the Height for 24, .2, in the 2d Column, beneath the former Number, is _only_ 7280.1. [Sidenote: 8th Step.]