The Answer is the same as the former, viz. .0004, with the Addition of a Cypher and decimal Point to the left, thus; .0004 becomes .00004, viz. the Expansion _with_ 4°, _on_ .1 Tenth of an Inch above 24 Inches. Then for the Expansion _with_ 4°, _on_ .178 Tenths, say, If the Expansion _with_ 4°, _on_ .1 Tenth above 24 Inches gives .00004 Part of an Inch, what will the Expansion _with_ 4°, _on_ .178 give? Thus; .1 : .00004 :: .178? Multiply the two last Terms, thus: .00004 .178 —————— 00032 00028 00004 ——————— 0000712: and, as in Multiplication of Decimals, the Product must have as many decimal Places, as are in the Factors; a Cypher must be added to the left Hand, thus: .00000712: but having divided that Product by the first Term .1, viz. a Decimal, the Answer is a Cypher less; viz. .0000712. This Answer is the Expansion _with_ 4°, _on_ .178 Tenths of an Inch above 24 Inches: prepare it for _Addition_, as the former, 24.178 .0097 .0000712 +practice+ of the first Part of _Case the 2d._ 394. For the Expansion of .6 Tenths of a Degree of Heat, (more than the 4 Degrees) on 24 Inches of the _coldest_ Barometer; it shoud be considered where such Tenths can lie in the Table. Now .6 Tenths of 1 Degree, (more than the 4°) are at some intermediate Point of the Thermometer between 1 and 2 Degrees: above 1; yet not so high as 2: or more than 1; yet less than 2. Therefore .6 Tenths of 1 Degree above 4 Degrees, are somewhere between the 4th and 5th Degree: above 4; yet not so high as 5: or more than 4; yet less than 5. Look in the Table (Section 363); first _with_ 4 Degrees of Heat, _on_ 24 Inches, and then _with_ 5 Degrees of Heat _on_ 24 Inches; and the respective Numbers are .0097 and .0121: and by taking the Expansion _with_ 4 Degrees _on_ 24 Inches, from the Expansion _with_ 5 Degrees _on_ the same 24 Inches; the Remainder will be the Expansion _with_ 1 Degree above 4° _on_ 24 Inches: viz. _with_ {5° = .0121} _on_ 24 Inches, as in whole {4° = .0097} Numbers. ————— Remainder, .0024 This therefore is the Expansion _with_ 1 Degree of Heat, above 4, viz. _with_ the 5th Degree, _on_ 24 Inches of the Barometer. Then say, if 1 Degree of the Thermometer (above 4, viz. the 5th Degree) gives by Expansion, a certain additional Height, or Part of an Inch, viz. .0024, _on_ 24 Inches of the Barometer; what Height will 6 Degrees give? Answer 6 Times _more_. Multiply the 2d and 3d Terms, and divide by the first, thus; 1 : .0024 :: 6? 6 ————— .0144 is the Expansion, or Height, in Parts of an Inch, for 6 Degrees. And farther, to proportion for the Decimal; say as .1 Tenth of a Degree gives a certain Tenth of the former .0024, in additional Height, viz. .00024; what Height will .6 Tenths give? Answer, .00144. Prepare this _Height_ for Addition to the Numbers already found. +practice+ of the 2d Part of _Case the 2d._