_End of the last Stage._ CHAPTER LXXVIII. PRACTICE OF THE FOURTH EXAMPLE,[134] FOR MEASURING SMALL HEIGHTS. [Sidenote: By this Example, _small_ Heights are easily measured.] Section 419. Attached Therm. _below_, 71°.0 Attached Therm. _above_, 70 .5 ————— Subtract, and there remains .5 Tenths of a Degree of Heat to be added to the _colder_ Barometer (which in the present Case is the _upper_, but might possibly have been otherwise) by the 1st Table. _First_, _with_ 0°.5 _on_ 29 Inches. To obtain which, begin _with_ 1°.0 _on_ 29 Inches = .002: _with_ 0°.1 above 1°, _on_ 29 = .0002: then _with_ 0°.5 above 1°, _on_ 29 = .001. Prepare it for Addition to the _colder_ Barometer. colder Barometer 29.985 Expansion _with_ .5 above 1°, _on_ 29 .001 —————— 29.986 _Secondly_, _with_ .5 Tenths above 1°, _on_ .985 Tenths above 29 Inches. To obtain which, (having already found the Height from Expansion _with_ .5 above 1°, _on_ 29 Inches, to be .001;) since the Expansion on .985 Tenths above 29 Inches, is somewhere above 29, yet below 30 Inches; find the Expansion _with_ .5 above 1°, _on_ 30 Inches, thus: first, _with_ 1°, _on_ 30 = .003 2d. _with_ 0°.1 above 1°, _on_ 30 = .0003 3d. _with_ 0°.5 above 1°, _on_ 30 = .0015 Subtract the Expansion _with_ .5 Tenths above 1°, _on_ 29 Inches, from the Expansion _with_ .5 Tenths above 1°, _on_ 30 Inches: viz. _on_ 30 = .0015 _on_ 29 = .001 ————— The Answer is .0005, the Height from Expansion, _with_ .5 Tenths above 1°, _on_ 1 Inch above 29, i.e. on the 30th Inch: Then, if 1 Inch above 29 gives .0005; .1 gives .00005: and 985 ——————— multiplied 00025 as whole 00040 Numbers, 00045 ———————— give .0004|925 add the former Number 29.986 and, for the three remaining Decimals, _may_ be substituted 1 Decimal in the fourth Place 1 ——————— colder Barometer of equal Heat } 29.9865 with the _warmer_ } 420. _When the Quicksilver in each Barometer indicates the same Number of Inches_, differing _but_ one _or_ two Tenths _at the most; (which will frequently be the Case, in levelling flat Countries, or measuring small Heights;—instead of the usual Method, (to find the Height of each Barometer_ separately, _with the Standard-Heat, by the_ 2d Column _of the 2d Table, as in Section 411;)—it will be more convenient,_