END OF THE SECOND STAGE.374. The Ends proposed in the third and last Stage of the Work, are, first, to add thegeneralTemperatures of the Air, or detached Air-Thermometers, at each Place of Observationaboveandbelow, into one Sum.Secondly, to divide that Sum: each Moiety of which is called themean Temperatureof the Air.Thirdly, to apply that Moiety to each Barometer, (both of which have been already brought to the Standard-Temperature of 31°. 24;) in order to prove whether the Moiety (or Quantity of Heat assigned to each Barometer by thegeneralTemperature of the Air)exceeded,fell short of, or equalled the Standard-Temperature of the Barometers, by the 2d Table.And fourthly, from the Moiety or mean Temperature of the Air, to find the true Height of the upper Barometer: which Temperature resolves itself into three Cases.375. 1st. If the Moiety or mean Temperature of the Air is greater than the Standard Temperature, viz. that to which the Barometers are now brought; find the Expansion of Air corresponding to suchExcessof Temperature by the fourth Table, which Height by Expansion, being added to the Height already found in the 2d Table, shews the true Height, viz. of the upper Barometer.N. B. The 3d and last Stage includes two Steps only, viz, 11th and 12th.376. 11th Step. The detached Air-Thermometerabovewas391⁄2Degrees.The detached Air-Thermometerbelowwas451st. Add them, for the whole Heat.2)841⁄22d. Formean Temperatureof the Air-Thermometers, or aMoietyof the Heat, divide by 2.421⁄43d. Deduct the Standard-Temperature of311⁄4——from either Moiety, and the Remainder11is the 11 Degrees of Heat, more than the Standard[123]for each Barometer.For 42°1⁄4, and 42°1⁄4, equal to 84°1⁄2, was the whole Height of the Air at both Places of Observation in the upper and lower Stations; of which whole Height the detached or Air-Thermometerabovereceived 39°1⁄2, and the detached or Air-Thermometerbelow, received 45°.377. 12th Step. Find the Height corresponding to the Expansion of Air, with Excess of Heat or Temperature above the Standard-Temperature of the Barometers: and add it (as in the first Example) to the Height of the upper Barometer, corresponding to the Standard-Temperature already found in thesecondTable, and the Sum is thetrueHeight of the upper Barometer.This is to be done by referring to the 4th Table, shewing Expansion of Air with Heat; for the Application of which there are separate Instructions: see the Explanation of the 4th Table.[124]378. The Expansion of Air, in the first Example, is found by the 4th Table to be Feet107.3 Tenthshigherthan the 4016.8, viz. the Remainder from the 2d Table (Section 371); which Numbers added give 4124.1 Feet: viz. the true Height of the upper Station required.
END OF THE SECOND STAGE.
374. The Ends proposed in the third and last Stage of the Work, are, first, to add thegeneralTemperatures of the Air, or detached Air-Thermometers, at each Place of Observationaboveandbelow, into one Sum.
Secondly, to divide that Sum: each Moiety of which is called themean Temperatureof the Air.
Thirdly, to apply that Moiety to each Barometer, (both of which have been already brought to the Standard-Temperature of 31°. 24;) in order to prove whether the Moiety (or Quantity of Heat assigned to each Barometer by thegeneralTemperature of the Air)exceeded,fell short of, or equalled the Standard-Temperature of the Barometers, by the 2d Table.
And fourthly, from the Moiety or mean Temperature of the Air, to find the true Height of the upper Barometer: which Temperature resolves itself into three Cases.
375. 1st. If the Moiety or mean Temperature of the Air is greater than the Standard Temperature, viz. that to which the Barometers are now brought; find the Expansion of Air corresponding to suchExcessof Temperature by the fourth Table, which Height by Expansion, being added to the Height already found in the 2d Table, shews the true Height, viz. of the upper Barometer.
N. B. The 3d and last Stage includes two Steps only, viz, 11th and 12th.
N. B. The 3d and last Stage includes two Steps only, viz, 11th and 12th.
391⁄2
45
2)841⁄2
421⁄4
311⁄4
——
11
is the 11 Degrees of Heat, more than the Standard[123]for each Barometer.
For 42°1⁄4, and 42°1⁄4, equal to 84°1⁄2, was the whole Height of the Air at both Places of Observation in the upper and lower Stations; of which whole Height the detached or Air-Thermometerabovereceived 39°1⁄2, and the detached or Air-Thermometerbelow, received 45°.
377. 12th Step. Find the Height corresponding to the Expansion of Air, with Excess of Heat or Temperature above the Standard-Temperature of the Barometers: and add it (as in the first Example) to the Height of the upper Barometer, corresponding to the Standard-Temperature already found in thesecondTable, and the Sum is thetrueHeight of the upper Barometer.
This is to be done by referring to the 4th Table, shewing Expansion of Air with Heat; for the Application of which there are separate Instructions: see the Explanation of the 4th Table.[124]
378. The Expansion of Air, in the first Example, is found by the 4th Table to be Feet107.3 Tenthshigherthan the 4016.8, viz. the Remainder from the 2d Table (Section 371); which Numbers added give 4124.1 Feet: viz. the true Height of the upper Station required.