CHAPTER LXXVIII.
PRACTICE OF THE FOURTH EXAMPLE,[134] FOR MEASURING SMALL HEIGHTS.
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 with the warmer | 29.9865 |
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,
1st. To subtract the lower Barometer from the upper. Then,
2dly. By the 3d Column of the same Table, find the difference, (viz. of one or two Tenths at the most) below the Inches and nearest Tenth of the lower Barometer.
And lastly, with that difference, find by the 3d Table, the Height at the Standard-Heat, corresponding to the remaining Decimals above the upper Barometer.
| 421. (1st.) From the lower Barom. viz. | 30.082 |
| Subtract the upper | 29.9865 |
| ——— | |
| Remaining Decimals above the upper | .0955 |
2d. Find, by the 2d Table, the Height corresponding to the Inches, and nearest Tenth above and below the Point at which the Quicksilver rests in the lower Barometer.
The Inches and nearest Tenth is
| above 30 Inches, correspond. to Feet | 1681.7 |
| and below 30.1, corresponding to | 1595.0 |
| ——— | |
| 86.7 |
which is the difference of .1 below 30.1.
Lastly. Find, by the 3d Table, with the difference, viz. 86 Feet, on the remaining Decimals, for the Height, in Feet, corresponding to the Standard-Heat.
| viz. | .09 | 77 | = | 77. Feet. |
| .005 | 43 | = | 4.3 | |
| .0005 | 43 | = | .43 | |
| ——— | ||||
| Answer, Height in Feet | 81.73 | |||
corresponding to .0955 above Inches 29.9865 Tenths of an Inch, of Quicksilver in the upper Barometer thus brought to the Standard-Heat.
422. Prepare for Expansion of Air from Excess above Standard-Heat, on the same Number of Feet:
| Detached Thermom. above | 76°. | |
| Detached Thermom. below | 68.0 | |
——— | ||
| Whole Heat | 144.0 | |
| Half Heat | 72.0 | (0 adding a Cypher) |
| Standard-Heat | 31.24 | |
| which deduct, and there remains | ——— | |
40.76: |
with which, by the 4th Table, find the Expansion of Air on Feet 81.73:
| First, with 40°, on 81.73, thus: | |||
on 80. | as 8000 | 777.6 = | 7.776 |
1. | as 1000 | 97.2 = | .0972 |
.7 | as 7000 | 680.4 = | .06804 |
.03 | as 3000 | 291.6 = | .002916 |
| ———— | |||
| 7.944156 | |||
| Second, with .76 on 81.73, thus: | |||
on 80. | as 8000 | 1477.4 = | .14774 |
1. | as 1000 | 184.6 = | .001846 |
.7 | as 7000 | 1292.7 = | .0012927 |
.03 | as 3000 | 554.0 = | .0000554 |
| ———— | |||
Expansion | .1509341 | ||
| add the former Expansion | 7.944156 | ||
| ———— | |||
| Sum of the Expansions, viz. Height in Feet from Excess of Heat above Standard, with 40°.76 on 81.73, | 8.0950901 | ||
| added to the Height at the Standard-Heat, in Feet | 81.73 | ||
| ———— | |||
| gives, in Feet and Tenths, the true Height of the Tarpeian Rock | 89.8|2. | ||
