View source for A Compensating Term for the "Side Force Component" Term in the Barometric Equation

{{Infobox paper
| title = A Compensating Term for the \"Side Force Component\" Term in the Barometric Equation
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_567.pdf Link to paper]
| author = [[Donald G Carpenter]]
| keywords = [[atmosphere]], [[atmospheric particle motion]], [[barometric]]
| published = 2000
| journal = [[Apeiron]]
| volume = [[7]]
| num_pages = 5
| pages = 143-147
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_567.pdf here]

==Abstract==

The derivation of the barometric equation concerns central forces in three dimensions. It has recently been shown that the sum of the incremental volume's side force components in the direction of the center of gravity (the <span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">??</span></span><span style="FONT-SIZE: small; FONT-FAMILY: SymbolPS">(</span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">-</span></span><span style="FONT-FAMILY: Times New Roman"><span style="FONT-SIZE: xx-small"><span style="FONT-SIZE: xx-small">2</span></span>''<span style="FONT-SIZE: xx-small"><span style="FONT-SIZE: xx-small">p z</span></span>''</span><span style="FONT-SIZE: small; FONT-FAMILY: SymbolPS">)</span><span style="FONT-SIZE: xx-small"><span style="FONT-FAMILY: Times New Roman">(</span></span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">D</span></span>''<span style="FONT-SIZE: xx-small"><span style="FONT-SIZE: xx-small"><span style="FONT-FAMILY: Times New Roman">x</span></span></span>''<span style="FONT-SIZE: xx-small"><span style="FONT-FAMILY: Times New Roman">)(</span></span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">D</span></span>''<span style="FONT-SIZE: xx-small"><span style="FONT-SIZE: xx-small"><span style="FONT-FAMILY: Times New Roman">y</span></span></span>''<span style="FONT-SIZE: xx-small"><span style="FONT-FAMILY: Times New Roman">)(</span></span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">D</span></span>''<span style="FONT-SIZE: xx-small"><span style="FONT-SIZE: xx-small"><span style="FONT-FAMILY: Times New Roman">z</span></span></span>''<span style="FONT-SIZE: xx-small"><span style="FONT-FAMILY: Times New Roman">)</span></span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">?? </span></span>force) must be included in the Cartesian&nbsp; rivation.That results in the side force component term <span style="FONT-SIZE: small; FONT-FAMILY: SymbolPS">(</span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">-</span></span><span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">2</span></span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">p z</span></span>''<span style="FONT-SIZE: small; FONT-FAMILY: SymbolPS">) </span><span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">being added to the differential equation, or </span></span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">dp dz</span></span>''<span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">=-??</span></span><span style="FONT-SIZE: large; FONT-FAMILY: SymbolPS"><span style="FONT-SIZE: large; FONT-FAMILY: SymbolPS">(</span></span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">NmMGz</span></span>''<span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">2 </span></span><span style="FONT-SIZE: large; FONT-FAMILY: SymbolPS"><span style="FONT-SIZE: large; FONT-FAMILY: SymbolPS">)</span></span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">+</span></span><span style="FONT-SIZE: small; FONT-FAMILY: SymbolPS">(</span><span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">2</span></span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">p z</span></span>''<span style="FONT-SIZE: small; FONT-FAMILY: SymbolPS">)</span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">??</span></span><span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">. Meteorological data does not, though, conform unambiguously to the corrected barometric equation.&nbsp; This implies that an approximately compensating term might exist. Such a term results from consideration of the central force due to atmospheric particle random motion perpendicular to the radial from the center of gravity in a central force field (the </span></span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">??+</span></span><span style="FONT-SIZE: medium; FONT-FAMILY: SymbolPS"><span style="FONT-SIZE: medium; FONT-FAMILY: SymbolPS">(</span></span><span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">2</span></span><span style="FONT-SIZE: small; FONT-FAMILY: SymbolPS">(</span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">f </span></span>''<span style="FONT-SIZE: small; FONT-FAMILY: SymbolPS">)</span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">p </span></span>''<span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">3</span></span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">z</span></span>''<span style="FONT-SIZE: medium; FONT-FAMILY: SymbolPS"><span style="FONT-SIZE: medium; FONT-FAMILY: SymbolPS">)</span></span><span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">(</span></span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">D</span></span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">x</span></span>''<span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">)(</span></span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">D</span></span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">y</span></span>''<span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">)(</span></span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">D</span></span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">z</span></span>''<span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">)</span></span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">?? </span></span><span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">force, where ?</span></span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">f</span></span>''<span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">? represents the degrees of freedom). The more-complete barometric equation is: </span></span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">dp dz</span></span>''<span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">= -</span></span><span style="FONT-SIZE: large; FONT-FAMILY: SymbolPS"><span style="FONT-SIZE: large; FONT-FAMILY: SymbolPS">(</span></span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">NmMG z</span></span>''<span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">2 </span></span><span style="FONT-SIZE: large; FONT-FAMILY: SymbolPS"><span style="FONT-SIZE: large; FONT-FAMILY: SymbolPS">)</span></span><span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">+??</span></span><span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">2</span></span><span style="FONT-SIZE: small; FONT-FAMILY: SymbolPS">(</span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">f</span></span>''<span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">-</span></span><span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">3</span></span><span style="FONT-SIZE: small; FONT-FAMILY: SymbolPS">)</span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">p</span></span>''<span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">3</span></span>''<span style="FONT-FAMILY: TimesNewRoman,Italic"><span style="FONT-FAMILY: TimesNewRoman,Italic">z</span></span>''<span style="FONT-FAMILY: SymbolPS"><span style="FONT-FAMILY: SymbolPS">??</span></span><span style="FONT-FAMILY: TimesNewRoman"><span style="FONT-FAMILY: TimesNewRoman">. </span></span><b><span style="FONT-SIZE: small; FONT-FAMILY: Arial,Bold"><span style="FONT-SIZE: small; FONT-FAMILY: Arial,Bold">. </span></span></b>

[[Category:Scientific Paper|compensating term force component term barometric equation]]

[[Category:Gravity|compensating term force component term barometric equation]]