## Sentence Examples

**P**. 211,**Paris**, 1869)**proposed****an****equation****of****the****form**(**p**+**po**)(**v**-**b**) =**RO**,**in****which****the****effect****of****the****size****of****the****molecules****is****represented****by****subtracting****a****quantity****b**,**the**"**covolume**,"**from****the****volume****occupied****by****the****gas**,**and****the****effect****of****the****mutual****attractions****of****the****molecules****is****represented****by****adding****a****quantity****po**,**the****internal****pressure**,**to****the****external****pressure**,**p**.**This****type****of****equation**,**was****more****fully****worked****out****by****van****der****Waals**,**who****identified****the****internal****pressure**,**po**,**with****the****capillary****pressure****of****Laplace**,**and****assumed****that****it****varied****directly****as****the****square****of****the****density**,**and****could****be****written****a**/**v**2 .**According****to****van****der****Waals**,**assuming****spherical****molecules**,**it****should****be****four****times**;**according****to****O**.**Van****der****Waals**,**in****a****famous****monograph**,**On****the****Continuity****of****the****Liquid****and****Gaseous****States**(**Leiden**, 1873),**has****shown****that****the****imperfections****of****equation**(14)**maybe****traced****to**two_causes: (**i**.)**The****calculation****has****not****allowed****for****the****finite****size****of****the****molecules**,**and****their****consequent****interference****with****one****another'****s****motion**,**and**(**ii**.)**The****calculation****has****not****allowed****for****the****field****of****inter-molecular****force****between****the****molecules**,**which**,**although****small**,**is****known****to****have****a****real****existence**.**To****allow****for****the****first****of****these****two****factors**,**Van****der****Waals****finds****that****v****in****equation**'04)**must****be****replaced****by****v**-**b**,**where****b****is****four****times****the****aggregate****space****occupied****by****all****the****molecules**,**while****to****allow****for****the****second****factor**,**p****must****be****replaced****by****p**+**a**/**v**2 .**The****variation****of****gases****from****Boyle'****s****law****is****represented****in****the****equation****of****Van****der****Waals****by****subtracting****a****constant****b****from****the****total****volume****to****represent****the****effect****of****the****volume****of****the****molecules****themselves**.**Perhaps****a****satisfactory****point****of****view****may****be****here****obtained****by****applying****the****van****der****Waals**'**equation****A**(**P**-{-**a**/V2)(**V-b**)=2T,**which****connects****volume****V**,**pressure****P****and****temperature****T**(**see****Condensation****Of****Gases**).**In****fact**,**the****quantity**41rp 2**K**,**which****we****may****call****with****van****der****Waals****the****molecular****pressure**,**is****so****great****for****most****liquids**(5000**atmospheres****for****water**),**that****in****the****parts****near****the****surface**,**where****the****molecular****pressure****varies****rapidly**,**we****may****expect****considerable****variation****of****density**,**even****when****we****take****into****account****the****smallness****of****the****compressibility****of****liquids**.**Van****der****Waals**,**G**.