When is a law too idealized to be usefully applied to a specific situation? To answer this question, this essay considers a law in hydrogeology called Darcy''s Law, both as it is used in what is called the symmetric-cone model, and as it is used in equations to determine a well''s groundwater velocity and hydraulic conductivity. After discussing Darcy''s law and its applications, the essay concludes that this idealized law, as well as associated models and equations in hydrogeology, are not (...) realistic in the sense required by the D-N account. They exhibit what McMullin calls mathematical idealization, construct idealization, empirical-causal idealization, and subjunctive-causal idealization. Yet this lack of realism in hydrogeology is problematic for reasons unrelated to the status of the D-N account. These idealizations are also problematic in applied situations. Their problems require developing two supplemental criteria, necessary for their productive application. (shrink)

In the history of thermodynamics, two dates stand out as especially important: 1824, when Sadi Carnot's brilliant memoirRéflexions sur la puissance motrice du feuappeared in print; and 1850, when Rudolf Clausius published his similarly titled paper ‘Ueber die bewegende Kraft der Wärme’. In this paper Clausius narrowly beat the Scottish physicist William Thomson to the solution of a puzzle which had been highlighted in the latter's recent publications: how could Carnot's theory, with all its intellectual attractions, be reconciled with the (...) newly discovered principle of the inter-convertibility of heat and work? Clausius's solution (as is well known) was to replace Carnot's axiom of heat conservation, with the axiom now known as the second law of thermodynamics. (shrink)