Laplace's Law [Retrospectroscope]

In the two preceding notes about Laplace's law [1], [2], we first recalled what it is and how it is frequently mentioned or applied in physiology, finding that in this particular case, there is an apparent separation between physiology and physics supposedly backing up the subject. Moreover, mistakes are almost a rule while amazingly and fortunately, the overall practical conclusions after very heavy simplifications are correct and well demonstrated by actual experiments and postmortem studies. The second note dealt with the mathematics of the law, and we believe that we practically exhausted all the pathways leading to the final formula, both when the wall thickness is negligible and when it is finite and significant. Now, our hat displays the epistemologist's sign, up- setting perhaps some readers, but with- out totally leaving out the quantitative view. Hence, the objectives of the note are established as follows: T general objective: To introduce, discuss, and eventually produce answers for the epistemological aspects associated with Laplace's law specific objective: To discern if a mathematical equation has the same reach when obtained from two different physical settings (in our case, a phenomenon found in capillaries and the behavior of hollow stretch- able cavities).