First law
What law describes the proportionality of the amount of a given substance to the amount of electricity passing through it?
Electrochemistry
Amount of substance Electrolysis Glossary of fuel cell terms Electrochemistry Harmelin v. Michigan
Amount_of_substance-Derived_quantities Electrolysis-Second_law_of_electrolysis Glossary_of_fuel_cell_terms-Expansion_ratio Electrochemistry-First_law Harmelin_v._Michigan-White's_proportionality_argument
When amount of substance enters into a derived quantity, it is usually as the denominator: such quantities are known as molar quantities. For example, the quantity which describes the volume occupied by a given amount of substance is called the molar volume, while the quantity which describes the mass of a given amount of substance is the molar mass. Molar quantities are sometimes denoted by a subscript Latin "m" in the symbol, e.g. "C""p",m, molar heat capacity at constant pressure: the subscript may be omitted if there is no risk of ambiguity, as is often the case in pure chemistry. The main derived quantity in which amount of substance enters into the numerator is amount of substance concentration, "c". This name is often abbreviated to "amount concentration", except in clinical chemistry where "substance concentration" is the preferred term (to avoid any possible ambiguity with mass concentration). The name "molar concentration" is incorrect, if commonly used. 
Faraday discovered that when the same amount of electricity is passed through different electrolytes/elements connected in series, the mass of substance liberated/deposited at the electrodes is directly proportional to their equivalent weights. 
  Expansion ratio is used in the context of liquefied and cryogenic substances. The expansion ratio of a substance is the volume of a given amount of that substance in liquid form compared to the volume of the same amount of substance in gaseous form, at a given temperature.  
Faraday concluded after several experiments on electrical current in non-spontaneous process, the mass of the products yielded on the electrodes was proportional to the value of current supplied to the cell, the length of time the current existed, and the molar mass of the substance analyzed. In other words, the amount of a substance deposited on each electrode of an electrolytic cell is directly proportional to the quantity of electricity passed through the cell. Below is a simplified equation of Faraday's first law: formula_7 Where "m" is the mass of the substance produced at the electrode (in grams), "Q" is the total electric charge that passed through the solution (in coulombs), "n" is the valence number of the substance as an ion in solution (electrons per ion), "M" is the molar mass of the substance (in grams per mole).
Justice White's point of departure was the fact that "the Amendment does not refer to proportionality in so many words, but it does forbid 'excessive' fines, a restraint that suggests that a determination of excessiveness should be based at least in part on whether the fine imposed is disproportionate to the crime committed." Accordingly, the Eighth Amendment imposed a strong proportionality requirement not simply on fines, but on all criminal punishments, including prison terms. White took issue with three premises of Scalia's argument. First, for White, the fact that the Framers were not as plain-spoken as Scalia would have preferred was no obstacle to concluding that the Eighth Amendment did indeed contain a proportionality requirement. Second, although the newly formed federal government did not, in 1791, have any "track record with respect to criminal law," they had lived under the regime of the several states for some time, and so there would be some benchmarks by which to evaluate proportionality of punishments. Third, even if the original understanding of the Eighth Amendment did not include a proportionality requirement, 20th-century decisions of the Court had imposed one. White takes Scalia to task for claiming at once that the Eighth Amendment must have no proportionality guarantee whatsoever and then that that guarantee can apply only in capital cases. White's argument proceeds from the premise that "the scope of the prohibition against cruel and unusual punishments has long understood the limitations of a purely historical analysis." In other words, when it comes to the Eighth Amendment, the Court must employ a flexible and dynamic interpretation. The Court therefore has recognized that a punishment may violate the Eighth Amendment if it is contrary to the evolving standards of decency that mark the progress of a maturing society. In evaluating a punishment under this test, we have looked not to our own conceptions of decency, but to those of modern American society as a whole in determining what standards have evolved, and thus have focused not on the subjective views of individual Justices, but on objective factors to the maximum possible extent." It is this type of objective factor which forms the basis for the tripartite proportionality analysis set forth in "Solem". Finally, White argued that the "Solem" test works well in practice. Simply because courts will be reviewing sentences for proportionality does not mean that courts will strike them down with great frequency. "Solem" requires a certain amount of deference to the legislature, and courts have proven able to apply that amount of deference. And although Scalia concedes that an egregious prison term—such as life in prison for overtime parking—would be unconstitutional, White faults him for striking such extreme punishments down in a principled manner. White also argues that adopting Scalia's view of the proportionality requirement would strike at the foundation of the Court's capital punishment jurisprudence, much of which would then "rest on quicksand". 