A CENTURY'S PROGRESS IN PHYSICS 347 



in many cases. Failure with other more permanent 

 gases was unexplained until the researches of Andrews 

 in 1863 showed that no amount of pressure will produce 

 liquefaction unless the temperature is below a certain 

 critical value. The method of reducing the temperature 

 in use to-day depends on a fact discovered by Kelvin and 

 Joule in connection with the free expansion of a gas. 

 These investigators allowed the gas to escape through a 

 porous plug from a chamber in which the pressure was 

 relatively high. With the single exception of hydrogen, 

 the effect of the sudden expansion is to cool the gas, and 

 even with it cooling is found to take place after the tem- 

 perature has been made sufficiently low. By this method 

 all known gases have been liquefied. Helium, with a 

 boiling point of 269 C., or only 4C. above the absolute 

 zero, was the last to be made a liquid, finally yielding to 

 the efforts of Kammerlingh Onnes in 1907. This inves- 

 tigator 2 finds that at temperatures near the absolute zero 

 the electrical conductivity of certain substances undergoes 

 a profound modification. For example, a coil of lead 

 shows a superconductivity so great that a current once 

 started in it persists for days after the electromotive 

 force has ceased to act. 



Electrodynamics. Faraday's representation of elec- 

 tric and magnetic fields by lines of force had been of 

 great value in predicting the results of experiments in 

 electromagnetism. But a more mathematical formula- 

 tion of the laws governing these phenomena was needed 

 in order to make possible quantitative development of 

 the theory. This was supplied by Maxwell in his 

 epoch-making treatise on "Electricity and Mag- 

 netism." Starting with electrostatics and magnetism, 

 he gives a complete account of the mathematical 

 methods which had been devised for the solution 

 of problems in these branches of the subject, and 

 then turning to Ampere's work he shows how the 

 Lagrangian equations of motion lead to Faraday's law 

 if the single assumption is made that the magnetic 

 energy of the field is kinetic. In the treatment of open 

 circuits Maxwell's intuition led to a great advance, the 

 introduction of the displacement current. Consider a 

 charged condenser, the plates of which are suddenly con- 



