from a change in the permeability of the axonal membrane to ions. Bernstein was also the first to introduce the Nernst equation for resting potential across the membrane. In 1907, Louis Lapicque suggested that the action potential was generated as a threshold was crossed, what would be later shown as a product of the dynamical systems of ionic conductances. A great deal of study on sensory organs and the function of nerve cells was conducted by British physiologist Keith Lucas and his protege Edgar Adrian. Keith Lucas' experiments in the first decade of the twentieth century proved that muscles contract entirely or not at all, this was referred to as the all-or-none principle. Edgar Adrian observed nerve fibers in action during his experiments on frogs. This proved that scientists could study nervous system function directly, not just indirectly. This led to a rapid increase in the variety of experiments conducted in the field of neurophysiology and innovation in the technology necessary for these experiments. Much of Adrian's early research was inspired by studying the way vacuum tubes intercepted and enhanced coded messages. Concurrently, Josepht Erlanger and Herbert Gasser were able to modify an oscilloscope to run at low voltages and were able to observe that action potentials occurred in two phases—a spike followed by an after-spike. They discovered that nerves were found in many forms, each with their own potential for excitability. With this research, the pair discovered that the velocity of action potentials was directly proportional to the diameter of the nerve fiber and received a Nobel Prize for their work. Kenneth Cole joined Columbia University in 1937 and remained there until 1946 where he made pioneering advances modelling the electrical properties of nervous tissue. Bernstein's hypothesis about the action potential was confirmed by Cole and Howard Curtis, who showed that membrane conductance increases during an action potential. David E. Goldman worked with Cole and derived the Goldman equation in 1943 at Columbia University. Alan Lloyd Hodgkin spent a year (1937–38) at the Rockefeller Institute, during which he joined Cole to measure the D.C. resistance of the membrane of the squid giant axon in the resting state. In 1939 they began using internal electrodes inside the giant nerve fibre of the squid and Cole developed the voltage clamp technique in 1947. Hodgkin and Andrew Huxley later presented a mathematical model for transmission of electrical signals in neurons of the