Then, as Hodgkin relates in his memoirs:

- "Finally there was the difficulty of computing the action potentials from the equations which we had developed. We had settled all the equations and constants by March 1951 and hoped to get these solved on the Cambridge University computer. However, before anything could be done we learnt that the computer would be off the air for 6 months or so while it underwent a major modification. Andrew Huxley got us out of that difficulty by solving the differential equations numerically using a hand-operated Brunsviga. The propagated action potential took about three weeks to complete and must have been an enormous labour for Andrew. But it was exciting to see it come out with the right shape and velocity and we began to feel that we had not wasted the many months that we had spent in analysing records."

*Numerical integration by hand-crank calculator*

Huxley began the slow work of using a Brunsviga 20 manually cranked calculator with numbers entered by a set of adjusting levers (projecting from the wheels that were rotated by the hand crank). The output was a line of digits on the wheels to be read and transcribed to paper. First, he found that the time and voltage sensitivities of the ionic conductances could be reproduced. Then the long process of numerical integration of the action potential began. Tabular records of the rate and state variables were entered into the the levers and transcribed from the dials for small increments of time. Huxley used a tedious iterative, error-correcting, numerical integration method to estimate and correct for numerical integration errors. The fact that the whole process for calculation of a 4-5 ms interval, showing the initiation of and recovery following an action potential, could be accomplished in 8 hours is astonishing. The calculated action potentials were -- with the exception of a small "gratuitous bump" late in the falling phase -- excellent reproductions of the experimental observations under a variety of conditions.

*Numerical integration today - -*

Of course, both the speed and power of today's desktop computers far surpass those of the 1950s, but it is interesting to compare by how much. The first numerical integration of the Hodgkin and Huxley equations on an early automatic computer in the United States took 30 minutes to accomplish what Huxley did in 8 hours (causing Kacy Cole to quip that this machine had "16 Huxley power"). With CPU clock speeds now (January 2000) in excess of 800 MHz, one's desktop computer can match the speed of an axon in calculating an action potential! But plotting takes a bit longer.