## Airy's work in engineering

We engineers hold mathematicians in high esteem, but mathematicians sometimes overlook their colleagues' contributions to engineering analysis. A good example is the MacTutor Archive's treatment of the seventh Astronomer Royal, Sir George Biddell Airy.

Of course, in the present case, there are three categories of structural engineers:

(1) those who have never heard of old George,

(2) those who can't understand why "Airy" (as in * Airy functions* ) is spelt with a capital A,

(3) the tiny minority whose members may have used * Airy functions * at least once in a career.

The latter set includes a subset, those who admire Airy's sensible arrival at a solution to a problem which puzzled him for, perhaps, as long as a milli-second or two. From France, word had been arriving at Greenwich that a grand new telescope was under construction and the world waited with bated breath the announcements of what wonders would be revealed. There was great cheer within the Royal Society and at Greenwich when what was revealed was that the French instrument was so overwieght that its longitudinal axis was deflected into a curve which, the astronomers were surprised to learn, affected more than heavenly bodies and thus rendered the telescope as useful as, perhaps, a boat anchor or circus cannon, but never as an aid to solving planetary orbital problems.

Airy said "*Hmmmm!* " and immediately wrote out something to the effect that

In spite of the fact that Airy spoke in italics he was sufficiently well-understood for the function,a state of plane strain in a two-dimensional solid, free from body forces, may be specified by three mutually orthogonal stress components. These may be stated as first-order differential equations. If the three stress components are equal to the appropriate second order partial derivatives of an arbitrary function,ψ, then they satisfy the equilibrium conditions.

*ψ*, to be called an

**Airy stress function**.

Airy was not concerned about fame: he wanted to be able to analyse, then synthesise, the tube for a great telescope at Greenwich.

JOC/EFR January 2000

The URL of this page is:

http://www-history.mcs.st-andrews.ac.uk/Extras/Airy.html