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## James Clerk Maxwell’s statue

In May I was in Edinburgh to compete in the Edinburgh marathon. On the day after the marathon I did a sight-seeing tour of Edinburgh. One of the things I saw was a statue to the Scottish mathematical physicist James Clerk Maxwell. The statue is at the Saint Andrew Square end of George Street, abut 300 metres from the famous Princes Street.

James Clerk Maxwell was an important physicist and mathematician. His most prominent achievement was to formulate the equations of classical electromagnetic theory. These four equations are known as Maxwell’s equations. They are shown on a small plaque at the rear of the statue’s plinth. The rear of the statue’s plinth. The larger plaque is illustrated in the bottom photograph. Below this is a small plaque with Maxwell’s four famous equations of electromagnetism. $\boxed{ \begin{array}{lcll} \nabla \cdot \vec{D} & = & \rho & (1) \\ & & & \\ \nabla \cdot \vec{B} & = & 0 & (2) \\ & & & \\ \nabla \times \vec{E} & = & - \frac{\partial \vec{B}}{\partial t} & (3) \\ & & & \\ \nabla \times \vec{H} & = & - \frac{\partial \vec{D}}{\partial t} + \vec{J} & (4) \end{array} }$

These equations are written in differential form, where the symbol $\nabla$ is known as the vector differential operator. I will explain the mathematics of vector differential operator, and the meaning of each equation, in a series of future blogs.

The four equations can also be written in integral form, which many people find easier to understand. In integral form, the equations become $\boxed{ \begin{array}{lcll} \iint_{\partial \Omega} \vec{D} \cdot d\vec{S}& = & Q_{f}(V) & (5) \\ & & & \\ \iint_{\partial \Omega} \vec{B} \cdot d\vec{S} & = & 0 & (6) \\ & & & \\ \oint_{\partial \Sigma} \vec{E} \cdot d\vec{\l} & = - & \iint_{\Sigma} \frac{\partial \vec{B} }{\partial t} \cdot d\vec{S} & (7) \\ & & & \\ \oint_{\partial \Sigma} \vec{H} \cdot d\vec{l} & = & I_{f} + \iint_{\Sigma} \frac{\partial \vec{D} }{\partial t} \cdot d\vec{S} & (8) \end{array} }$ The inscription on the front of the statue’s plinth. It reads “James Clerk Maxwell 1831-1879”.

### 7 Responses

1. […] wanted to get back to explaining Maxwell’s equations, which I mentioned in this blog of the statue to James Clerk Maxwell that is in Edinburgh. Before I do that I thought I would cover […]

2. on 20/06/2013 at 14:08 | Reply jon may

I am a tour guide frequently in Edinburgh and I greatly admire this statue, but I haven’t been able to identify the circular object with a handle that Maxwell is holding. Can you help? With thanks in advance
Jon May

3. on 05/10/2014 at 13:52 | Reply marcelhendrix

I’ve allways wondered about that too!

It is probably meant to be a planimeter (Maxwell invented one), although it looks more like a circular sliderule. The planimeter Maxwell invented looks quite a bit different from the thing on the statue, though.

(Isn’t Maxwell wearing remarkably modern looking shoes 🙂

• on 11/10/2014 at 07:22 | Reply marcelhendrix

I’ve learned now that the statue shows him holding his ‘color top’, a spinning disc with colored paper, used to learn more about the physiology of color vision.

• on 11/10/2014 at 07:58 RhEvans

Thanks for that info. Interesting!

4. […] with the dog, holding the disc? Why, James Clerk Maxwell, of course. You may remember him from such equations as ‘Gauss’s law’, and not forgetting his big hit ‘Faraday’s law of […]

5. on 16/03/2020 at 21:02 | Reply Steve Jones

One irony is that the elegant form of those four equations using vector calculus on his statue are not the work of James Clerk Maxwell. He had 22 rather unwieldy equations, and it was Oliver Heaviside who reformulated then using vector calculus (and in a slightly different way not quite equivalent to Maxwell’s equations). Oliver Heaviside was an independent co-formulator of vector calculus, and was also responsible for a lot of terms used in the area. Terms such as inductance, permittivity, permeability and reluctance along with several others.

Heaviside also developed transmission line theory and patented co-axial cable in England. He was the first to use what is now known as the Dirac delta function. He also predicted the existence of an ionisation layer in the upper atmosphere (partly names after him).

He was, however, a very odd and eccentric individual being self-taught and frequently at odds with the scientific establishment. However, there’s not a part of electronics and telecommunications untouched by his work.