THERE is a scientist with a shock of grey hair - perhaps she brushed against a Van de Graaff generator, one of the few things I remember from my school science classes - who is bouncing up and down in George Square as she explains how James Watt had an idea, while strolling across Glasgow Green, which changed the world. Carol Trager-Cowan, from Strathclyde University's physics department, has gathered a dozen or so interested souls around her as she pumps her arms up and down to show how a steam engine works.

Engines were terribly inefficient, with all the heating and cooling going on to drive the pistons, until Watt in 1765 had this sudden thought that the steam could be cooled in a separate condenser, so the pistons themselves did not have to be cooled and reheated, and thus engines could be far more flexible and cost-effective. It really began the industrial revolution, changing manufacturing across the world.

She explains it so well that for a few minutes I can actually understand what Watt did. It's clouded over a bit now of course, as even understanding how a Bunsen burner worked at school was a challenge to me, but Carol's enthusiasm is contagious.

We have gathered in George Square as part of the Glasgow Science Festival which is running a walking tour in the centre of Glasgow to explain Glasgow's impressive scientific heritage which is now much forgotten.

I'm ashamed to admit that I didn't even know that James Watt had a statue in George Square. Sir Walter Scott I knew slap bang in the middle, Rabbie Burns, Queen Victoria on horseback, even William Gladstone I could point out. James though is sitting down staring across the road at Greggs. Carol explains that the statues are all of writers, politicians and royalty apart from two scientists - the only two statues of people sitting down. Not sure why scientists needed to rest. It perhaps suggests they had to sit at desks to write down their ideas and experiments.

So above the clatter of the passing traffic, Carol tells us about Watt, the instrument maker at Glasgow University, who had his inspirational moment at Glasgow Green, who also invented an early photocopier, came up with the term horsepower which is still used today, and whose initial W is on all lightbulbs around the world as the term "Watts" for electrical power is also a world standard. Not bad for a Greenock boy.

But then we're off across the square to look at the 100 foot measuring line laid out on the square - another line nearby measures a chain, which is about 66 feet. There are 10 chains in a furlong, which I think was an ancient measurement that appeared on the backs of our brown jotters at school. And only now am I using it.

On the wall of the City Chambers is a further measuring device for inches, feet and a yard, which the sign solemnly states is accurate at 62 degrees Fahrenheit as the metal could expand and contract at other temperatures. The idea is that if you were buying something the seller could measure the cloth or whatever accurately at the square. Don't know when they were last used but someone on the tour tells us that a friend returning home from buying material at Remnant Kings pulled it out to check they been given the right length right here at the square. Oh and it was correct, so well done Remnant Kings.

Then across the square for the statue of the second scientist, Thomas Graham, who is sitting down looking pensive with his chin resting on his knuckle. "An unsung hero," says Carol. "We have a lot of those in Glasgow."

So Thomas was a chemistry professor. A bit rubbish at teaching apparently as he couldn't keep any discipline in his classes, but was great in the laboratory where he discovered much about the diffusion of gases. He came up with the earliest form of kidney dialysis which is still in use today. He also ran the Royal Mint, and improved the country's coinage with the use of alloys. Not bad for a Glasgow boy.

But there is no stopping Carol's enthusiasm as she marches us off along Ingram Street to the Ramshorn kirkyard. Now the kirkyard is another of Glasgow's hidden gems. It's a pleasant oasis of grass just yards from the bustle of George Square, but many folk who pass do not realise it is open to the public.

Here we have the remains of John Anderson who, apart from his own scientific discoveries, wished to spread education to as many people as possible, and his limited Anderson's University, through many academic twists and turns, eventually became Strathclyde University. But Carol wisely wants to keep everyone's attention, so she draws our attention to the metal cages that kept graves safe from the grave-robbers in the early 1800s.

At the time only the bodies of hanged murderers could be used by medical students so the more unscrupulous would use other bodies, and thus grave-robbing flourished. However in 1818 Airdrie weaver Matthew Clydesdale was hanged for murdering an old man in a drunken rage. The execution was at Jail Square in the Saltmarket, and his body was whisked away in a cart to Glasgow University which in those days was just up the road. In front of a crowded theatre, anatomists Andrew Ure and James Jeffray passed electric currents through various parts of the body. Limbs twitched violently, the face grimaced, and even the lungs gave the impression of breathing again. Sensational stuff. As Carol read out an account of the experiments: "Several spectators were forced to leave the apartment from terror or sickness, and one gentleman fainted.”

Ghoulish, but it did lead circuitously to the electric defibrillator of today's medicine. So even a drunk from Airdrie has helped the path of science, although there are no plans to give Matthew Clydesdale a statue at George Square.

The Glasgow Science Festival is held every June, bringing science to over 50,000 people. It's good to know that Glasgow has spawned more than just comedians and footballers.