He did so by building a test carriage, powered by four men working levers. It carried varying amounts of ballast to represent the weight of a full-sized engine. When he was satisfied that the system worked, the test carriage was adapted to take a boiler and drive gear built by Gateshead engineer John Waters.
The engine was tested for the first time early in 1813, and although this makeshift machine was short on steam and lacked power, it did enough to convince Blackett that they were on the right lines and they could proceed with a second, purpose-built locomotive.
For his own part, Hedley was confident enough to take out a patent for the design and specifications on March 13th.
Yet strangely, he does not seem to have been totally convinced about smooth-wheel adhesion, for the patent includes the idea of pointed teeth projecting from the wheels and digging into the ground between the sleepers, for extra grip, although this was never used in practice.
Hedley designed the next locomotive himself and it was built by Timothy Hackworth - Wylam's blacksmith foreman who would go on to become a great locomotive builder himself - and Jonathan Forster, the mine's enginewright.
This second engine was running early in 1814, drawing eight loaded chaldrons at five miles an hour. Its success soon attracted the attention of George Stephenson, by now the enginewright at Killingworth Colliery to the north of Newcastle, who became a frequent visitor to Wylam.
Stephenson was a close friend of Forster and as he was in the process of developing a locomotive for his own employers, it is not difficult to guess at the reason for his calls.
In truth, Stephenson was not the great mechanical innovator that many people thought. His talents lay not in invention but in picking other people's brains and putting their ideas to practical use - something that was quite common in the Industrial Revolution.
The breakthrough that made the steam locomotive a practical proposition was undoubtedly Hedley's discovery that a smooth wheel running on a smooth rail could provide enough friction for an engine to pull a train of loaded wagons.
But boiler design was equally important - and where Hedley quickly realised that fitting his boilers with a return flue doubled the area in which heat could be transferred to the water, Stephenson was still persevering with an inefficent, straight-through design well into the 1820s.
It was not until Stephenson built his 'Rocket' for the Liverpool-Manchester Railway in 1829 that he introduced the multi-tube boiler that was to become the standard for future steam engines.
But he certainly didn't invent the concept - in 1828, Yorkshireman Dr William Harland had built, patented and tested a road car with a multi-tube boiler. Interestingly, Harland was a friend of Stephenson's.
Although we don't know the true nature of the relationship between Hedley and Stephenson - if there were any - we can judge Hedley's opinion of his rival in later life.
Puffing Billy as modified to an eight-wheel configuration, to spread the weight and reduce wear on the rails.
After detailing his experiments to prove that smooth-wheel adhesion worked, he told Lardner: "...in your highly-popular lectures, you stated that Mr Stephenson was the Father of the Locomotive engine.
"Now I do not wish to detract one iota from the celebrity to which Mr Stephenson is entitled - he has done much for the locomotive engine; but ... it appears that a locomotive engine was not constructed by Mr S. before 25th July 1814.
"Long before this period, the use of horses on the Wylam Railroad was superceded by the locomotive engines, and a large annual sum in the course of being saved to the colliery. My patent bears the date 13th March, 1813.
"In conclusion, I beg to say that I am the person who established the principle of locomotion by the friction or adhesion of the wheels upon the rails, and further that it was the engines on the Wylam railroad that established the character of the locomotive engine in this district."
Hedley, in fact, was displaying remarkable restraint. Lardner may have held his lecture audiences enthralled, but he was by no means universally respected - one contemporary branded him an 'egregious ass.' Yet this was the man who helped to build the Stephenson myth.
As for Hedley himself, had he been more single-minded in the development of steam power then his name, and not Stephenson's, might be the one people remember today. But locomotives and railways were only ever a means to an end for a man to whom mining was an all-consuming interest.If Hedley had one failing, it was an inability to imagine just where his ideas might lead. Stephenson had no such problem.