but how did he solve the problem of expansion of the flywheel..?
Differential expansion. Brass, being an alloy of copper, expands and contracts
more when compared to steel (and the temperatures being the same).
So, he put a brass "tire" (tyre?) on the outside of the steel balance wheel. When done correctly, the brass tire's expansion would counteract that of the steel wheel. The outside diameter of the brass increases, but the inside diameter
decreases, which squeezes the steel wheel, which is busy trying to expand. Same with contraction. The brass tire wants to contract more than the steel wheel, so the steel resists the "squeezing" of the brass tire.
When in equilibrium, the wheel does not change dimension (diameter) at all, despite the two alloys fighting with one another.
A story about the Elgin Watch Company, from the July issue of Harper's New Monthly Magazine, 1869:
How shall it (the watch) be made to go uniformly through summer and winter? A steel rod maybe fitted into a hollow steel cylinder so perfectly that it will not drop out of its own weight, and yet it can be turned or pulled out by the thumb and finger, and it moves with the softness of velvet rolling on velvet. Hold the same rod in the shut hand for five minutes and the warmth of the flesh will expand it so that one can not drive it in with a sledge-hammer. Then put it in a refrigerator and it will contract till it rattles in the cylinder. If the metal is brass, temperature affects it still more. Winter will so contract the balance-wheel of a watch that it may gain two minutes in a day; or it may be thrown out of time by a few hours' sleigh-riding, or by hanging all night against a cold wall. Uneven temperature is the deadly foe of uniform time-keeping.
In 1767 John Harrison was awarded a premium of L20,000, under an offer of the British Parliament- which had been standing fifty three years-for any invention which should so far overcome this difficulty as to enable shipmasters at sea to determine longitude within thirty miles of accuracy. He gained it by applying to ship chronometers the principle of the compensation-balance, now used in all fine watches. It is simply a balance-wheel with outer rim or tire of brass, and inner rim and cross arm of steel. The cold, which would Contract steel alone and make the circumference of the wheel less, equalizes that by contracting the brass still more, the brass being so confined that its contraction enlarges the wheel. Under the influence of heat the steel's expansion would enlarge the wheel, but then the greater expansion of the brass contracts it. When these two influences are so nicely adjusted that the one exactly counterbalances the other, the watch will keep equal time whether in Alaska or Havana.
http://www.antique-pocket-watch.com/elg ... watch.htmlInterestingly, 1 English Pound in 1767 is worth 1510 English Pounds today. Which means Mr. Harrison's prize of 20,000 pounds was worth the equivalent of 30,200,000 pounds today. Translated into dollars, that's $48,648,123....
Not too shabby for a day's work, hey? Told y'all it was one of those "Now, how come I didn't think of that?" types of things... brass expands more than steel, so if you put them together, they'll fight each other to stalemate...