Next in order of publication of his results stands the name of Colding, a Danish engineer, who about the year 1843 presented a series of memoirs on the steam engine to the Royal Society of Copenhagen, in which he put forth views almost identical with those of Mayer. Last in publication order, but foremost in the importance of his experimental treatment of the subject, was our own countryman, Dr. Joule of Manchester. “Entirely independent of Mayer, with his mind firmly fixed upon a principle, and undismayed by the coolness with which his first labours appear to have been received, he persisted for years in his attempts to prove the invariability of the relation which subsists between heat and ordinary mechanical power.” (We are quoting from Professor Tyndall’s valuable work on “Heat considered as a Mode of Motion.”) “He placed water in a suitable vessel, agitated the water by paddles, and determined both the amount of heat developed by the stirring of the liquid and the amount of labour expended in its production. He did the same with mercury and sperm oil. He also caused discs of cast iron to rub against each other, and measured the heat produced by their friction, and the force expended in overcoming it. He urged water through capillary tubes, and determined the amount of heat generated by the friction of the liquid against the sides of the tubes. And the results of his experiments leave no shadow of doubt upon the mind that, under all circumstances, the quantity of heat generated by the same amount of force is fixed and invariable. A given amount of force, in causing the iron discs to rotate against each other, produced precisely the same amount of heat as when it was applied to agitate water, mercury, or sperm oil. * * * * _The absolute amount of heat_ generated by the same expenditure of power, was in all cases the same.” “In this way it was found that the quantity of heat which would raise one pound of water one degree Fahrenheit in temperature, is exactly equal to what would be generated if a pound weight, after having fallen through a height of 772 feet, had its moving force destroyed by collision with the earth. Conversely, the amount of heat necessary to raise a pound of water one degree in temperature, would, if all applied mechanically, be competent to raise a pound weight 772 feet high, or it would raise 772 pounds one foot high. The term ‘foot pounds’ has been introduced to express in a convenient way the lifting of one pound to the height of a foot. Thus the quantity of heat necessary to raise the temperature of a pound of water one degree Fahrenheit being taken as a standard, 772 foot-pounds constitute what is called the _mechanical equivalent_ of heat.”