philosophers from the time of Newton downwards, and foremost among these must be ranked the late James Prescott Joule, who was the first to measure accurately the exact amount of work corresponding to a given quantity of heat. In measuring heat (as distinguished from temperature) it is customary to take as a unit the quantity necessary to raise a given weight of water from one specified temperature to another. In measuring work, it is customary to take as a unit the amount necessary to raise a certain weight at a specified place to a certain height against the force of gravity at that place. Joule's unit of heat is the quantity necessary to raise one pound of water from 60 deg. to 61 deg. F., and his unit of work is the foot-pound, _i.e._ the quantity necessary to raise a weight of one pound to a height of one foot. Now the quantitative relationship between heat and work measured by Joule is expressed by saying that the mechanical equivalent of heat is about 772 foot-pounds, which means that the quantity of heat that would raise one pound of water 1 deg. F. would, if converted into work, be capable of raising a one-pound weight to a height of 772 feet, or a weight of 772 lbs. to a height of one foot. This mechanical equivalent ought to tell us exactly how much power is obtainable from a certain weight of coal if we measure the quantity of heat given out when it is completely burnt. Thus an average Lancashire coal is said to have a calorific power of 13,890, which means that 1 lb. of such coal on complete combustion would raise 13,890 lbs. of water through a temperature of 1 deg. F., if we could collect all the heat generated and apply it to this purpose. But if we express this quantity of heat in its mechanical equivalent, and suppose that we could get the corresponding quantity of work out of our pound of coal, we should be grievously mistaken. For in the first place, we could not collect all the heat given out, because a great deal is communicated to the products of combustion by which it is absorbed, and locked up in a form that renders it incapable of measurement by our thermometers. In the next place, if we make an allowance for the quantity of heat which thus disappears, even then the corrected calorific power converted into its mechanical equivalent would not express the quantity of work practically obtainable from the coal.