( .0304) = 14,600 × .8445 + 62,000 (.0425 - -----) + 4000 × .0091 = 14,765 B. t. u. ( 8 ) This coal, by a calorimetric test, showed 14,843 B. t. u., and from a comparison the degree of accuracy of the formula will be noted. The investigation of Lord and Haas in this country, Mabler in France, and Bunte in Germany, all show that Dulong's formula gives results nearly identical with those obtained from calorimetric tests and may be safely applied to all solid fuels except cannel coal, lignite, turf and wood, provided the ultimate analysis is correct. This practically limits its use to coal. The limiting features are the presence of hydrogen and carbon united in the form of hydrocarbons. Such hydrocarbons are present in coals in small quantities, but they have positive and negative heats of combination, and in coals these appear to offset each other, certainly sufficiently to apply the formula to such fuels. High and Low Heat Value of Fuels--In any fuel containing hydrogen the calorific value as found by the calorimeter is higher than that obtainable under most working conditions in boiler practice by an amount equal to the latent heat of the volatilization of water. This heat would reappear when the vapor was condensed, though in ordinary practice the vapor passes away uncondensed. This fact gives rise to a distinction in heat values into the so-called "higher" and "lower" calorific values. The higher value, _i. e._, the one determined by the calorimeter, is the only scientific unit, is the value which should be used in boiler testing work, and is the one recommended by the American Society of Mechanical Engineers. There is no absolute measure of the lower heat of combustion, and in view of the wide difference in opinion among physicists as to the deductions to be made from the higher or absolute unit in this determination, the lower value must be considered an artificial unit. The lower value entails the use of an ultimate analysis and involves assumptions that would make the employment of such a unit impracticable for commercial work. The use of the low value may also lead to error and is in no way to be recommended for boiler practice. An example of its illogical use may be shown by the consideration of a boiler operated in connection with a special economizer where the vapor produced by hydrogen is partially condensed by the economizer. If the low value were used in computing the boiler efficiency, it is obvious that the total efficiency of the combined boiler and economizer must be in error through crediting the combination with the heat imparted in condensing the vapor and not charging such heat to the heat value of the coal.