_Third_, to the waste or loss of heat in the hot gases which escape up the chimney or smoke stack. The temperature of the fire in a locomotive fire-box in a state of active combustion is probably from 3,000 to 4,000 degrees. This heat is in part radiated and conducted to the heating surface of the fire-box, and it is found that more water is evaporated by this portion of the heating surface in proportion to its area than by any other in the boiler. The gases when they enter the tubes transmit a portion of their heat to the surfaces with which they are first in contact. The amount of heat thus transmitted, as has been stated, is in proportion to the _difference_ in temperature of the gases inside the tubes and that of the water outside. After passing over the part of the tube with which the gases are first in contact, they then arrive at another portion of the tube surface with a diminished temperature, and the rate of conduction is therefore diminished; so that each successive equal portion of the heating surface transmits a less and less quantity of heat, until the hot air at last leaves the heating surface and escapes up the chimney with a certain remaining excess of temperature above that of the water in the boiler, the heat corresponding to which excess is wasted.[99] It is, therefore, desirable to extract as much heat as possible from the gases before they escape from the tubes. Now it will be impossible to heat the water outside of the tubes hotter than the gases inside. When the temperature of the water is equal to that of the gases, no more heat will be transmitted from one to the other. If the temperature of the water is 350 degrees, that of the gases in the tubes will never be any lower, but will escape into the smoke-box with not less than that amount of heat. If, however, the cold water is introduced at the front end of the tubes, so that the surface with which the gases are last in contact has a temperature considerably lower than 350, then an additional amount of heat will be transmitted before they escape. It is, therefore, important that the cold feed-water should be admitted near the front end of the boiler, so that the products of combustion will be in contact with the coldest part of the heating surface last, and thus give out as much of their heat as possible before they escape. As a matter of fact, the gases escape at a much higher temperature. Experiments made by the writer showed that the temperature in the smoke-box of a locomotive when first starting was 270 degrees, and when working at its maximum capacity on a steep grade and with a heavy train it was as high as 675 degrees. The average temperature while running was, in three trials on different parts of the road, as follows: Average steam pressure, 98.8 lbs.; average temperature, 499.8 lbs. Average steam pressure, 106 lbs.; average temperature, 535.1 lbs. Average steam pressure, 112.2 lbs.; average temperature, 554 lbs. [99] Rankine.