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and ventilation, formulated, several years ago, a very valuable rule for proportioning direct radiation, which is expressed by the following formula:

$R=0.9(t-t_{1})(0.60G+0.10W+0.0025C)FJ\div t\,$

where $F\,$ is a factor depending on the method of heating (0.8 for low-pressure steam) and $J\,$, a factor depending on the exposure, which Mr. Willetts puts as 1.0 for ordinary south and east exposures and 1.4 for north and west. The other letters in the formula have the same reference as in the formulas previously given, but Mr. Willett states that $t\,$ should be taken 10 degrees higher than the lowest recorded temperature of the locality in question. With $t_{1}\,$ taken at minus 8 degrees; $t\,$, 70 degrees; $F\,$, 0.8; and $J\,$, 1, Mr. Willett's formula becomes:

$R=0.48G+0.08W+0.002C\,$.

This equation compares very closely with Mills, though less allowance is made for the cubic contents and more for the wall surface. The writer considers that if $J\,$, in Mr. Willett's formula, be taken as 1. for south and east exposures, it is sufficient in most cases to take it as 1.2 for north exposures. For such exposures, therefore, the same formula can be used as for south and east rooms and the radiation increased one-fifth.

Carpenter's rule for direct radiation.—Prof. Carpenter, in his work on heating and ventilation, has devised a formula which is very carefully derived. He first calculates the amount of heat lost from the room in question and then the amount of radiating surface necessary to offset this heat, using coefficients for heat transmission which he substitutes in his formula. According to Prof. Carpenter's method, the heat in British thermal units lost from a room for every degree difference in temperature between the inside and outside air is $h=nC\div 55+G+(W\div 4)\,$, in which $G\,$, $C\,$, and $W\,$ represent the quantities previously assigned them, and $n\,$ is the number of times the air of the room is to be changed per hour. Prof. Carpenter states that for direct radiation it is necessary to take $n=2\,$ for ground-floor rooms and $n=1\,$ for others, to allow for leakage of air. The quantity, $nC\div 55\,$ gives the number of heat units necessary to raise $nC\,$ cubic feet of air 1 degree in temperature. Prof. Carpenter states that the radiating surfact should be equal to $R=[(t-t_{1})\div (T-t)a]h\,$ in which $t\,$ is the required temperature of the room, $t_{1}\,$ the outside temperature, $T\,$ the temperature of the steam in the radiator, and $a\,$