76 Applications of the Formulas 



perature which it would indicate would be that of the air modi- 

 fied by the mutual radiation between its bulb and the surroundings, 

 and in consequence it would show a temperature lower than that 

 of the air. It is necessary to prevent radiation from the bulb to 

 the walls of the room by surrounding the bulb with several con- 

 centric envelopes open at top and bottom, and the air between 

 the envelopes should be rapidly renewed. The effect on a ther- 

 mometer of the fall of temperature of the inner surface of the walls 

 would evidently be felt by a person in the room, and consequently 

 in order that the sensation of heat should remain the same, the 

 temperature of the air must be increased as the temperature of the 

 inner surface of the walls decreases. 



874. The two cases which we have been considering are 

 never precisely fulfilled in practice ; in the first case the inner sur- 

 faces of the unexposed walls are never exactly at the temperature 

 of the air, on account of their radiation to the other walls and the 

 windows ; in the second case there are always portions of the inner 

 surface of the rooms, such as the ceilings and floors which are not 

 exposed to exterior cooling, and often there exist interior walls, 

 such as those separating the naves of churches. These walls are 

 heated by air and radiate to the inner surfaces of the outer walls. 

 Finally in both cases, if there is heating by radiating surfaces, by 

 stoves, radiators or pipes, the rays of heat reach the inner surfaces 

 of the walls and raise the temperature of these surfaces. But, as 

 we shall see further on, we may consider the effects produced by 

 these two cases as the extreme limits of those which are generally 

 met with in practice. 



DISCONTINUOUS WALLS 



875. So far we have supposed the walls to be continuous, 

 but if they were made up of walls with parallel surfaces, separated 

 by intervals occupied by air, the quantity of heat transmitted 

 might be considerably smaller. If we suppose the intervals to be 

 sufficiently large to permit free movement of air, we may admit 

 without fear of departing very far from the truth, that the quantity 

 of heat transmitted across the air spaces is represesented by 



Q (x x' ), x and x' representing the temperatures of the surfaces 

 forming the air space. If the air space was filled up with a mate- 

 rial of thickness e and conductivity C the heat transmitted would 



