48 PROCEEDINGS OP THE AMERICAN ACADEMY 



These diminutions of temperature, each corresponding to a known 

 temperature of the bar, are laid off as ordinates of a second curve, 

 each ordinate corresponding to an ordinate of the first curve, which 

 expresses. the temperature of tlie bar at any point. Thus every ordi- 

 nate of the second curve will give the loss of temperature per minute, 

 from that portion of the bar which is at the temperature given by the 

 corresponding ordinate of the first curve. And the area of a definite 

 portion of the second curve multiplied by the specific heat of the glass 

 gives the amount of heat lost from a corresponding definite portion of 

 the bar, in unit of time. 



If we have a vertical section of any substance, of thickness x, one 

 face at the constant temperature t^ and the other at the temperature t, 

 and k = the conductivity of the substance, the quantity of heat that 

 passes through an area A in unit time = Q, where 



X A '0 — ^ 



X 



If the section is an infinitely thin lamina of thickness d x, and if d t = 

 the difference of temperature of the two sides, — 



A d± 



d X 



K=. ~ -r- ■=, at the limit, ^ Tr~ • 

 ' A Dxt 



Dj can be found for any point of the bar, by finding the tangent 

 at the corresponding point of the first curve. Hence if ^ = area of 

 cross-section of bar, S ■= the specific heat of the glass, and " area " = 

 the area of the second curve beyond the point in question, the conduc- 

 tivity at that point is -ff^ = -7- -y— - . 



The area of the second curve beyond the point in question, multi- 

 plied by S, evidently equals the whole amount of heat that passes, in 

 unit time, through the section of the bar at that point; for the end of 

 the bar is at the same temperature as the air. 



I used a bar of flint glass, about 30 cm. long and 1.1 cm. in diameter. 

 One end was inserted in the side of a metallic vessel, and heated to 

 100° by boiling water. The other end was supported on a piece of 

 wood. Two screens of card-board were placed in front of the can 

 and lamp to prevent the bar being heated by radiation. Seven points 

 were marked on the bar : the first, 3 centimeters from the can, and 

 the others, 1, 2, 3, 5, 7, and 9 centimeters from the first point. The 

 temj^eratures were measured by a thermopile made by a junction of 

 copper and iron wires, fastened like two links of a chain, so that they 



