608 PROCEEDINGS OF THE AMERICAN ACADEMY. 



giving off heat to the guard-ring in the imagined arrangement. This 

 part should evidently be more than half. A considerable variation in 

 this particular would make no great difference in the estimate of the 

 total outflow from a to the guard -ring. We shall make no serious 

 error if we assume that the outgiving arc of a is the same part of a 

 circumference as the receiving arc, 22 cm. bent to a radius of 5.5 cm. 

 As the radius of a is 0.5 cm., we take 2 cm. as the length of the 

 effective arc on a in the case imagined. In circular measure the 

 length of each arc is 1.27 tt. 



In the case of steady flow, if q represents the number of calories 

 transmitted per second from 1 cm. length of a to the corresponding 

 1 cm. length of guard-ring, and if k stands for the thermal conductivity 

 of the packing, while T stands for temperature, we have for any ring 

 of radius r and width dr, 



— k X 1.21 IT r -^ = q, or dT = — , ^ . . — . 

 dr ^ /; X 4 r 



Integrating between limits we get 



4 a; ri 



At 100° for #1 — ^2 = 1 we have q = 0.0101 -M6 = 0.00063, whence 

 ^100 = 0.00038. 



At 218° for i^i — ^2 = 1 we have q = 0.0134 -M6 = 0.00084, 

 whence ^-ois = 0.00050. 



Of course no great accuracy can be claimed for a result obtained by 

 so many rude approximations ; but it seems unlikely that these ap- 

 proximations have introduced an error so great as 25 per cent into the 

 estimated values of k. 



If now we seek to compare these values of k for loosely packed asbes- 

 tos fibre with the values obtained by other investigators, we fail to iind 

 any information given in the 1905 edition of Landolt and BlirnKtein 

 concerning the thermal conductivity of this material. If we look at 

 the values of k given for other fibrous materials, we see figuring prom- 

 inently in tables of physical constants the values obtained many years 

 ago by Professor George Forbes for haircloth, cotton-wool (divided), 

 cotton-wool (pressed), flannel, and coarse linen. These values range 

 from 0.0000402 for haircloth to 0.0000298 for coarse linen. They at 

 first seem to make the values obtained above for asbestos packing 

 rather improbable and tend to strengthen the suspicion of consider- 

 able air currents through this packing. But the values found by 

 Forbes are, in all probability, decidedly too small, for they are consider- 



