Conductivities of Cements and other Substances. 407 

 Now for the lower brass disk 



2?/q = 27rr/7rr 2 = 2/5-7 = '35l i 

 while ky_ for brass ="25, and it will be shown presently that 

 /< 1 = -0003 about. Hence a /PI* = '02, and since the thick - 



- qh 



ness of the plate is 1*3 cm. the maximum value of the expression 

 in brackets is 



cosh -026 + ^ 003 sinh '026 = 1-00 18 ; 

 •25 x V2 



or the temperature of the lower plate varies less than J per 

 cent., and for the purpose of the present experiment may be 

 taken to be uniform throughout and equal to the indication 6 l 

 of the thermometer in the centre of the disk. The tempera- 

 ture of the lower disk is therefore given completely by the 

 equation 



The rate of flow of heat into the lower disk, the thickness of 



which is 1*3 centim., is given by k x -j- for #=1*3. It is 

 therefore dx 



=h \Ar {#i- 0o} ( sinh -026 + ^= . cosh '026 } 



V gfc 1 I hy/Eh } 



V gk x 



= (^i-^o) (l'00026 h + -026 *, \/^- ) 



= (^i-^o)(/'i + -00013) 



= (^i-^o)(/ii + V), say, where /*/ = '00013, 



If k is the internal, h the external conductivity of the medium 

 under test, the temperature at a point x above its under 

 surface is given by : — 



Q- O = (0i- 0o) { cosh \J^r . a + B sinh y^| . x j , 



where B is a constant, the value of which is fixed by the 

 Phil. Mag. S. 5. Vol. 41. No. 253. June 1896. 2 M 



