Thermal Conductivity of Vulcanite. 1 9 



*A cosh(^') =k, [a, cosh(^) + B 2 sinh (^)J 



A 2 sinh (^-') + B 2 cosh (*Jp\ = A 3 siuh {^-\ + B 3 cosh (^'\ 



* 2 [A 2 cosh(^ + B 2 si„hpf)] 



= ^[A3 0osh(^ , ) + B 3 s;nh(^-')], 



Ao sinh( — ) 4- B 3 cosh ( — | = — t~t~\j 



and where ,t p is the pih root in order of magnitude of the 

 Bessel's equation J (#)=0. 



If, for brevity, we denote the quantities 



sinh(^), cosh(^), sinh(^), cosh(^), 



Sln H"T-> C ° Sh V a } 



by .9, c, s'j c y , s", c", and (2, respectively, 

 A,= 



- kJcjsQ 



~ c 'sXk x -\)\k£s'\sc"-cs n )+k z cc , \cc'-ss")}+{k,c' 2 ^ 



If in the special case where k x and k 3 are equal, we write 

 k l = fjLk 2 = k i , we get 



A 1 = 



c's\ix-i){s'Xsc''-cs'')+ f ic'Ucc''-ss'')l+(fic' 2 -s' 2 )^fis''(ss n -cc n )-\-c n (s''c-sc'')y 



with corresponding values for the other coefficients. 



Similar results can easily be obtained for a case where 

 the cylinder is supposed to be built up of more than three 

 disks. 



By the use of these equations it is possible to determine 

 how much the presence of a thin disk of metal between two 

 disks of some poorly conducting material affects temperatures 

 near the axis of the cylinder under different temperature con- 

 ditions at the curved surface of the cylinder. We inferred 

 from our computation, which involved a great deal of labour, 

 that with probable temperature conditions in the side faces of 

 a prism of the dimensions we generally use, the thermal 

 elements do not sensibly distort the isothermal surfaces within 



02 



