of Thermal Conductivity and Emissivity. 287 



The constants a, b ly /3 1? &c. are determined by the method 

 of least squares from the observations made. 



If a, &„ ft ly &c. and a', fr/,/3/, &o. are the constants for the 

 two points A and B respectively, and x the distance between 

 them, then 



1 — Ve3 x and /3—j3' = qx 



(see Ann. Chim. Phys. lxvii., 1863). 

 Hence g and q can be determined, and 



gq = -j — <™ d " = (jEr—r)-2> 



where ?i=l, 2, 3, &c, according as you use the constants of 

 the 1st, 2nd, 3rd, &c. sine term ; 



c = specific heat of the rod ; 



S = density of the rod. 

 Hence k and h can be determined from each sine term. In 

 the experiments as carried out only the first, and perhaps the 

 third, sine terms are available for these determinations, as the 

 others are very small, the even terms being especially so. 

 Besides these, there is the " a " term of the above formula (the 

 constant term of the Fourier series), which is large, and repre- 

 sents the mean excess of temperature of the rod. From this 

 term we get 



kr 



a' 



If we use the previously determined value of k, we can get 

 from this equation a secon 1 value of A. This will be referred 

 to later on. 



The rods experimented upon were three brass rods (com- 

 mercial specimens) of roughly -^, ^, and ^ in. diameter ; their 

 lengths were about 3, 5, and 6 ft. respectively. They were 

 cleaned, but not polished. The time-period of the alternations, 

 and the positions of A and B, were chosen so that the cycle of 

 changes gone through should be as nearly as possible the same 

 in the three cases. 



The specific heat was determined by heating a portion of 

 each rod to 100° in a Regnault's apparatus in the usual way. 

 The following are the results obtained : — 



Diam. of Rod .... | in. J in. f in. 



•0937 -0943 -0945 



•0948 -0952 '0938 



•0953 -0942 



Approx. rise of temp. ) n7 1aQ 1tQ n n , 



of calorimeter . . j °' 7 l 2 l 8 de S n Csnt 



