150 Prof. Tait on Thermal Conductivity. 



We have, first, terms containing x only: — 



/5B 2 j + | CV 2 -*. 



These terms show how the mean temperature is altered 

 throughout. 



Next, we have the single term 



^t?£ C 2 e~ 2m * cos (±KmH - 2mx). 



This is a small wave of half period, which we need not further 

 consider. 



Finally, we have, as the modification of the original wave, 



Ce~™ | (^-^ Bx + m (*+& B.? 2 ) cos (2fcm 2 t -mx) 



- m (*+& Bx 2 sin (2mn 2 t- mx) j . 



These terms, when combined with the harmonic part of the 

 assumed value of u, may be put in the form 



Ce- TO i*cos (2fcm 2 t—m 2 x); 

 where 



m 1 = m[l -. — -B —-Bx), 



\ 4m 4 / 



m 2 = ?ny 1 j — oxh 



We thus see the effects of the introduction of the quantities a 

 and j3 upon the amplitude and phase of the wave ; and it is 

 evident that they are of the greater consequence the greater is 

 the difference of mean temperature at the sides of the slab. 



Hence the only legitimate mode of applying Angstrom's 

 method is to keep the mean temperature the same throughout 

 the slab. This can easily be effected. 



It is obvious, moreover, from the values of m x and m 2 above, 



o . k 



that Angstrom's method gives the value of - for the mean of 



c 



the mean temperatures indicated by the two thermometers. 



Only there is always the extraneous factor 



which is usually very nearly unity. 



I have worked out by the above method the case of two 

 harmonic waves (in the value of u), one of half the period of 



