and 



the Heat-conductivity of Stone. 

 v = Ne- mt , 



247 



. . (6) 



where N and m are supposed to be constant for the curve. 



Now it is easily seen that when K is considerable with regard 

 to r } as in ordinary balls of metal, the period after which all 

 other terms than the first are negligible is exceedingly short, 

 and that this period is longer as the conductivity is less or the 

 radius of the ball is greater ; and as we intend to use observa- 

 tions made after this period, there is a certain size of ball for 

 any given material which is most convenient for experiment, 

 so that it is of some importance to get a rough idea of the 

 values of K and E before deciding on the size of the ball. 

 From certain considerations of the possible errors in this me- 

 thod of determining K, it will also be seen, further on, that it 

 may sometimes be necessary to make two sets of experiments on 

 a given material — the first to determine K roughly, the second 

 with accuracy. 



Using the observations of which we have spoken, it is evident 



that -r— , which can easily be measured from the curve 



plotted from the observations, is m of equation (6), and that 

 N may be determined from any observation, since 



so that if a time-curve has been drawn from the observations, 

 m and N may be obtained from a very great number of points 

 in the curve. Also v is known; and 



N" sin a. — « cos a 

 2v Q a — sin a cos a 



(7) 



so that a. can be calculated. To calculate a. when we know 

 the value of this expression, a Table of the following kind will 

 be found useful, in which it may be assumed that increase 

 in the expression, for small increments, is proportional to a: — 



a, in degrees. 



«,, in radians. 



sin a. — « COS a. 



a, — sin a. COSa 



11459 

 115-89 

 12000 

 131-50 

 14716 



1-9998 

 20225 

 20944 

 2-2953 

 2-5685 



0753 



0-738 

 0-757 

 0-813 

 0-893 



