the Heat-conductivity of Stone. 263 



Now we have seen from the curves AB, CD (fig. 5), that 



the conditions of equal and small errors in K and E necessitates 



a being about 120°; consequently conditions (13) require that 



CV 2 



— f^- must be equal to, or greater than, 3298*1. But equation 



, O 2 



(12) requires that -~- should be less than 4*343*; 



.*. 4-343* must be > 3298*1, 

 or 



t must be > 759 seconds ; . . (14) 



and this result is independent of the values of C, r, K, and E. 

 If, however, it be desired to obtain the minimum possible error 

 in K only, then the curve A B (fig. 5) shows us that a should 

 be about 140°; therefore conditions (13) require that 



O 2 



-^r- should be equal to, or greater than, 4489*2. 



Combining this with equation (12), we see that 



4*343* must be > 4489*4, 

 or 



t must be > 1034 seconds, 



a result also independent of the values of C, r, K, and E. 

 Condition (14) is independent of the values of C, r, K, and 

 E ; but substituting in equation (12) known values of C and 

 K, we obtain a higher inferior limit for t. In our experiments, 

 for example, 



C = 0*5738, 

 and 



K = 0*006 about; 



so that for a ball of 6*9 centims. radius, equation (12) leads 

 to the result that 



t must be >1072 seconds. 



If, again, we only wish that the possible error in E shall be a 



Cr 2 

 minimum, then a should be small ; consequently -^- may be 



small, and therefore t ; that is, we may use the curve from the 

 beginning. 



We might here return to our Table of the values of -^- ; 



and remembering that a must be about equal to 120 to give 

 small and equal possible errors in K and E, we could deter- 

 mine the size of the ball of given conductivity and emissivity 

 most suitable for experiment. Thus we might show that, even 



