the Heat-conductivity of Stone. 249 



and we find from the Table given above that 



«=146°-76 

 = 2*561 radians. 



Therefore K, which equals 



_ 0-00197 x 0-5788 x(5-5)' 2 



(2-oiJiy 

 = 0-00520; 



and E, which equals — ( 1— ), 



1 r \ tan a/ 



= 0-00464, 



the value of ct obtained above being, as will be explained near 

 the end of the paper, outside the limits within which small 

 errors in K and E may be expected. 



Proceeding in a slightly different way, and determining 

 each value of N" from each separate value of m y and using the 

 mean value of N as before, we find 

 K=0-00518, 

 E = 0-00502, 

 the considerable difference between this value of E and that 

 obtained above illustrating what we say at the end of the paper 

 regarding errors. 



The above observations were made very early in the inves- 

 tigation, when we were not sufficiently impressed with the 

 importance of keeping the external temperature really con- 

 stant ; and hence the values of - -=- differ considerably at dif- 

 ferent parts of the curve. We shall afterwards, however, give 

 our reasons for believing that this does not much alter the 

 value of K, although it seriously affects that of E. 



YT. In September 1876 we obtained the curve AAA, PL X. 

 fig. 2, for the cooling of the centre of a stone ball 6'9 centims. 

 radius, initially heated to 69°- 62 C, the temperature of the 

 stream of water flowing outside being carefully measured at 

 every instant and plotted, giving the curve a a a, fig. 2, the 

 scale for time in both curves being such that X represents 

 fifty minutes. To obtain K and E from these curves we em- 

 ployed four different methods, as follows : — 



First method. — The external temperature having been plotted 

 from the time when the curve for the internal temperature be- 

 came logarithmic, the external-temperature curve was pro- 

 duced until it cut the axis corresponding with time nought, 



