the Heat -conductivity of Stone. 251 



were led to make the assumption that if T° C. is the tempera- 

 ture of the centre and x° C. is the outside temperature at any 

 instant, and if T ° C. was the initial temperature of the centre, 

 then Fourier's equation becomes 



a2Kt 



T-*=2(T -«) 



or 



Sin a. — a. COS a 

 a — sin a cos a 



Cr2 



log (T-#)= log 2 + log (T — x) + log 



Sin a — a COS a 



(9) 



* 2 Kt 



a — sin a cos a (V 2 " 

 Differentiating with respect to t, we have 



1 d , m s ^^..^ 



O 2 ' 



^^^ T ^ T -a? d* 



a 2 K 



from which 7^-5-, or m, can be found : and when this is deter- 



mined we can find a, since we can find from equation (9) the 

 value of 



sin a — a cos a 



sm a cos a 



which is called R in the following list of numbers, obtained 

 from the curves AAA and a a a. 



t. 



T. 



X. 



m. 



B. 



aP 



K. 



E. 







61-62 















1050 



4470 



19 00 



000114 



0840 



186 90 



000546 



000281 



1200 



40-37 



18 69 



115 



0-846 



1311 



541 



289 



1350 



3676 



18-38 



114 



0835 



185 90 



553 



277 



15(M» 



33-68 



18-08 



113 



0-824 



1337 



5d7 



265 



1650 



30-98 



1776 



111 



795 



129-98 



608 



242 



1800 



28 75 



17 46 



108 



0756 



11979 



675 



220 



1950 



26-80 



1715 



106 



0726 



113-33 



741 



199 



2100 



2521 



16-94 



104 



0700 



107-87 



793 



187 



2250 



23-88 



1674 



105 



0717 



111 44 



758 



194 



2400 



2273 



16-60 



108 



0772 



12H5 



639 



223 



2550 



2170 



16-50 



115 



0-919 



152 36 



443 



249 



Mean K = 0-00624. 



Mean E = 0-00237. 



Third method. — Assuming that the curve from 1050 seconds 

 is logarithmic, and satisfies the equation 



where N and m are constants, and that the outside tempera- 

 ture o?° C. is constant but unknown, we can find by the method 



ldv 



of least squares the value of aP and of 



v dt 



, or m, in the 



