the Heat-conductivity of Stone. 

 Table (continued). 



261 



a, in 



degrees. 



«, in 



radians. 



a, 



tana 





, sin a 



lOg ; . 



a — Sin a COS a 



380 

 390 

 400 

 410 



6-632251 

 6-806784 

 6-981317 

 7-155850 



18-221958 



11-789695 



8-320010 



6-004471 





2-7339632 

 2-8945736 

 2-9958956 

 T-0605549 









420 

 430 

 440 

 450 



7-330383 

 7 504916 

 7-679449 



7-853982 



4-232199 

 2-731566 

 1-354095 

 





10988471 

 T- 1166483 

 1-1178020 

 T-1049101 







1-000000 



460 



8-028515 



- 1-415644 



2-415644 



T-0795630 



470 



8-203047 



- 2-985665 



3-985665 



T-0423199 



480 



8-377580 



- 4-836798 



5-836798 



2-9925255 



490 



8-552113 



- 7176075 



8176075 



29278685 



500 



8-726646 



-10-400014 



11-400014 



2-8433814 



510 



8-901179 



-15-417294 



16-417294 



27288930 



520 



9075712 



-24-935314 



25-935314 



2-5620578 



530 



9-250245 



-52-460735 



53-460735 



22655615 



540 



9-424778 



CO 





— CO 



1 



In determining the most suitable size for our ball there are 

 some other points to be considered: — 



Fi?>st, for a given size of ball let us find the period after 

 which the time-curve for v becomes a simple logarithmic curve 

 — that is, the period after which 



sinai 



03 



<xi sin ui cos a x 

 is many times greater than 



sina 2 



a#Kt 



a 2 — sma 2 cos«2 — 

 Now for values of a such as we have been considering, the 

 first trigonometrical coefficient is found to be two or more 

 times the second, so that the second term will be negligible 

 for a value of t such that, 



* 2 Kt 



cr2 >100e" 



or 



**Kt 



log 10 e>2' 



a 2 Kt 

 C/2 





Uv 



u» 



