324 On the Conduction of 'Heat in a Spherical Mass of Air. 



■ 



mJTT. 



Left-hand 

 member 



of (55). 



•4942 

 •1799 

 •0871 

 •0510 

 •0332 

 •0233 



! 



i. 



mjf'ir. 



Left-hand 

 member 

 of (55). 



1 



1-0994 

 2-0581 

 3-0401 

 4-0305 

 5-0246 

 6-0206 



•3 



10 



n 



12 



70177 



8-0156 



90138 



100125 



110113 



12 0104 



0175 

 •0134 

 •0106 



•0086 

 •0071 

 •0060 



2 



3 



4 



5 



6 



Thus the solution (51) of our problem is represented by 

 ^/e = -4942^ 1 -°" 4 ^' + -1799^ 20581 ^ , + . .. . . (56) 

 where by (9) , with omission of g and restoration of a, 



t f lt = iT 2 v^a 2 (57) 



The numbers entered in the third column of the above 

 table would add up to unity if continued far enough. The 

 verification is best made by a comparison with the simpler 

 series (52). If with t zero we call this series 2' and the 

 present series 2, both 2 and 2' have unity for their sum, and 

 accordingly yL' — 2 = 7 — 1, or 



111 



7 



£(j+£+i.+v-).-*" 



1=41. 



Here 67/71- 2 = '8573, and the difference between this and the 

 first term of 2, i. e. *4942, is "3631. The differences of the 

 second, third, &c. terms are '0344, '0082, '0026, -0011, '0005, 

 ♦0000, &c, making a total of '4099. 



P. 



(fO). 



f. 



,56). 



•00 



1 0000 

 •7037 

 •6037 

 •4811 

 •4002 

 •3401 

 •2926 



•60 1 



•70 



2538 

 2215 

 1940 

 1705 

 1502 

 0809 

 0441 



•05 



•10 



•80 



•20 



•30 



•90 



100 ! 



150 



2-00 



•40 



•50 





i 1 



We are now in a position to compute the right-hand 



