30 PROCEEDINGS OF THE AMERICAN ACADEMY. 



at 0° C. The terms of the series which give the final temperature may 

 be found without much difficulty by the aid of the numbers in the third 

 column of Table V, Their values are 



1. +61.3980 



2. —19.6480 



3. + 7.8876 



4. - 3.7116 



5. + 1.8474 



6. - 1.0224 



7. + 0.5938 



8. — 0.3568 



9. + 0.2198 



10. - 0.1382 



11. + 0.0882 



12. - 0.0570 



13. + 0.0372 



14. - 0.0246 



15. + 0.0162 



16. — 0.0110 



17. + 0.0074 



18. — 0.0050 



19. + 0.0034 



20. - 0.0022 



etc., so that the temperature required is 47°. 12+ C. 



The terms of the series which give the final temperature at points for 

 which z = 1, r = 2, can be found in a similar way by the help of the 

 numbers in the third column of Table VI. Their values are 



