THERMAL CONDUCTIVITIES OF ROCKS 271 



The calculation of /„(.v) is being continued to a; = 20. The computation 

 of Kn{x) has been performed for x = 6-o(o- i)ii -5 with 10 figure accuracy. 

 The determination of the early zeros of y„{x) by inverse interpolation from 

 the 12 decimal values of jfn{x) already computed for x = o-o(o- 1)25 -5, 

 n = 2(1)20 is in progress. An additional term in the asymptotic series for 

 the zeros of jfnix) and Yn{x) has been determined and the coefficients 

 computed. 



Table of Powers. — The computation for this volume, and the preparation 

 of copy are almost complete, but some checks have still to be applied. 



Airy Integral. — This w^ork, when complete, will form a part-volume of 

 some 46 pages, including introduction. The greater part of the copy has 

 already been prepared, and the remainder will be ready shortly. The 

 Committee proposes to proceed as soon as possible with the separate 

 publication of this table. 



Legendre Functions. — Some delay has occurred in the production of these 

 tables as a part-volume, for which authority for publication was obtained 

 last year (see 1937 Report). The entire material has, however, been set up. 



Sheppard Tables. — Authority has been obtained from Council for the 

 separate publication of the tables handed to the Committee by the family 

 of the late Dr. W. F. Sheppard, and referred to in last year's Report. The 

 unfinished table, alluded to last year, has been completed. AH the tables 

 have now been checked and every entry verified. Sheppard 's table of the 

 common logarithm of the tail area of the normal curve, to 12 places of 

 decimals at interval o • i , has been sub-tabulated to form an 8 decimal 

 table at interval o-oi. This small extension of the original scope of the 

 volume is in response to a demand for a detailed table of this important 

 function, which is much needed in statistical work. An introduction is 

 being prepared, and the whole should be ready for press shortly. 



Miscellaneous. — In response to an informal suggestion, the Committee is 

 preparing a card-index of mathematical tables to supplement existing 

 bibliographies. This should form a very valuable source of reference for 

 members of the Committee, and be a means of enabling them to answer 

 outside enquiries. It should be mentioned also that the Committee has 

 been in touch with the Tables Committee of the National Research Council 

 of America, which is engaged under the Works Progress Administration in 

 the calculation of certain tables of mathematical functions. 



Reappointment. — The Committee desires reappointment, with a grant of 

 £200, which would be expended mainly on calculations for further volumes 

 of Bessel functions. 



THERMAL CONDUCTIVITIES OF ROCKS. 



Report of Committee appointed to consider the direct determination of the 

 Thermal Conductivities of Rocks in mines or borings where the tempera- 

 ture gradient has been, or is likely to be, measured (Dr. EzER Griffiths, 

 F.R.S., Chairman ; Dr. D. W. Phillips, Secretary ; Dr. E. C. 

 BuLLARD, Dr. H. Jeffreys, F.R.S., Dr. E. M. Anderson, Prof. W. G. 

 Fearnsides, F.R.S., Prof. G. Hickling, F.R.S., Prof. A. Holmes, 

 Dr. H. J. H. Poole). 



I. Introduction. — The heat flow at the surface of the earth is a measure 

 of the heat being generated below ; a knowledge of its variations from 



