THERMAL CONDUCTIVITIES OF ROCKS 273 



checked before the volume is published, and it is expected that the volume 

 will appear before the end of 1937. 



Work on the preparation of a second volume, to contiin functions of 

 higher integral order (up to w = 20) has continued. The calculation of 

 values of I«(x) for n = 2(1)22 and x = oi(oi)6-o has been completed 

 under the supervision of Dr. Thompson, and of values of Kk^^x) for « = 2(1)20 

 and X = o • 1(0 ■ 1)6 -5 under the supervision of Dr. Bickley. Further work 

 has been carried out on the calculation of kn(x), i.e. x" Kn{x), up to .\;= 6 at 

 interval o • i for n = 0(1)20. 



Table of Poivers. — Most of the powers required, in addition to those given 

 in Glaisher's table (see 1936 Report), have now been completed. Con- 

 siderable progress has also been made towards checking the whole, and in 

 the preparation of copy, mainly on the National machine. Valuable 

 assistance in the computation has been given by Miss E. J. Ternouth and 

 Mr. C. E. Gwyther. 



Airy Integral. — During the last year the scope of the proposed table 

 (see 1936 Report) has been much enlarged. The computation of pivotal 

 values over the extended range has now been completed, and the methods 

 of subtabulation and preparation of copy are under consideration. 



Sheppard Tables. — Council authority is being sought for the separate 

 publication of certain tables related to the probability integral of the normal 

 curve, which were handed to the Committee by the family of the late 

 Dr. W. F. Sheppard. One table of the ratio of tail area to ordinate of the 

 normal curve, to 12 places of decimals at interval 001, together with 

 reduced derivatives, was left incomplete by Dr. Sheppard, and the Com- 

 mittee has completed the calculations. 



Legendre Functions. — Authority has been obtained from Council for the 

 separate publication as a part-volume of these tables (see 1936 Report). 

 The tables are in the press, and will appear as the first of the series of part- 

 volumes which the Committee proposes to issue. 



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

 £200. A whole-time computer could be employed throughout the year on 

 calculations of Bessel functions and the Airy integral. 



THERMAL CONDUCTIVITIES OF ROCKS 



Report of Committee appointed to investigate 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., from Section A ; Dr. E. M. 

 Anderson, Prof. W. G. Fearnsides, F.R.S., Prof. G. Hickling, 

 F.R.S., Prof. A. Holmes, Dr. J. H. J. Poole, from Section C). 



It has appeared that the disturbance of the measured temperature gradient 

 in irregular country is likely to be appreciable, since the outer surface is 

 constrained to be at atmospheric temperature, and the mean decrease of 

 temperature with height in the air is about a fifth of that in the crust. A 

 formula for the appropriate allowance has been found by Dr. Jeffreys ; the 

 theory is an application of the potential theory of Green. 



It has been found that temperatures in a borehole can, with suitable 



L .; 



