276 REPORTS ON THE STATE OF SCIENCE, ETC. 



The temperature at seven points along these bars is measured by thermo- 

 junctions. From these the temperature drop across the specimen T and 

 the temperature gradient p in the bars are determined. If there were no 

 loss of heat by convection and the specimens were in perfect thermal 

 contact with the bars, the conductivity of the specimen, k would be given 

 by 



k = CpSIT 



where S is the thickness of the specimen and C is a constant that may be 

 determined by measurements on a substance, such as fused silica, whose 

 conductivity is known. 



The loss of heat by convection may be reduced by enclosing the apparatus 

 in a bell-jar across which run paper discs. The remaining loss may be 

 estimated from the departure of the temperature distribution in the bars from 

 linearity and allowed for. 



The error from the lack of perfect thermal contact between the bars and 

 the specimen may be eliminated by making measurements on specimens of 

 two different thicknesses. For this elimination to be satisfactory it is de- 

 sirable that the contact should be as good as possible. Experiments on the 

 best method of joining the specimens to the bars are in progress. Painting 

 with a thin layer of very thick cellulose varnish seems the most promising 

 method. If the specimen is pressed on the bars while the varnish is still 

 tacky the minute irregularities in surfaces of the specimen and the bars are 

 filled with celluloid. 



The preliminary tests of the apparatus are being made with specimens 

 from Kingsclere, when it is working satisfactorily measurements will be 

 made on the Pevensey specimens. 



A specially careful investigation will be made on the Cambridge Gault 

 for comparison with the values obtained by the methods described in § i . 



(5) Theoretical Investigations. — If the surface of the earth is not a plane 

 of constant temperature there will be irregularities in heat flow that may 

 mask those due to variations in conductivity and in the generation of heat. 

 Dr. Jeffreys has devised a method of allowing for these ; his investigation, 

 which has been published in Vol. 4 of the Geophysical Supplement to the 

 Monthly Notices of the Royal Astronomical Society, shows that the dis- 

 turbance Su of the temperature gradient at a depth Z below the surface is 

 given by 



CO 



r r'^ — 2,z^ 

 ^•" = 1^ (^2 4_ g2)8 rdr . . . (i) 



where v is difference between the mean temperature at sea level round a 

 horizontal circle of radius r and that at sea level under the station ; that 

 is z; is the mean value of 



ip-p')h 



where p and p' are the temperature gradients in the earth and in the air 

 and h is the difference between the height of the station and the mean height 

 of the circle. From (i) expressions may be derived for the disturbance at 

 the surface and for the mean disturbance down to any depth. Certain 

 special cases may be evaluated analytically, for example the gradient at the 

 bottom of a hemispherical cavity is three times that at a distance from the 

 cavity, and the gradients at the crests and troughs of a series of parallel 

 simple harmonic ridges and valleys of height zA and wavelength X differ 



