T. Deighton 221 



layer begins to affect the couduction between them to a similar extent. 

 The result obtained in the beaker experiment is easily understood since 

 the surface of the conducting layer being plane, only small segments 

 of tores carrying an appreciable fraction of the current pass through 

 this layer, and the segment is less the greater the current density in 

 the tores. An attempt to solve the matter completely by mathematics 

 led in all cases to expressions integrable only over restricted ranges or 

 in very slowly converging series, putting this method of procedure out 

 of court for practical purposes. A series of rough approximations led 

 to results not out of keeping with those obtained. 



CONCLUSION.S FROM ABOVE ExPERI.MENT.S. 



These results are of practical importance as they show what may and 

 what may not be expected from this method of moisture determination. 

 It is clear in the first place that what is obtained is the mean resistance 

 of a volume of soil which may for practical purposes be considered as 

 of rather greater extent than a sjahere whose poles are the electrodes, 

 something the shape of an apple with the electrodes at the calyx and 

 stalk, since the fraction of current passing outside a selected tore falls off 

 very sharply beyond d = 45°, and soon becomes negligible. The moisture 

 content will also refer to this volume of soil and local and depth varia- 

 tions will be obliterated. If therefore we desire to measure the moisture 

 content at any depth we must place the electrodes at such a distance 

 apart that the moisture gradient can be considered uniform in the 

 volume of soil concerned when the deficiency above the level of the 

 electrodes will be counterbalanced by the excess below this level. More- 

 over if the distance is more than a few inches it will be necessary to take 

 account of the tendency of the current to dip down into the moister 

 layers, or to continue the simile above, of the downward bend in the 

 core of the apple. Secondly the electrodes should really be of such a 

 size that they may be considered small in comparison with the distance 

 apart as otherwise the calculations do not strictly hold and the new 

 conditions ought to be investigated afresh. The necessity of obtaining 

 good contact with the soil puts a practical limit to the size of the electrode 

 and it was found in consequence that 3" apart is about the lower limit 

 for the electrode distance. The distance apart must moreover be chosen 

 with a view to confining the current or such part of it as matters to the 

 portion of soil concerned, e.g. a distance of 15'-20', while probably giving 

 illuminating information on forest land would usually be quite useless 

 in ordinary arable farming. Finally it seems possible that considerable 



