ON TEHKESTRIAL MAGNETISM AND ATMOiSrnERIC ELECTRICITY. 757 



within the tube, the additional current flowing through it, owing to the change of 

 resistance, will be 



{p-p')nl 



K + S 



» 



where R denotes the resistance of the tube, and S the resistanco of the ground 

 between A and B. If the resistivity p' is of the order of magnitude of that of 

 copper, it will be small compared to p, and may be neglected in the above 

 expression. 



Imagine now this tube of flow between A and B to consist of two overlapping 

 tubes, one of material equal to that of the rest of the ground, the other of copper, 

 and let the latter tube be lifted out of the ground without altering its total 

 resistance, but keeping its connection at A and B. The current traversing the 

 lifted-up part will remain the same as before, provided that the electromotive forces 

 of induction are not sufficient to produce an appreciable current in a circuit made up 

 of the original and displaced position of the tube, a condition which will be satisfied 

 in the case of earth currents, except perhaps at times of great magnetic storms. 



We have now an arrangement equivalent to that used in earth-current observa- 

 tions, for the only effect of the earth plates at A and B will be to diminish the 

 earth resistance S. 



The observed current i will be connected with u by the relation 



t = J- . 



R + S 



The resistance R + S is measured by the introduction of an electromotive force 

 e in the circuit; if the observed current, under these circumstances, be increased 

 by a quantity i', the equation 



ei 



will give the curient density of the earth current. It is seen that u is proportional 

 to the conductivity of the material of which the ground is made up, and that a 

 knowledge of that conductivity, which may vary from day to day, according to 

 the amount of moisture contained iu it, is therefore essential to a correct inter- 

 pretation of earth-current observations. 



If the circuit is a long one, S may be small compared to R, and the latter 



quantity will be ^—, a being the cross section of the wire, so that 



i p' 

 a p 



which shows that the current densities in the wire and ground are in the propor- 

 tion of their conductivities. 



The above investigation points to the importance of measuring the conductivity 

 of the ground wherever earth-current observations are made. Samples of the soil 

 taken from different depths would probably give different results, and would then 

 indicate how the current density varies with depth. 



6. 0)1 the Construction of Magnetic Observatories. By Dr. Snellen. 



A magnetic observatory should fulfil the following purposes. As it is desirable 

 that regular observations be made in many places of the absolute values of the 

 magnetic elements, a base-station is required for the reduction of observations. Also 

 it is desirable to observe continuously regular variations of these elements. And, 

 finally, there ought to be facilities for carrying on researches connected with 

 magnetism in general. 



A combination of two observatories, one for absolute measurements and another 

 for observing and recording continually the variations of the earth's magnetism, 

 will fulfil these conditions. It is desirable to have them in separate buildings. 



