8 PROFESSOR CARGILL G. KNOTT ON 



of two pairs of coils. In this way the magnetic induction produced by the " sectional " 

 current along, say, the A tube could be directly compared with the magnetic induction 

 produced by the " axial " current along the B tube ; and vice versa. 



To complete the investigation it was necessary to know the laws governing the mag- 

 netic action of the axial current. At first it seemed sufficient to assume, in accordance 

 with the usual view, that the magnetic force due to the axial current was inversely as the 

 distance in the iron substance as well as in the air spaces, and that with the currents used 

 the value of the force was small enough to warrant us taking the permeability as constant 

 throughout the iron. There were hints, however, that these assumptions were not even 

 approximate^ true. Accordingly, a series of experiments was undertaken in which the 

 circular inductions due to various axial currents were carefully measured. In some experi- 

 ments the induced currents were measured on a ballistic galvanometer ; in others the 

 induced currents were measured by balancing them against the induced currents produced 

 in the secondary of a standard pair of coils in whose primary the axial current was made 

 to flow. The results obtained by both methods were in good agreement ; and I give here 

 only the one series. It was the last in point of time, and was very carefully carried 

 out by Mr Sawada, a graduating student in physics of the Imperial University of Japan. 



The quantity directly measured was the total induction across a radial section of the 

 tube. It can obviouslv be written in the form 



/a 

 i'~Rdr , 



where I is the length of the tube, a and b the external and internal radii, R the magnetic 



force at a point distant r from the axis, and // the permeability at this point. In general 



// will be a function of R. If, however, // is unity, we know that R has the value 2i/r 



where i is the total current passing axially through the tube. In this case the integral 



gives us what might be called the total " normal induction " across the radial section of 



the tube. Its value is 



a 2 

 U log - 2 . 



Dividing by the area of the section, viz., l(a - b), we get the average magnetic force 

 influencing the tube. Thus we may calculate what might be called the average permea- 

 bility m, where 



„2 r 



fii log 



' b 

 or fjih = S3 . 



« 2 r , 



j§- - J /j. Rdr , 



Here S3 is measured experimentally, and b is calculated in terms of the current and the 

 known dimensions of the tube. The values of these quantities are given in the following 

 table. 



