510 PROFESSOR KNOTT ON SOME RELATIONS BETWEEN 



and at convenient stages the deflections of the mirror magnetometer were noted. To 

 reduce these readings to definite units it was necessary to know the position of the 

 magnetic pole corresponding to the longitudinal magnetism produced. To assume this 

 pole to lie at the end of the wire did not commend itself as a necessarily sufficient 

 approximation, and the following method was adopted instead. 



Let the reading a mark the position of the magnetometer on a horizontal centimetre 

 scale in line with the wire, and let x be the unknown position of the nearer pole of the 

 wire as measured on the same scale. Then, if I is the length of the wire — more correctly, 

 the distance between the poles — and m the strength of the pole, we have for the field at 

 the position a the value 



m\(ct-x)- 2 — (a + l — x)- 2 }. 



For a given cyclic twisting with a given current let the range of deflection of the 

 magnetometer mirror be the angle 6. Then the above expression is proportional to 

 tan i 6. Let now the position a be changed to a', everything else remaining the 

 same. For the same cyclic range, the angle of deflection of the magnetometer mirror will 

 be changed say from 9 to 6'. We have then at once the equation 



tan- 



(a-x)- 2 -(a + l-x)~ 2 2 



(a'-x)- 2 -(a'+l-x)- 2 ~ 



tati- 

 2 



from which the quantity x can be calculated. It was found that the term involving the 

 length of the wire was negligible to the degree of accuracy possible in the experiment- 

 When x is known, the distance of the pole from the magnetometer magnet is known also, 

 being (a — x) or {of — x) according to the position chosen. In terms of this distance and 

 the known horizontal component of the earth's field, the magnetic intensity in the wire 

 can be calculated from the observed deflection. 



17. Results for Nickel. — The most complete series of experiments is for nickel wire 

 No. 1 (diameter = 0*86 mm.). Table IV. contains the numbers for it given in full detail. 

 The first column gives the currents along the wire, and the second the stages of twist in 

 degrees at which readings were taken. The third and fourth columns, under the one 

 heading " Intensity," give the magnetic moments per unit volume (in C.G.S. electro- 

 magnetic units) corresponding to the successive stages of twist. The third is read 

 downwards and the fourth upwards ; and in this way the cycle is completed. The fifth 

 column, headed " Lag," gives the difference between the intensities that correspond to the 

 same nominal stage in the twisting. When this difference is positive we have true 

 magnetic lagging ; when negative, we have what might be called magnetic priming. The 

 next column, headed " Area-^- ir" contains numbers proportional to the areas of the closed 

 or nearly closed cyclic graphs. These numbers may be taken as measuring the average 

 magnetic lags for the different combinations of current and cyclic twisting. The last 



