164 PROFESSOR K. PEARSON AND MISS A. LEE ON THE VIBRATIONS 



laborious, but as no investigation had been made of the damping out of an electro- 

 magnetic field, the work seemed worth undertaking. Some remarks may be made on 

 the methods by which the arithmetic was carried out. 

 The equation to the curve being written 



sin 2 = c X $ (r), 



COS 27T - - | Y 



c was given the values y^, y\,-, T^Q, ^, and the limiting values of r ascertained, for 

 which 6 was real, r was then given a series of values between these limits altering 

 by small differences, and the values of sin calculated ; frequent values of r were 

 taken at portions of the curve where it was found to be turning, and thus a close 

 approximation found to its form. The original diagrams on a scale of a metre to the 

 inch were formed by joining up the calculated points and painting in the curves so 

 formed. These were afterwards reduced by photography.* 



The dying out of a part of the field of a particular strength is well illustrated in 

 the diagrams. Take the dying out of strengths greater than 50 represented by 

 the fine continuous line. In fig. 25 we see the last sensible loop of the field containing 

 greater strengths than this passing away. Up to fig. 33 we can still trace this 

 portion of the field as a dot. But in fig. 29 the oscillator has ceased to give fresh 

 centres even of this strength, and in fig. 34 they have passed away entirely. Figs. 

 30 to 41 give the shrinking up and final disappearance of parts of the field with a 

 strength greater than 30. Figs. 53 to 56 show the outward passage of the last 

 loop of the field with a strength greater than 10, and another ten diagrams would 

 have sufficed to show no trace of strengths greater than 1. 



(4.) We will now proceed to find the electric and magnetic forces from (vi). 

 First, the electric force, Z, in direction of the axis of the oscillator : 



ml 

 Z=-A^ 



2irr/X 



Jo /< r \ \ [ ft r \}~ 



cos < JTT I I + v > sin < 2ir : / \ 



X 1 4- (2cos-0 shr0) - ' ' x '' 



Second, the electric force, R, perpendicular to the axis of the oscillator : 



h The diagrams have lost very considerably in the process of photography and engraving. It may 

 possibly be that some of the finer loops and dots will appear not at all, or at least unclearly, after the 

 blocks have been somewhat used. We hope shortly to have kinematograph films of the original diagrams 



