﻿514 Prof. J. A. Pollock on the 



cycle of operations. In figs. 52 and 53, if the timing Lad 

 been accurate and friction negligible, the parabolas would 

 have been bounded bj straight lines at 45 degrees to the 

 axis of coordinates. 



Still keeping the amplitudes equal and the frequencies as 

 before, the remaining initial conditions are now changed. 

 In fig. 54 A and C are released from their extreme outward 

 positions by means of rods carried on the pendulums B and D. 

 The rod on B strikes the amplitude-prop of C while a hooked 

 rod on D releases A. A and C are released simultaneously, 

 and in this case the style was in contact with the prepared 

 surface from the commencement. The equations to the trace 

 .are 



x = a cos [{2p + h}t + tt] +a cos [{2p + Styt + ir] ," 

 y—a cos [{/> + 2/i}*+3w/2]+ a cos [pt + ir/2~\. 



Again neglecting frictional decrement we see that the com- 

 plete trace would be bounded by the circle A ,2 + ?/ 2 = 4a 2 . 

 The pen was removed when t=7r/2h, when the path was 

 approximately rectilinear along the axis of y. If the trace 

 had been continued, parabolas would have been drawn with 

 their concavities in the opposite direction, the completed 

 figure being symmetrical about both axes. The parabolas 

 touch the curve 



4aV+^ 2 (y 4 -40ay-32a i )-8(y 2 -2a 2 ) 3 =0, 



the cusps of which are on the y axis at distances +ay/2 

 from the origin, the apex of the figure that we have traced 

 coinciding with one of the two double points of the envelope. 

 The portions of the curve between these double points con- 

 stitute the effective envelope. 



LIV. The Mature of the Large Ions in the Air. By J. A. 

 Pollock, D.Sc, Professor of Physics in the University of 

 Sydney *. 



IN 1905 Langevin f discovered that in addition to the 

 small gas ions, with a mobility of about I'D, there are 

 iu the air much larger ones which have a mobility of only 

 1/3000. Although our knowledge of the properties of these 

 large ions is very slight, yet from the few facts which are 

 known some deduction may be made as to the nature of the 

 ionic structure. 



* Communicated by the Author. 



t Langevin, Comptes JRendus, cxl. p. 232 (1905). 



