PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 73 



same room has a coil the swings of which decay at a decreasing rate 

 as the amplitudes grow less. 



In his Anleitung zur Bestimmung der Schwingungsdauer einer 

 Magnetnadel (1837), Gauss describes a suspended magnet the loga- 

 rithmic decrement of the swings of which increased on a certain occa- 

 sion from 1168 X 10 -6 to 1301 X 10~ 6 in 422 oscillations. The actual 

 value of the logarithmic decrement for this magnet and for a given 

 amplitude varied from day to day, being usually smaller in cloudy 

 weather. 



II. After a number of records had been made like that reproduced 

 in Figure 1, a small vertical mica damping vane of about 3 square 

 centimeters area, was fastened symmetrically to the little glass rod 

 which carried the mirror of the swinging system, and a new series of 

 records were obtained. The restoring moment was the same as before, 

 but the moment of inertia had been increased somewhat, as well as the 

 resistance due to the air. Under these circumstances the period was 

 much longer than before, while the manner of decay of the amplitudes 

 was much the same. Figure 2 (Plate 1) represents on a reduced scale 

 one of the smaller photographs. Figure A was plotted from a large 

 record in which the crests of successive oscillations were 4.5 milli- 

 meters apart at the beginning of the diagram and nearly 4.9 millimeters 

 at the end. Such a gradual change of period during the motion often 

 accompanies the swinging of a magnet under the torsional forces of 

 a stretched wire. 10 



The values, in ten thousandths of a radian, of a number of successive 

 amplitudes, as obtained from the photograph, were: 597, 556, 518, 

 481, 448, 419, 390, 367, 341, 320, 300, 280, 262, 246, 230, 217, 203, 190, 

 179, 168, 159, 148, 140, 132, 124, 117, 111, 104, 98, 92. 



These numbers, used as ordinates of points with equally spaced 

 abscissas, give a curve of the form shown in Figure A by the full line 

 WHCDK. The dotted line VCDG shows a curve of the family 

 y = A • e~ al , which coincides almost exactly with the full line be- 

 tween the points C and D. 



The curves HT, CL represent attempts to determine the constants 

 of an equation of the form (6) which should yield a curve of amplitudes 

 like the observed curve. Both HT and CL pass exactly through two 

 adjacent points of the line WHCDK, and the other points were deter- 

 mined by a series of applications of the equation (8). Some of the 

 characteristics of certain of the records which I obtained resemble 

 those of oscillations under a resistance proportional to the square of 



10 Guthe, Physical Review, 1908. 



