PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 81 



of the solenoid, and, receiving the light from a small round hole in a 

 brass plate in the slide holder of a distant Schuckert projecting lan- 

 tern, throws it upon a sheet of bromide paper wound upon the drum 

 D, where a small very sharp image of the hole is formed. The drum 

 may be turned uniformly at very various speeds, either by clockwork or 

 by an alternating motor actuated by a 60 cycle, 110 volt street circuit. 

 The magnetic field about the suspended magnet can be given any de- 

 sired value within wide limits by sending through G a suitable steady 

 current from a battery of large storage cells. A current from another 

 similar battery sent through the coil K serves to deflect the magnet 

 out of the meridian against the given restoring field. When the cur- 

 rent in K is suddenly interrupted, the suspended system oscillates with 

 continually decreasing amplitude about the horizontal meridian and 

 makes a record of its motion upon the photographic paper. In order 

 that the seam in the paper on the drum may not come at an undesirable 

 place in the record, the break in K's circuit is made automatically by 

 the drum when it reaches a given position, but the system of relays 

 by which this is accomplished is not indicated in the figure. 



Experience gained with this apparatus shows that if the original 

 deflection caused by a steady current in K is not more than 5° or 6°, 

 and if the intensity of the magnetic field about the magnet is not too 

 great, the record obtained after K's circuit has been suddenly broken 

 is such that it is possible to draw a curve of the family y = A- e at which 

 shall, within the errors of observation, pass through all the crest of 

 the diagram except the first two or three. We may assume that the 

 motion in a case like this could be mathematically explained on the 

 assumption that a body of fixed moment of inertia (7), — quite different, 

 however, from the moment of inertia of the actual suspended system 

 swinging in vacuo, — is oscillating under the action of the restoring 

 moment due to the magnetic field and a retarding moment equal at 

 every instant to the product of a damping coefficient (2 a) and the 

 angular velocity of the system. If the intensity of the field about the 

 magnet be somewhat changed, I will have nearly its old value, but 

 the damping coefficient, though constant for a given system swinging 

 with a given period, has a new value when the period is changed. The 

 change of the damping coefficient usually follows the direction of the 

 change indicated by Stokes's theoretical treatment of the resistance 

 encountered by a sphere making harmonic oscillations of small am- 

 plitude in a viscous liquid. It is usually rather difficult to determine 

 the apparent moment of inertia of the system (7) with accuracy from 

 observations of the period of the oscillations (for there generally is a 

 fixed period), the value of the damping factor, the intensity of the ex- 

 vol. XLrv. — 6 



