PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 71 



number of crests in the middle of the diagram, it will usually fall some- 

 what below the observed curve at each end. It will be convenient 

 to instance a few typical cases at the outset. 



I. P'igure 1 (Plate l) is a copy of a photographic record obtained 

 from a short-period mirror galvanometer. The one-centimeter-long 

 needle of this instrument, made of watch spring, was mounted on a 

 short, stout, inflexible piece of glass fibre, together with a minute bit 

 of very thin mirror, and the fibre was suspended, like the coil of a ma- 

 rine d'Arsonval galvanometer, 9 between two pieces of extremely fine 

 gimp, under gentle tension. The light from an electric projecting 

 lantern about twenty feet from the galvanometer, shining through a 

 small hole in a brass plate used as a lantern slide, fell upon the 

 galvanometer mirror, and a sharp image of the hole was formed on a 

 piece of sensitive paper on a horizontal revolving drum at a consider- 

 able distance from the mirror. The needle was first deflected a little 

 off scale by a steady current sent through the coils of the galvanom- 

 eter when the light was screened, the screen was then removed and a 

 record of the manner of decay of the amplitude of the excursions of 

 the needle obtained when the galvanometer circuit had been suddenly 

 broken. The moment of the couple due to the mutual action of the 

 magnet and the earth's field was relatively inappreciable. Three dif- 

 ferent drums and three pieces of chronograph clock work were used in 

 making the records discussed in this paper, but for the fastest speeds an 

 electric motor driving a worm gear accurately cut for the purpose by 

 Mr. G. W. Thompson, the mechanician of the Jefferson Laboratory, 

 was employed, and this left nothing to be desired. The apparatus was 

 put together by Mr. John Coulson, who helped me in all the work 

 and took many of the photographic records. Most of these records, 

 of which I have a very large number, were about 50 cms. long and 

 20 cms. wide, but much larger ones could be obtained if desirable. 



On one of the photographs taken with the apparatus just described a 

 series of measurements of the amplitudes of the oscillations, as depicted 

 on the diagram, were made at times, represented by whole centimeters 

 from the time origin, on the figure. The successive values for the ex- 

 cursions were: 1260, 1006, 791, 646, 521, 420, 349, 280, 231, 190, 159, 

 131, on a scale of equal parts, and, at the scale distance used, these 

 numbers were accurately proportional to the angular amplitudes of the 

 needle at the times concerned. If, then, the resistance to the oscilla- 

 tions were proportional to the angular velocity, it should be possible 

 to draw a curve of the family y = A- e~ al the successive ordinates of 



9 See M, Figure 3. 



