70 PROCEEDINGS OF THE AMERICAN ACADEMY. 



and the curve 6 = -£ e~~ at 



passes through all these points, which are spaced at equal time inter- 

 vals T. 



If, then, the curve which represents as a function of the time (t) the 

 deviation (6) of a swinging body from the position of equilibrium be 

 drawn, and if the motion be of the kind defined by the equation (21), 

 the maxima will be spaced at equal time intervals, and it will be possi- 

 ble to pass through all the crests a curve of the family 8 — Ce~ at 

 where C and a are constants. It is easy to see whether or not this last 

 condition is satisfied in any given case, if one has measured a series of 

 successive amplitudes on the same side (di, d 2 , d 3 , d±, d 5 , . . . d T ). If 

 we measure t from the date of the first of these elongations, the de- 

 sired curve must have an equation of the form 6 = d\e~ at , and aT 

 may be determined from any other amplitude (say the Arth) for 



4 = d l e-*-V aT . 



If the value of aT thus found be the same for all values of k, the 

 condition is satisfied. Sometimes when the period of the oscillation is 

 extremely short, the maximum points seem to form a continuous 

 curve, unless the diagram be much drawn out horizontally. In such a 

 case as this one may use, in making the test just described, not a 

 series of successive amplitudes on the same side of the position of equi- 

 librium, but points on the curve, taken at convenient values of t equally 

 spaced. 



The Damping of the Quick Oscillations of a Light System 

 suspended between two stretched wlres by the resist- 

 ANCE of the Air and Frictional Forces in the Wire. 



It will appear from the observations recorded in this paper that if a 

 small magnetic needle be mounted horizontally with a minute gal- 

 vanometer mirror upon a short, stiff, vertical piece of wire or glass 

 filament stretched between two vertical pieces of fine wire, and if the 

 needle be turned horizontally out of its position of rest through an angle 

 of say 5° and then allowed to oscillate, the curve drawn through the 

 crests of the oscillations as represented on a photograph record will 

 usually not coincide exactly with any exponential curve of the family 

 mentioned above. If a curve of this family be drawn nearly through a 





