80 PROCEEDINGS OF THE AMERICAN ACADEMY. 



the variations in thickness of felt are taken as abscissas ; then draw 

 through the points the best fitting curves and average the correspond- 

 ing ordinates taken from the curves thus drawn ; and with these aver- 

 age ordinates redraw both families of curves. The points shown on 

 the diagram are of course the original results obtained experimentally. 

 In general they fall pretty close to the curves, although at times, as in 

 the points noted, they fall rather far to one side. 



The following will serve to present the points of particular interest 

 revealed by the family of curves in Figure 12, where the absorption by 

 the several thicknesses is plotted against pitch for abscissas. It is to 

 be observed that a single thickness scarcely absorbs the sound from 

 the eight, four, and two foot organ pipes, Ci 6-4, C2 128, and C3 256, 

 and that its absorption increases rapidly for the next two octaves, 

 after which it remains a constant. Two thicknesses absorb more — 

 about twice as much — for the lower notes, the curve rising more 

 rapidly, passing through a maximum between C4 512 and C5 1024, and 

 then falling off for the higher notes. The same is true for greater 

 thicknesses. All curves show a maximum, each succeeding one cor- 

 responding to a little lower note. The maximum for six thicknesses 

 coincides pretty closely to C4 512. The absorption of the sound by 

 felt may be ascribed to three causes, — porosity of structure, compres- 

 sion of the felt as a whole, and friction on the surface. The presence 

 of the maximum must be ascribed to the second of these causes, the 

 compression of the felt as a whole. As to the third of these three causes, 

 it is best to consult the curves of the next figure. 



The following facts are rendered particularly evident by the curves 

 of Figure 13. For the tones emitted by the eight-foot organ pipe, 

 Ci 64, the absorption of the sound is very nearly proportional to the 

 thickness of the felt over the range tested, six thicknesses, 6.6 cm. 

 The curves for notes of increasing pitch show increasing value for the 

 coefficients of absorption. They all show that were the thickness of the 

 felt sufficiently great, a limit would be approached, — a fact, of course, 

 self-evident, — but for C5 1024 this thickness was reached within the 

 range experimented on ; and of course the same is true for all higher 

 notes, Ce 2048 and C, 4096. The higher the note, the less the thick- 

 ness of felt necessary to produce a maximum effect. The curves of 

 Ci 64, C2 128, C3 256, and C4 512, if extended backward, would pass 

 nearly through the origin. This indicates that for at least notes of so 

 low a pitch the absorption of sound would be zero, or nearly zero, for 

 zero thickness. Since zero thickness would leave surface effects, the 

 argument leads to the conclusion that surface friction as an agent in 

 the absorption of sound is of small importance. The curves plotted 



