September 13, 1901.] 



SCIENCE. 



403 



sphere of secular contraction and the pro- 

 cess of isostacy. 



(cZ) The effects of secular contraction on 

 the length of the sidereal day. 



' The Energy of Condensation of Stellar 

 Bodies ' : Professor K. S. Woodward. 



The problem considered in this paper is 

 that of the energy due to the gravitational 

 condensation of gaseous matter from a 

 state of infinite diffusion to a finite spher- 

 ical mass in which Laplace's law of density 

 holds. The problem is worked out in its 

 generality, formulas specifying the distri- 

 bution of density, pressure, and potential 

 in the mass being given. Special attention 

 is given to the probable case of the fixed 

 stars of a vanishing surface density. 



' The Physical Basis of Long Range 

 Weather Forecasts ' : Professor Cleveland 

 Abbe, TJ. S. Weather Bureau. 



In the absence of the author and of the 

 member who was to present it this paper 

 was read by title. The papers by Professor 

 See and Dr. Moulton were presented by 

 Professor Howe. Those by Professor Dick- 

 son, Mr. Keyser, Mr. Parkhurst, Dr. 

 Hutchinson and Professor Macfarlane were 

 read by the secretary. All the other papers 

 were presented by their authors. Several 

 other papers were read before the joint 

 session of Sections A and B. These will be 

 included in the report of Section B. 



G-. A. Miller, 

 Secretary of Section A. 



ON THE STABILITY OF VIBRATIONS. 



Observations. — The following experiment 

 seems to me to be an interesting illustra- 

 tion of the equation of the damped har- 

 monic oscillation. It also presents a strik- 

 ing illustration of the stability of a given 

 type of vibration. 



The necessary apparatus is very simple, 

 consisting of an ordinary open organ pipe 

 (say c" of the one foot octave) and a cylin- 

 drical tin box, 4-5 cms. in diameter and 5-6 



cms. long, with a central hole at one end 

 about 1 cm. in diameter. This is adjusted 

 so as to be of the same period as the organ 

 pipe. A Konig's resonator will do equally 

 well, but if the box has a slightly loose lid, 

 it brings out other phenomena also deserv- 

 ing notice. 



The experiment is as follows : Using a 

 resonator giving h' to e", depending on the 

 intensity of the blast and with a loose (not 

 sealed) lid, let it be placed symmetrically 

 to the slit of the pipe at a distance, .-c, from 

 it, as shown in the figure. Then as x de- 

 creases from a large distance, to say 3 cms., 

 the resonator trembles violently (felt with 

 the finger), but neither raises nor depresses 

 the note. As x decreases further to 1.7 

 cms., no marked effect occurs, but pressure 

 in the influx of the organ pipe will force 

 out the octave, which it did not do before. 

 Between a; = 1.7 and = 1.5 there is destruc- 

 tive interference ; a mere whifiing is heard 

 from the combined instrument, but an im- 

 pure octave may be forced out by pressure. 

 Finally, when x decreases further to say 1.1 

 cms., a clear d" suddenly breaks forth and 

 is the chief feature of the experiment. For 

 smaller distances (1.1 to .7 cms.) the d" 

 flattens again to c". 



The same sharpening is produced when 

 the resonator is placed on top of the open 

 organ pipe, mouth inward. If two resona- 

 tors ^re used, one as in figure, the other on 

 top, the sharpened note of the one is further 

 sharpened by the other. 



When the so-called destructive interfer- 

 ence occurs there is no vibration in the 

 resonator; but on pressing the finger against 

 its bottom, the e" may again be heard. 



If the lid of the resonator be cemented on 

 with wax, or if a round Konig resonator be 

 used, there is no whifiBng. The interval, 

 X, of instability is then very small (about 

 .2 cm.) so that the note passes very sud- 

 denly from c" to d" . Too loose a lid merely 

 depresses the tone at short distances. 



