Janiauy :!U. 1903.] 



SCIENCE. 



175 



posures in the three cases. In general, 

 shutters of this grade with timing devices 

 are wholly unreliable. 



On the Distribution of Pressure around 



Spheres in a Viscous Fluid: S. R. Cook, 



Case School of Applied Science. 



When a single sphere is set in motion 



in a perfect fluid at rest at infinity, its 



motion is completely determined by the 



velocity potential due to the motion of 



the sphere; and the pressure around the 



sphere is given by 



fj dr - 



(1) 



"Where v is the velocitj' potential and u 

 is the velocity of the sphere at time t. 



"When H is constant (1) may be written 

 in the form 



P 



= ir ! f cos' — 



(2) 



where is measured from the direction of 

 motion. 



The curve for the pressure of a perfect 

 fluid around a sphere was given, and also 

 the curve for the pressure of air, which 

 was determined by measuring the pres- 

 sure of the air around a glass sphere by 

 means of a water manometer while the 

 air is flowing with a constant velocity past 

 the sphere. The two curves differ, in 

 that, for a perfect fluid the curve is sym- 

 metrical with respect to both axes, as may 

 be seen from (2), while for a viscous fluid, 

 i. e., air, the curve is symmetrical with 

 re.speet to the axis parallel to the direction 

 of flow, but not with respect to the axis at 

 right angles, the pressure at the rear being 

 less than that in front of the sphere. 



The pressure was also determined for 

 two spheres moving in line of centers and 

 for two spheres moving perpendicular to 

 the line of centers. The equations which 

 represent the pressure for a perfect fluid 

 were given and the eni-\-es of pressure 



around the spheres compared with the 

 curves obtained by measurements of the 

 pressure in air. It was found that two 

 spheres moving in the line of their centers 

 in a perfect fluid are repelled, but when 

 moving in a aqscous fluid are attracted. 

 For spheres moving perpendicular to their 

 line of centers in a perfect fluid they were 

 attracted, and in a viscous fluid repelled. 

 These results agree with results given 

 in a former paper on 'Flutings in a Sound 

 "Wave' and corroborate the theory there 

 advanced as an explanation of the cause 

 of the flutings in a Kundt-tube. 



A Portable Apparatus for the Measure- 

 ment of Sound: A. G. Webster, Clark 

 University. 



An improved form of the instrument 

 shown at the Boston meeting, 1898. 



The apparatus consists of two parts, a 

 'phone,' or apparatus for emitting con- 

 tinuously a pure tone, whose intensity is 

 measured in absolute units (watts), and 

 of a 'phonometer,' or instriunent which 

 measures at any point the intensity of the 

 sound emitted by the phone or other source 

 of sound measuring the absolute compres- 

 sion of the air. The amplitude of a dia- 

 phragm forming the back of a resonator is 

 measured by the displacement of fringes in 

 an interferometer, observed stroboscop- 

 ically. Both parts of the apparatus are 

 portable, and suitable for field work. 



Tlic Mechanical Efficiency of Musical In- 

 struments as Sound Producers: A. G. 

 Webster, Clark University. 

 The sound emitted was measured by the 

 phonometer, by comparison with the phone 

 placed in the same place where the instru- 

 ment was. The input of energy was ob- 

 tained by measurement of the pressure, 

 and time rate of air consumption for wind 

 instruments, and by the pull of the bow 

 and velocity for stringed instruments. 

 Preli)ninary results were given for the 



