110 



SCIENCE. 



[N. S. Vol. XVII. No. 420. 



was shown that the instrument changed 

 greatly in azimuth by reversal. 



Note on a Geometrical Analysis: Professor 

 James S. Miller, Emory Virginia. 

 Read by title. 



Coitcerning Bolzano's Contributions to As- 

 semllage Theory: Dr. C. J. Kjeysee, 

 Columbia University, New York City. 

 Eead by title. 



The Constants of the Equatorial: C. W. 



Frederick, U. S. Naval Observatory, 



Washington, D. C. 



This paper contained a description of a 

 method for deriving the constants of an 

 equatorial from observations of circum- 

 polar and equatorial stars. The position 

 of the polar axis of the instrument is de- 

 termined from observations of ^ Ursse Miu- 

 oris and Polaris near the times of culmina- 

 tion and elongation; also other constants 

 are involved. CoUimation and the flexure 

 of the tube are derived from observations 

 of equatorial stars. Very simple formulae 

 are required in the reduction of these ob- 

 servations. 



The effect of the constants in varying 

 the parallel of the micrometer is also con- 

 sidered, and a short process indicated by 

 which micrometer measurements may be 

 corrected for these instrumental disturb- 

 ances without undue labor. 



A Relation between the Mean Speed of 

 Stellar Motion and the Velocity of Wave 

 Propagation in a Universal Gaseous Me- 

 dium, Bearing upon the Question of the 

 Nature of Ether: LuiGi d'Axjeia, 3810 

 Locust Street, Philadelphia, Pa. 

 If the universe were involved in a pri- 

 mordial gaseous medium in equilibrium of 

 temperature, then assuming the density to 

 vary inversely with some power, n, of the 

 distance from the center of this universal 

 gaseous globe, which would be the center 

 of the universe, it is found that n^2, or 



the density varies inversely with the square 

 of distance. If to and lo^ denote respec- 

 tively the density of the medium at any 

 distance z and the mean density of the 

 concentric sphere of radius z, then 



(Jq = 3w 



and 



in which u is the mean square speed of 

 the particles of the medium and K the 

 gravitation constant. 



Denoting by «• the density of the me- 

 dium in the solar system, and by S the 

 distance of this system from the center of 

 the universe, it is found that 



' 6-^KS' 



Bodies moving in circular orbits around 

 the center of the universe, at all distances, 

 would all have the same velocity 



and it is found that u^:=3/2Vf,^; and if 

 V is the speed of wave propagation m 

 the gaseous medium, it is found also that 

 y^ ^ 5/6vo^. As Vg must be nearly equal 

 to the mean speed of stellar motion, about 

 19.3 miles per second according to Kap- 

 teyn, it is concluded that the ether can 

 not be a gravitational gas, since this gas 

 could not transmit energy with velocity 

 much greater than 17.6 miles per second. 

 Hence, the ether must be imponderable. 



Denoting by B and X> the mean radius 

 and the mean density of the earth, and by 

 g the acceleration of gravity, it is shown 

 that 



and assuming S = 159 light years, an es- 

 timated distance of Nova Persei, and as- 



