Connective Equilibrium of a Spherical Mass of Gas. 459 



diminution in intensity for a length of two centimetres of 

 large tubing would be quite unnoticeable. Also it should be 

 remembered that, to explain the location of a sound by dif- 

 ferences in intensity, the idea of a sound shadow produced 

 by the head was introduced, as it was evident that the dif- 

 ference in length of path of the sound to the two ears was 

 not sufficient a cause. 



The writers of this paper are not well enough acquainted 

 with physiology to offer any explanation of the way the mind 

 takes cognisance of phase-differences of tones. The theory 

 of the mechanism of hearing advanced by Helmholtz seems 

 entirely unsuitable, for a simple rod-like filament of the 

 auditory nerve, vibrating sympathetically to waves of sound, 

 apparently has no apparatus for recognizing phase-differences. 

 So far as we know there has been but little adverse criticism 

 of Helmholtz 's work on the ear except in one instance. 

 Dr. Howard Avers, after a careful and laborious examination 

 and measurement, maintains that his theory of audition is 

 incorrect. Unfortunately the work of Dr. Ayers is not at 

 hand, so a comparison of his theory with our experiments is 

 not possible at present. 



Before the laws of this effect can be stated completely a 

 large number of experiments must be made, and it is hoped 

 that those planned to be done this year will prove adequate. 



Cambridge, England, 

 January 1907. 



XXXYI. On Connective Equilibrium of a Spherical Mass of 

 Gas subject only to the Mutual Gravitation of its paints. By 

 J. Prescott, Lecturer in Mathematics at the Manchester 

 School of Technology*. 



BEFORE attacking the question from a mathematical 

 standpoint, let us get some idea from physical con- 

 siderations, how the radius of the sphere of zero density 

 depends on the mass of the gas. 



Suppose that, when a mass of gas acted on by no forces 

 except its own gravitation has taken up its equilibrium state, 

 it were possible suddenly to double its density at every point 

 by placing in every portion of space an exactly equal and 

 similar mass ol gas to that which already occupies the space. 

 The pressure would be doubled everywhere, and therefore 

 the resultant of the pressures acting on the gas enclosed 

 within any given space would be doubled. But the mass 

 within the space would be doubled, and the attracting mass 



* Communicated bv the Author. 



