December 20, 1901.] 



SCIENCE. 



973 



varying more than 10 per cent. The gradient 

 at such places is 8 to 10 feet per mile. 



Professor Schlicter's paper was discussed by 

 Professors C. R. Van Hise, J. B. Johnson, F. 

 W. King, F. E. Turneaure and E. A. Birge. 



Mr. Pfund discussed the ' Dispersion and Ab- 

 sorption of Selenium.' By devising a new 

 method for depositing films of the aniline dyes 

 on glass and for photographing the interference 

 fringes produced by a Michelson interferometer, 

 the dispersion of amorphous selenium, a com- 

 paratively opaque substance, has been success- 

 fully studied. The refractive index of selenium 

 rises with extraordinary rapidity until at the 

 limit of the photographic field it reaches a value 

 of 3.13, one of the very highest known. In 

 general, the light-absorbing power of selenium 

 lies between that of the aniline dyes and that of 

 the metals. With a small concave grating, it 

 has been found that selenium absorbs light 

 more and more strongly as the end of the ultra- 

 violet spectrum is approached, instead of there 

 being a region of retransmission. 



C. K. Leith. 



DISCUSSION AND CORRESPONDENCE. 



THE MATHEMATICAL THEORY OF THE TOP, 



SIMPLIFIED. 



To THE Editor of Science : Professor A. G. 

 Greenhill has been good enough to show me 

 his terse method of treating the top integrals. 

 As this is a subject on which Professor Greenhill 

 speaks authoritatively, and will interest a num- 

 ber of your readers, in particular his many 

 friends in Sections A and B of the American 

 Association, I suggest that it be published in 



Science. 



Carl Barus. 

 Brown University, Providence E. I., 

 November 20, 1901. 



Let the vector OH represent the resultant 

 angular momentum of a symmetrical top ; spin- 

 ing about its point O is a small smooth fixed 

 cup, as in the Maxwell top. 



Since the axis Og of the torque of gravity is 

 always horizontal H will describe a curve (a 

 Poinsot herpolhode), in a fixed horizontal plane 

 at a height OG above 0, the vertical vector OO 

 representing the constant component G of angu- 

 lar momentum about the vertical. 



We assume that the component G^ of the 

 angular momentum of the top about its axis 00 

 remains constant, as there is nothing to alter itj 

 if the top is symmetrical. 



Fig. 1. 



Expressed by Euler's angles 6 and V the vec- 

 tor OH has the components (Figs. 1 and 2) 



(1) OC=zG\ CK=A^sin^'^^, KU=A^'^^, 



Ai denoting the moment of inertia of the top 

 about an axis through O perpendicular to OC. 



The velocity of H is equal to the torque of 

 gravity Wgh sin '&, so that, denoting the polar 



Fia. 2. 



coordinates of H in the horizontal plane GHS! 

 by fi and ^, and resolving in the radial direc- 

 tion GH. 



(2) ^ = Wgh sin i? cos GHK=Wgh sin i? — 



