496 Mr. T. Chaundy: Method of Line-Coordinates for 

 § 7. Summary. 



In various physical phenomena connected with the sepa- 

 ration of an electron from an atom a characteristic frequency, 

 v, or a corresponding potential V (determined by the quantum 

 relation Ye = hv) is met with. There appears to be a simple 

 relation between this quantity and N, the atomic number 

 of Moseley. In a number of cases the product Nv can be 

 expressed in the form nv E or (n-\- ^)v E , where n is an integer 

 and v^ is a fundamental electronic frequency. This funda- 

 mental frequency is identical with Rydberg's constant in 

 spectral series, 3*289 x 10 15 sec. -1 . 



This relation is found to hold in connexion with (1) the 

 maximum of the photoelectric effect, (2) the threshold 

 frequency or long-wave-length limit of the photoelectric 

 effect, (3) the ionization potential of a gas, (4) the " electron 

 affinity" deduced from thermionic measurements. 



The relation is discussed from the standpoint of the 

 Quantum Theory. 



XLVII. A Method of Line-Coordinates for Investigating the 

 Aberrations of a Symmetrical Optical System. By Theo- 

 dore Chaundy, M.A., Christ Church, Oxford (attached to 

 Munitions Inventions Department)* . 



THE coordinates of a straight line in space of three 

 dimensions, though, of course, well-known to mathe- 

 maticians, seem scarcely to have received that general use to 

 which from their fundamental character they are entitled. 



The present application of line-coordinates to the theory 

 of Geometrical Optics takes the standpoint of considering a 

 typical ray of a beam of light passing through the optical 

 system, regarding that ray as completely determined by 

 knowledge of its six coordinates. The effect, then, of any 

 series of refractions undergone by such a ray can be stated 

 in terms of the contemporaneous transformations undergone 

 by the coordinates of the ray. Since, in knowing the 

 behaviour of every ray in its passage through an optical 

 system, we are in full possession of the geometrical facts of 

 the system, it is clear that formulae expressing the coordinates 

 of a typical ray, at any stage of its passage, as functions of 

 its coordinates before incidence, constitute a complete 

 conspectus of the geometrical properties of the system. 



* Communicated by the Author. 



