uu 
THE 
LONDON, EDINBURGH, and DUBLIN 
PHILOSOPHICAL MAGAZINE 
AND 
JOURNAL OF SCIENCE. 
[SIXTH SERIES.] 
JUNE 1908. 
LXII. Hamilton s Principle and the Five Aberrations of 
von Seidel. By Lord Rayleigh, O.J/., Pres.R.S* 
LARGELY owing to the fact that the work o£ Hamilton, 
and it may be added of Coddington, remained unknown 
in Germany and that of v. Seidel in England, it has scarcely 
been recoo-nized until recently hoy* easily v. Seidel's general 
theorems relating to optical systems of revolutions may be 
deduced from Hamilton's principle. The omission has been 
supplied in an able discussion by Schwarzschild, who expresses 
Hamilton's function in terms of the variables employed by 
Seidel, thus arriving at a form to which he gives the name 
of Seidel's Eikonal f . It is not probable that Schwarz- 
schild's investigation can be improved upon when the object 
is to calculate complete formula? applicable to specified com- 
binations of lenses ; but I have thought that it might be 
worth while to show how the number and nature of the five 
constants of aberration can be deduced almost instantaneously 
from Hamilton's principle, at any rate if employed in a 
somewhat modified form. 
When we speak, as I think we may conveniently do, of 
five constants of aberration, there are two things which we 
should remember. The first is that the five constants do not 
stand upon the same level. By this I mean, not merely that 
some of them are more important in one instrument and some 
* Communicated by the Author. 
t The word Eikonal was introduced bv Brims. 
Phil Mag.S. 6. Yol. 15. No. 90. June 1908. 2 Z 
