248 Proceedings of the Eoyal Society of Edinburgh. [Sess. 
Fulcher (Astrophysical Journal, vol. xxxvii, p. 60, 1913) has discussed 
the variation in the intensity of the lines when low potential discharges 
are used. Dr Merton (Proc. Roy. Soc., vol. xcvi, p. 382, 1920) has 
investigated the effect on the spectrum when the hydrogen is at a partial 
pressure of less than a millimetre in a vacuum tube containing helium at 
a pressure of about 40 mm. He found that under this condition the 
secondary spectrum differs from that obtained from pure hydrogen. 
A large number of lines have their intensities enhanced in the tubes 
containing helium, and a number of new lines appear. There is another 
class of lines whose relative intensities are unaffected by the presence 
of helium ; whilst a third class become weaker and disappear. In this 
paper no attempt is made to discuss the intensities of the lines given, 
but it is evident that a modification of the physical conditions causing 
the hydrogen molecule to lose an electron will modify the orbit which 
the remaining electron describes. Sommerfeld has shown that in the case 
of helium the number of different ways in which the same X is obtained 
gives a measure of the intensity of the line. A change, therefore, in 
the physical conditions will serve to make certain orbits more likely 
to be the initial orbits from which the electron jumps to other orbits, 
and hence a variation in intensity is to be expected. 
Analysis. 
It is well known that if a curve can be described by a particle under 
central forces to each of n fixed points, when the forces act separately, 
it can be described under the action of all the forces, provided the particle 
is projected properly. 
If is the velocity of the particle at a point when under a central 
attraction to the /cth centre, then 
dv^ n dr^ 
and 
where is the central acceleration, r^ the distance, and p^ the perpendicular 
from the /cth centre on the tangent to the curve of radius of curvature p. 
If V exists such that the conditions 
and 
are satisfied 
