$to Dr. Hersc hel*s Experiments for investigating 
through any number of successive transmissions or reflections 
whenever this image comes to the eye, a set of rings will again 
he seen, which is a dependent one. Many proofs of the de- 
pendency of second, third, and fourth sets of rings upon their 
primary one may be given ; I shall only mention a few. 
When two sets of rings are seen by a lens placed upon a 
looking-glass, the center of the secondary set will always re- 
main in the same plane with the incident and reflected rays 
passing through the center of the primary one. If the point 
of contact, by tilting is changed, the secondary set will follow 
the motion of the primary set; and if the looking-glass is 
turned about, the secondary will be made to describe a circle 
upon that part of the looking-glass which surrounds the pri- 
mary one as a center. If there is a defect in the center or in 
the rings of the primary set there will be exactly the same 
defect in the secondary one; and if the rays that cause the 
primary set are eclipsed, both sets will be lost together. If the 
colour of the primary one is changed, that of the secondary 
will also undergo its alternate change, and the same thing will 
hold good of all the dependent rings when three or four sets 
of them are seen that have the same primary one. 
The dependency of all the sets on their primary one may 
also be perceived when we change the obliquity of the incident 
light ; for the centers of the rings will recede from one ano- 
ther when that is increased and draw together when we lessen 
it, which may go so far that by an incidence nearly perpendi- 
cular we shall bring the dependent sets of rings almost under 
the primary one* 
