( i4S ) 
tion of the Rainbow, other Arches, within every one 
of the principal, of the fame Colour, though much 
more faint : and this for divers Succedions, as long as 
thele weak Lights, which in every Arch grow more 
and more oblcure, fhall continue vifible. Now as the 
Arches produced by each Colour will be varioufly 
mixed together, the diverfity of Colours obferved by 
Dr. Langwith may well arife from them. 
The precife Diftances between the principal Arch of 
each relpedlive Colour and thele fainter correfpondent 
Arches depend on the Magnitude of the Drops of Rain. 
In particular, the Imalleft Drops will make the fecon- 
dary Arches of each Species at the greatell Dillance 
from their refpedtive principal, and from each other. 
Whence, as the Drops of Rain increale in falling, 
thefe Arches near the Horizon by their great Nearnels 
to their relpecfiive principal Arches become invifible. 
AND now. Sir, we are upon the Rainbow, I lliall 
here take the Freedom of letting down two Propoli- 
tions, which I have formerly conlldered, relating to 
this Subjedl. For the greater Brevity I lhall deliver 
them under the Form of Porilms ; as, in my Opinion, 
the Ancients called all Propolitions treated by Ana- 
lyfis only. 
PROPOSITION I. 
a given refraUting Circle, whofe refraciing 
bovver is given, the Ray is given in Rojition, which 
pajjing parallel to a given *T>iameter of the Circle /> 
refried by that Circle to a Roint given in the Cir- 
cumference of it. 
Let 
