to ½ pr , and p being = n / m - n , the focal distance in Glass will be = r , in Water 1½ r , but in Diamant ⅓ r .
I am sensible that these Examples are too much for the compleat Analyst, though I fear too little for the less Skilful; it being very hard, if possible, in such Matters, so to write, as to give satisfaction to both; or to please the one, and instruct the other. But this may suffice to shew the extent of our Theorem, and how easie a Reduction adapts any one case to all the rest.
Nor is this only useful to discover the Focus from the other proposed data , but from the Focus given, we may thereby determine the distance of the Object; or from the Focus and Distance given, we may find of what Sphere it is requisite to take another Segment, to make any given Segment of another Sphere cast the Beams from the