Sky & Telescope - September 2016 - 30

Eye and Scope

Dawes Limit
Find your

Phillip Kane

The famous resolving-power rule that William Rutter Dawes determined
for telescopes may not apply to you. Try these close double stars to ﬁnd out.

The Reverend William R. Dawes was one of the most
outstanding observers during the golden age of gentleman astronomers in mid-19th-century England. His
proliﬁc double-star and planetary observations are
still highly regarded today (see, for example, "William
Dawes' Jupiter" in last November's Sky & Telescope, page
48). Dawes is most remembered, though, for his simple
rule for how sharply a telescope of any given size ought
to resolve. His formula is

In other words, a 4.56-inch (116-mm) telescope should
have a resolving power of exactly 1 arcsecond, a scope
twice that diameter should resolve 0.5″, and so on.
Dawes, however, was more circumspect about his
rule than many astronomers now realize. He described
it as being speciﬁcally for double stars with "two stars of
the sixth magnitude." As he wrote in 1867,
I examined with a great variety of apertures a vast number of
double stars, whose distances [separations] seemed to be well
determined, and not liable to rapid change, in order to ascertain the separating power of those apertures, as expressed in
inches of aperture and seconds of distance. I thus determined
as a constant, that a 1-inch aperture would just separate a double star composed of two stars of the sixth magnitude, if their
central distance was 4.56″, the atmospheric circumstances
being moderately favourable . . .

r = 4.56″/a
where r is the resolving power in arcseconds and a is the
aperture in inches. Or if you prefer,

r = 116″/a
when a is in millimeters.

EAGLE EYE Rev. William Rutter Dawes (1799-1868)
earned that nickname for his meticulous work on planets
and double stars using a succession of refractors.

September 2016 sky & telescope

THE OBSERVATORY / PUBLIC DOMAIN

Notice the speciﬁc limitation to doubles composed of
two stars of the 6th magnitude. Others also stressed this
qualiﬁcation over the years in their paraphrasing of the
Dawes standard. But many observers today take it as a
hard and fast property of a given telescope aperture, and
telescope manufacturers typically list it as such on their
speciﬁcations page.
Several things complicate the picture. For one,
unequal double stars must be wider to be resolved with
the same telescope, sometimes much wider (see the box
on page 31). And for equal pairs, Dawes' selection of 6th
magnitude was a good choice; some research suggests
that both brighter and fainter equal-magnitude pairs are
harder to resolve and thus would not provide the ﬁnest
test. Louis Bell, in his 1922 book The Telescope, wrote:
If the stars are decidedly bright there is increase of apparent
diameter of the [stellar] disc due to the phenomenon known
as irradiation, the spreading of light about its true image on
the retina which corresponds quite closely to the halation
produced by a bright spot on a photographic plate. If, on the
contrary, the stars are very faint the total amount of light available is not suﬃcient to make contrast over and above the background suﬃcient to disclose the two points as separate.

Sky & Telescope - September 2016

Table of Contents for the Digital Edition of Sky & Telescope - September 2016