by John Church
I’ve often wondered what actual methods Charles Hastings used when designing the 6-1/4” objective now sitting at the business end of our fine refractor in Washington Crossing State Park. I’ll start by quoting Hastings’ own words on p. 39 of Vol. 2 of the Sidereal Messenger for 1883:
“Anxious to test still farther the theory [i.e. the theory which he had developed from scratch when starting his lens design work, see below], I constructed an objective of 6-1/3 inches aperture [reduced to 6-1/4 inches by Byrne’s cell] of entirely different materials and curves resembling those chosen by Fraunhofer in most of his objectives. This also was made strictly in accordance with the theory and with the most gratifying results, Of interest to the optician is the fact that its focal length differed by less than 1/10 of an inch from that given by calculation. [Note: H. designed for a focal length of 91 inches, while this lens has an actual focal length of 91.07 inches, i.e. 2313 mm.] This lens is now in the possession of Mr. C. H. Rockwell, at Tarrytown, N.Y., and was used by him at Honolulu in observing the last transit of Mercury. Though I have not had the opportunity for testing the telescope in astronomical work which I could wish, the ease with which I saw ζ Bootis double in 1879 (Hall 0”.55, 1874.4) and γ2 Andromedae elongated during the same summer, convinces one that it is of the highest excellence, even independently of the severe physical tests to which it has been subjected in my hands.”
The theory that Hastings was referring to was elaborated at some length in an article in the American Journal of Science for March 1882 (Third Series, Vol. XXIII no. 135), p. 167. The general idea was to concentrate the greatest amount of visible light energy into the smallest possible area. By considering the intensities of the various wavelengths of light, he arrived at the conclusion that the wavelength for the minimum intercept distance (i.e. back focus or distance from the rear vertex of the rear element of the achromat) for paraxial (i.e. nearly central) rays should be 5614 A., which is a solar line visible in a good spectroscope and very close to the wavelength of maximum sensitivity of human vision. He also concluded that when achromatism was considered, the marginal rays for the C line (6561 A.) and a wavelength as close as possible to 4990 A. should be united. He found that the closest spectroscopic line readily available was at 5005 A. Hence this was his recommendation, and it fact it was achieved in our actual objective (Sky & Telescope for March 1979, p. 294).
Hastings didn’t publish the actual calculations which led him to these conclusions. However, he did write the following passage in this same article:
“The second objective had a clear aperture of 6-1/4 inches and a focal length of 91 inches. The crown lens is in advance and the curves are such as to satisfy, for a first approximation, the conditions proposed by Sir John Herschel [Phil Trans.1821, p. 222]. This form, though ordinarily known as Herschel’s, cannot be said to differ from that chosen by Fraunhofer at a date earlier than that of the publication of Herschel’s paper.”
The so-called “Herschel condition” is that spherical aberration should vanish not only for objects at infinite distances (i.e. astronomical objects), but also at nearer points for use as a terrestrial telescope. This would also allow easy testing of lenses in the workshop and on convenient daytime objects in the vicinity. It continues to be a useful principle in this area, but it’s mathematically incompatible with the Abbe or “sine condition” that both spherical aberration and coma should be made as small as possible in astronomical telescopes. It’s fortunate however that satisfying the Herschel condition coincidentally leads to objectives with very low coma that are usually perfectly satisfactory for astronomical work.
In the second article of this series I plan to go more completely into the Herschel condition and determine if Hastings actually tried to make our objective follow Herschel’s formulas.