How Did Hastings Design Our Objective? Part Two

by John Church

Objectives for smaller telescopes are sometimes designed to conform to the “Herschel condition” proposed by John Herschel in two papers in the early 1820’s.  These objectives perform well at nearby distances as well as on celestial objects at infinity in restricted fields of view. They don’t, however, completely satisfy Abbe’s 1873 sine condition for zero coma, although they usually show very little of this particular aberration.  

Hastings wrote that our present lens resembled a Herschel in design, but he didn’t reveal his actual calculations.  I find that at 5614 A., near the middle of the visible spectrum, A. E. Conrady’s quantity known as “offense against the sine condition” (OSC) is – 0.00026 for our lens: this is small, but not zero.  When scaled to the size of our lens, I find an OSC value of + 0.00022 for one purposely-designed Herschel lens (Boutry, “Instrumental Optics” p. 143) at 5460 angstroms, also near the middle of the spectrum.  These values are far below Conrady’s maximum tolerance of  +/–  0.0025 for a visual teslescope.

Objectives can be designed to show OSC values of +/- 0.00001 or even less.  The formula set that I gave in Sky & Telescope for November 1984 (based on the 18th-century work of Clairaut and d’Alembert as adapted in 1887 by C. Moser) does this quickly.  The spot diagrams in my January talk show that coma for our lens is indeed very small, even as far as half a degree off-axis (full field one degree, or about two moon diameters).

Hastings concentrated on correcting spherical aberration, and he succeeded with this in all his work.  He was also an early supporter of making the minimum focus at the middle and brightest part of the visible spectrum near 5600 A. instead of at the usual longer wavelength of the sodium D2 line at 5890 A.  He did this in the form of our 1879 lens and a 4-inch flint-in-front predecessor, as well as with larger objectives made later.

I’ve recently been able to “deconstruct” Herschel’s design procedures as published in an Edinburgh scientific journal in 1822.  This wasn’t easy due to Herschel’s use of an algebraic sign convention differing from the one used today, and his numerical tables required nonlinear interpolation. My provisional conclusion is that our 1879 lens isn’t a Herschel type.  Neither did Hastings use the older and better methods of Clairaut and d’Alembert.  Whatever particular method Hastings did use, it still resulted in an excellent lens.

After the weather gets better, I intend to make some simple empirical tests to see how our lens works on objects 50 to 75 feet away. According to Conrady, Fraunhofer made such tests in the halls of his workshop at the Benediktbeuern cloister in Bavaria.  If so, then he might have been making Herschel-type objectives, consciously or otherwise.  After March 1821 he would likely have known about Herschel’s published work.

Interestingly, as shown 12 years after making our lens, Hastings by then had become less of an admirer of Herschel’s design methods (Sidereal Messenger Vol. X, 1891, p. 315).  This was part of a long essay on the history of telescopes delivered as an address at the dedication of the Goodsell Observatory at Carleton College in June of 1891.  At this period Hastings was a consultant to Brashear and had designed the 16.2-inch lens of Carleton’s new telescope.

Herschel did visit Benediktbeuern in 1824 (Fraunhofer died in 1826).  Herschel had hoped to learn more about Fraunhofer’s secret methods of making exceptionally fine optical glass, but in this he was disappointed  (Myles Jackson, “Spectrum of Belief”, MIT Press, 2000).

Speaking of Fraunhofer, it’s odd  that he seems to have been unaware of the 1760’s work of Clairaut and d’Alembert on fully correcting coma.  Fraunhofer left so few written records that we’ll probably never know if he did or not.  In support of his not knowing is the fact that at least some of his finest products do have a small amount of coma, as mentioned in my 1984 article.

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