Amateur Astronomers Association of Princeton

by John Church

In recent issues of Sidereal Times I’ve been discussing whether our 1879 Hastings objective was designed using John Herschel’s 1822 procedure.  Herschel’s method was a major advance that gave very good results for its time.  As part of my investigation, I adapted it for an Excel spreadsheet.

Sixty years earlier in France, Clairaut and d’Alembert had published design methods equivalent to the best ones even today. However, their equations were too complicated for general use.  Besides the goal of helping opticians in their design efforts, Herschel proposed that a refractor should be able to focus sharply on both distant astronomical objects and nearby land objects.  This is unimportant for permanently mounted refractors, but could be useful for smaller hand telescopes.

As mentioned in the April Times, the four surface radii of the Hastings lens elements are somewhat different from what Herschel’s formulas would have required.  However, air-spaced doublet achromats with surfaces shaped in the general neighborhood of the “Herschel condition” are relatively forgiving for visual use at f/10 and above.  For wide low-power fields and photographic applications where coma should be minimized, fully optimized design methods should be used instead.

We’re fortunate that our Hastings objective comes fairly close to the best possible design.  I became interested in how well it would perform on nearby objects.  Fraunhofer is said to have tested his own lenses this way in the long galleries of the Benediktbeuern monastery. Dave and Jennifer Skitt and I did some similar tests on the afternoon of April 18^th.  We mounted a book with small print at distances of 95 and 60 feet and used eyepieces to give us 105 to 116 power. 

Focusing at such short distances requires racking an eyepiece much farther out than for sky objects.  I brought an extension tube that I use on my own 4-inch Edmunds refractor. We obtained sharp images of the book print, somewhat better at 95 feet than at 60 feet as might have been expected.  Although I have no record of Hastings having actually tested his objective this way, my guess is that he did do this before releasing the lens to Byrne for the final cell, tube, and mounting.  One of his papers mentioned some successful 1879 observations of close double stars before letting the lens go, so he must have had a temporary mount of his own. 

I plan to do a similar test with my own refractor.  Other club members with refractors of different sizes and focal ratios might be interested in trying this experiment themselves if they have suitable extension tubes.  I would like to hear about any results.  Those with reflectors might also like to try it.

So far, I have found no evidence that Herschel did actual experiments on lenses designed by his equations and reduced to practice.   He had made a fine contribution to applied optics and went on to other areas.