This answer to When was the first true Gregorian telescope built? explains:

Newtonian uses one concave and one flat mirror (or just one concave).

Gregorian uses two concave mirrors, and

Cassegrain uses one concave and one convex mirror.

All these mirrors should be parabolic in an ideal situation. First Gregorian was made by Hooke in 1673.

This was 5 years before John Hadley was born. Hadley made a parabolic mirror in 1721, for a Newtonian telescope btw.

There was certainly known that for Newtonian telescope optics, at some point when the f/no becomes small enough spherical aberration will limit the resolution rather than diffraction, and that a more parabolic shape can avoid this particular problem.

When grinding optical surfaces, near-spheres are the easiest, the tend to come naturally. There are ways to make them aspherical known to present-day amateur telescope makers.

But I don't know anything about how Hadley's first parabolic mirror was made parabolic, nor how it was tested to verify its asphericity, nor what it was used for; a Newtonian telescope or a more complex system with two or more curved surfaces.

Question: How did Hadley do it and why exactly? How did Hadley make the first parabolic telescope mirror, verify its asphericity, and for what kind of telescope was this work done?

  • $\begingroup$ Can you explain your last question? I thought it was pretty clear these were all astronomical 'scopes; only the Moon and planets (and their moons) are resolvable objects, so those would be what can be viewed more clearly (on-axis) with a parabolic mirror. $\endgroup$ May 19, 2021 at 12:32
  • $\begingroup$ @CarlWitthoft I see what happened, I'd clarified the question in the body of the question but the title didn't get fixed. It now reads the same as in the body of the telescope. $\endgroup$
    – uhoh
    May 19, 2021 at 12:58
  • $\begingroup$ @CarlWitthoft What about double stars as resolvable objects? $\endgroup$
    – D. Halsey
    Jun 23, 2021 at 23:06
  • 1
    $\begingroup$ @D.Halsey I'm assuming you mean resolve as two separate point sources; I used to have a great table of the brighter star-pairs and their angular separation, which can be compared to the angular resolution possible without adaptive optics. Sadly lost that somewhere in the past. $\endgroup$ Jun 24, 2021 at 12:51

1 Answer 1


How did Hadley do it?

John Hadley published "The method of casting, grinding, and polishing the specula of reflecting telescopes" which probably has a good description of how he did it. Unfortunately I couldn't find that document. Luckily John Mudge published "Directions for making the best composition for the metals of reflecting telescopes; together with a description of the process for grinding, polishing, and giving the great speculum the true parabolic curve." in 1777 which gives an in-depth step by step process of how a mid 18th century astronomer would make a parabolic mirror.

Step 1: Make your speculum blank.

Speculum is a alloy of copper an tin that could be polished to a high mirrored surface. Its what telescopes at the time were made of.

Step 2: Make a spherical mirror.

This was hand ground and done the same way we do it today with ceramic chips imbedded in a blank, and a lot of hand grinding.

Step 3: Make it parabolic.

Starting on page 38 of the linked PDF he gives his procedure. His explantion is,

"In order to give the speculum the last and finishing figure, which is done by a few strokes it must be particularly remarked, that by working the metal round and round, the sphere of the polisher by this means growing less, it wears faster in the middle: and as a segment of a sphere may become parabolic, by means of opening the extremes gradually from within outward, so it may be equally well done by increasing the curvature in the middle, in certain ratio, from without inwards."

Normally when making a telescope mirror random strokes are made, and when you've done this a lot they average out into a spherical shape cut out of a blank. You can actually mess it up by grinding in a circular path which will make your mirror more parabolic. His method seems to be to take a spherical mirror, and then start in the middle polishing in a circle. This turns it into a parabolic mirror.

Why exactly?

It had been know since antiquity that a parabola focuses parallel rays onto the foci. It was James Gregory in 1663 who predicted that a parabolic mirror would correct spherical aberration and chromatic aberration.

How did he verify its asphericity?

Assuming he started with a spherical mirror that then was ground further. The mirror couldn't be spherical. Correct me if I'm wrong, but manipulating a sphirical mirror in this way, and have it still produce an image, could only result in a parabolic shape.

The only test in the above document was to test separate parts of the mirror to determine image quality. He would set up the mirror into a telescope. Then he would cover the aperture. First he would only allow light to hit the center radius to see if it produced a good image. Then he would move to the middle covering the center and the outer radius to see if he produced a good image. Finally doing the same with the outer radius.

The apparatus used.

For what kind of telescope was this work done?

He used it in a parabolic Newtonian in 1721, and later a true Gregorian telescope.

  • $\begingroup$ Thank you for your wonderful and "historic" answer! I think you have to work hard to grind anything other than a sphere. Identical spherical surfaces are the only surfaces that slide over each other perfectly in all directions. To make a parabola, you need to preferentially remove material from the edges I think. $\endgroup$
    – uhoh
    Jan 31, 2022 at 23:34
  • $\begingroup$ @uhoh, flat surfaces also slide over each other perfectly in all directions, but only if you make them three at a time. $\endgroup$
    – Mark
    Feb 1, 2022 at 4:52
  • $\begingroup$ @Mark when mirrors are ground by hand, the mirror blank and grinding tool are both flat, and as the process continues they become concave and convex respectively (for primaries). That's two surfaces, of essentially equal and opposite curvature, where's the third? $\endgroup$
    – uhoh
    Feb 1, 2022 at 5:08

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