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Lastly, zeta (ζ) and pi (π) to epsilon (ε) and kappa (ko) original: "ko"; likely a variant for the Greek letter kappa will be sufficiently plain to anyone who simply considers the diagram original: "Scheme".
By this method, four-fifths of the length of the tube is reduced original: "taken away". This is the maximum reduction possible using four reflections where each reflection spans the entire length of the tube. A smaller portion of the length may be reduced in any given proportion. For example, in the second design original: "contrivance" shown in the second figure, two-thirds of the length is removed. In that diagram, the same letters correspond to the objective lens original: "Object-Glaſs", the eyepiece original: "Eye-Glaſs", the bends original: "flexures" of the side rays of the light beam original: "Pencil", and the reflecting plates that cause those bends. The third and fourteenth figures represent the tube shortened by two or three reflections, which serves to reduce the tube by only two-thirds. These are useful for someone with very strong eyesight and a small aperture on the objective lens, especially when the sun is near the horizon or its light is dimmed by fog, thin clouds, or similar conditions.
If it is considered more convenient for this long tube to remain horizontal—thereby eliminating the need for a pole or machine original: "Engine" to raise it—the device may be constructed like the one in the fourth figure. There, the same letters correspond to all the parts mentioned above. Alternatively, it could be built like the design in the sixth figure; since the letters in both diagrams match the previous ones, they will be easy to understand.
Now, in all of these designs—and twenty other similar inventions that could be devised—using one, two, three, or four reflecting plates, the viewer looks directly toward the sun. Therefore, there will be little difficulty in finding the sun once the lenses original: "Glaſſes" are fixed at their proper distances and positions.
At the same time, during their public meeting at Arundel House, I also explained several other ways to make very long telescopes original: "Glaſſes" easier to use for observing other celestial objects using only one reflecting plate. This involved a fixed tube—placed either vertically, horizontally, or at an angle—since the orientation does not affect the ability to see an object in any part of the sky, provided other conditions do not interfere and the object can be found as easily as with standard telescopes of the same length. However, I will discuss these elsewhere.
These designs involving four reflections may be used