Frank Dyson

The Potential of an Anchor Ring

In this Paper I have developed a method of dealing with questions connected with Anchor Rings. If r, θ, ϕ be the coordinates of any point outside an anchor ring, whose central circle is of radius c , then ∫π dϕ/√(r2+c2 - 2cr sinθ cosϕ ) is a solution of Laplace’s equation, finite at all external points and vanishing at infinity. Let this be called I. Then dI/dz is another solution; and two sets of solutions may be found by differentiating I and d I/ d z any number of times with respect to c . These solutions are symmetrical with respect to the axis of the ring. In the first set z is involved only in even powers; in the second set in odd powers.

Sir William Herschel, 1738–1822

AT the age of thirty-five years, William Herschel, a distinguished and prosperous musician, was impelled to explore the heavens. He found a small telescope which he had hired insufficient for his needs, and with great skill and patience constructed larger and larger instruments. After his days work, he spent a great part of the night observing the stars. The conclusions he drew from his observations were characterized by an originality, boldness and splendour of outlook which have placed him among the greatest astronomers. “We ought”, he writes, “to avoid two opposite extremes. If we indulge in a fanciful imagination and build worlds of our own we must not wonder at going wide from the path of truth and nature.... On the other hand, if we add observation to observation, without attempting to draw not only certain conclusions, but also conjectural views from them, we offend against the very end for which observations ought to be made. I will endeavour to keep a proper medium ; but if I should deviate from that, I could wish not to fall into the latter error.”

Preliminary Determination of the Wave-Lengths of the Hydrogen Lines, Derived from Photographs Taken at Ovar at the Eclipse of the Sun, 1900, May 28

The spectrum of the “flash” obtained in observations of solar eclipses furnishes a method of determining the wave-lengths of the hydrogen series with great accuracy, as these lines are strongly shown and sharply defined. As the determination of these wave-lengths is somewhat removed from the general subject of eclipse spectroscopy, it seemed suitable for a separate paper.