Michelson-Morley's 1887 paper: structural analysis via word spectra of earth and ether

Title should reflect content. This rule is obvious. But how the words are arranged in the title determines the structure of the paper. Let us look at the famous paper by Albert Abraham Michelson and Edward Morley in 1887: \begin{equation} \label{eq:michelson-morley} Title:\ On\ the\ relative\ motion\ of\ the\ Earth\ and\ the\ luminiferous\ ether. \end{equation} We treated this title as an equation, because we shall show that it can be expressed as an equation. In order to rewrite Eq.~(\ref{eq:michelson-morley}) as an equation, we do the following steps:

• Replace ":" by "=", "of" by "$\times$" or juxtaposition multiplication, and "and" by "$+$".
• Set $T = title$, $r = relative$, $m = motion$, $\epsilon = earth$, $L = luminiferous$, and $\xi = ether$.
• Make the adjectives as subscripts of nouns.  "Motion" is a noun while "relative" is its adjective, so we write $m_r$.  "Ether" is a noun and "lumineferous" is an adjective, so we write $\xi_L$.  

Using these three rules, we can now express Eq.~(\ref{eq:michelson-morley}) as \begin{equation} \label{eq:T is mr epsilon xiL} T = m_r (\epsilon + \xi_L). \end{equation}

We see in Eq.~(\ref{eq:T is mr epsilon xiL}) that $\epsilon$ (earth) and $\xi$ ether have equal footing as terms inside the parenthesis. So we expect the paper to talk about the earth and the ether at the same time in the discussion of their relative motion.  Michelson and Morley can adopt either of the two writing methods or both:

• Method 1:  Series Structure.  Paragraph 1 talks about the earth, Paragraph 2 talks about the ether, and Paragraph 3 talks about their relative motion.
• Method 2: Parallel Structure.  There is only one paragraph and most of the sentences mentions both the earth and the ether and their relative motion

The series and parallel structures are analogies borrowed from electric circuit theory.

Fig. 1.  Occurrence of "Earth" and "Ether" in the Michelson-Morley paper.  The paper starts from the right (top of the paper) marked by the scroll bar arrow and the paper is read to the left (bottom of the paper)

One way of analyzing the structure of Michelson-Morley's paper is analyze the occurrence of the words "Earth" and "Ether" in their manuscript.  To do this, we go to the web page containing Michelson-Morley's paper, click CTRL+F and type "Earth" in the search box.  The occurrence of the word "earth" will be highlighted in yellow along the scroll bar.  Repeat the process for the word "Ether".  What you get is similar to the atomic spectra of two different elements.  We shall call this the word spectra.  Notice that the word spectra of "Earth" is very similar to the word spectra of "Ether".  If we define a word occurrence distribution function $f(x)\delta x$ for the two spectra, such that the smallest interval size $\delta x$ contains several spectral lines for each word, then we see that the overlap integral of the two distributions functions would be positive, which is a mark of parallel writing structure.  If the overlap integral is zero, then the writing has a series structure.

Another way of analyzing the paper's structure is to construct a circuit diagram of the paper, with "Earth" and "Ether" as circuit elements.  I will talk about this in another post.