Lord Rayleigh, a.k.a. John William Strutt, 3rd Baron Rayleigh (1842–1919), was, in my opinion, a quintessential mathematical and experimental physicist and, indeed, a classical applied mathematician of the highest order for his era. Among the many honors he received, the most prestigious was the 1904 Nobel Prize in Physics “for his investigations of the densities of the most important gases and for his discovery of argon in connection with these studies.” He was one of the very few members of so-called British “higher nobility” who won fame as an outstanding scientist.

His collected scientific papers are published in three scholarly books of two volumes each as shown.

Question 1:

  • The coffee mug is of a typical size: diameter ≈ 8 cm, height ≈ 10 cm. The thickness of each book varies slightly, but we can ignore that. Therefore, each book, by comparison, is about 6.5 cm thick and 25 cm high. The width across each page can be estimated as ∼15 cm. Typically, on my bookshelf there are ∼200 numbered pages/cm (i.e., ∼100 individual pages), so the number of pages in all six volumes (three tomes) is ∼3 × 6.5 × 200 ≈ 3900 pages.

  • A typical page (replacing equations by writing) has ∼40 lines with ∼12 words/line, or ∼500 words/page. Hence, the number of words in total is ∼3900 × 500 ≈ 2 × 106.

Question 2: The density of paper varies, but for typical academic books (the Dover edition was published in 1964), it is ∼800 kg/m3. (A single sheet of paper will generally float until it absorbs water.) The volume of each of the three books is ∼6.5 × 15 × 25 cm3 ≈ 2400 cm3 = 2.4 × 10−3 m3. Hence, the total volume is ∼7 × 10−3 m3. Hence, the total mass is ∼8 × 102 kg/m3 × 7 × 10−3 m3 = 5.6 kg.

In fact, there are approximately 3700 pages, and the whole set has a mass of 5.4 kg (using my wife’s kitchen scales). I didn’t count the number of words because I’m working on my next Fermi column!