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The rare noun gelotometre (also gelotometer) designates a notional laughter gauge.
This noun is from ancient Greek γέλως (i.e., gélōs), γέλωτ- (i.e., gélōt-), meaning laughter, and the suffix -metre (also -meter), forming nouns designating measuring instruments (this suffix is from ancient Greek μέτρον (i.e., métron), meaning measure).
These are, in chronological order, the earliest occurrences of the noun gelotometre that I have found:
1-: From Imaginary Conversations of Literary Men and Statesmen (London: Henry Colburn, 1828), by the English author Walter Savage Landor (1775-1864) [volume 3, chapter 9: Duke de Richelieu, Sir Fire Coats, and Lady Glengrin, page 304]:
To dance on Sundays, to enjoy the delights of music, the purest of delights, the greatest, the most humanizing, are things unlawful: the Catholic and Protestant are covenanters here. They may celebrate the Lord’s day, but they must be as gloomy as if it were the devil’s. A gauger comes round, and measures every man’s smile; and we may expect the Society for the Suppression of Vice to offer a reward for a gelotometre, which Johnson * would have defined a diatonic instrument whereby the cachinnations of laughter may be mensurated.
* The reference is to the English lexicographer Samuel Johnson (1709-1784), author of A Dictionary of the English Language (1755).
2-: From A New English Dictionary on Historical Principles; Founded mainly on the Materials collected by the Philological Society (Oxford: The Clarendon Press, 1901) [volume 4: F and G, page 96, column 2]:
Geloto˙meter. nonce-wd. [f. Gr. γέλως, γέλωτ- laughter + μέτρον measure: see -meter.] A gauge for measuring laughter.
1828 Landor Imag. Conv. III. 304 We may expect the Society for the Suppression of Vice to offer a reward for a gelotometre.
3-: From Solution of Cross Word 37, published in The Saturday Review (London, England) of Saturday 17th October 1931 [page 507, column 1]:
Solution.—[…] Down.—Gelotometer.
—Note: The clue given in Cross Word 37, published in The Saturday Review (London, England) of Saturday 3rd October 1931 [page 438, column 2], was as follows:
Down 1. Laughter gauge.
4-: From a theatrical review, published in the Hastings & St. Leonards Observer (Hastings, Sussex, England) of Saturday 23rd July 1932 [page 6, column 2]:
Perhaps the funniest of all lightning comedies was acted by the Fol-de-Rols this week—a novelty entitled “Mrs. ’Arris Sees Pink.” […] To describe this ludicrous tangle of cross purposes were futile; everybody who likes a laugh ought to see it. There were other eminently entertaining numbers […].
All these numbers greatly excited the risibility of the large audiences. Indeed, so laughter-provoking is the present company that it is almost a pity Mr. Norman Gray has not installed a gelotometer in order to record it.