Formula
Collier's New Encyclopedia (1921)
in chemistry, an expression by means of symbols, especially letters and numbers, of the chemical elements contained in a compound; in medicine, a prescription. In mathematics, a formula is the expression of a general rule or principle in algebraic symbols. For example, the equation- (a+b)(a - b)=a²-b² is a formula, being the algebraic expres sion of the fact that the sum of two quantities multiplied by their difference is equal to the difference of their squares. If a rule or principle is translated into algebraic expressions, the result is a formula; conversely, if a formula is translated into ordinary language, the result is a rule or principle. In Church history, a formula is a formal enunciation or declaration of faith or doctrine. The formula of concord was a confession of faith upon the points on which the Lutherans differed from the Calvinists, especially in connection with the Eucharist. The issue of such a document was suggested by Augustus, Elector of Saxony, who employed James Andreä to ascertain opinions on the subject, and draw it out. His chief assistants were Martin Chemnitz, Nicholas Selnecker, Andrew Musculus, Christopher Cörner, and David Chyteus. The formula was published in 1580, all clergymen and schoolmasters being required by the Elector to subscribe to it. It indorsed the opinions of Luther, and widened the breach with the Swiss and other reformed Churches. The formula consensus was a formula drawn up in 1675, by John Henry Heidegger, a celebrated divine, of Zurich, at the instance of his clerical brethren, to preserve the Calvinistic doctrine from the slight modifications of it introduced by the French divine, Amyraut, and others. It was annexed by by the magistrates to the common Helvetic formulas of religion. Its effect was found adverse rather than favorable to peace. It was abolished in the canton of Berne and the republic of Geneva in 1686, and ultimately became incapable of enforcement anywhere.
What Has Changed in the Last Century
The senses Collier's listed in 1921 all survive: chemists still write H2O, mathematicians still call (a+b)(a−b)=a²−b² a formula, and the Formula of Concord (drafted 1577, printed in the Book of Concord in 1580) is still the Lutheran confession described here. What has shifted is which meaning a reader reaches for first. Since the 1920s "formula" in everyday English has come to mean manufactured infant feed, and since 1946 the racing classes named Formula One, Two and Three; since the spreadsheet arrived with VisiCalc in 1979, millions of people type formulas daily without meeting algebra. Chemical formulae themselves are now derived from instruments rather than combustion analysis alone — X-ray crystallography and mass spectrometry give structures the 1921 writer could only infer.
Written for this edition, 2026.