I was reading Bayes' essay "An Essay towards Solving a Problem in the Doctrine of Chances" and noticed the following bit of notation

confusing bit of Bayes' Essay

The meaning of the n+1 term is clear from the rest of the essay (in modern terms it would be surrounded by parentheses rather than have the bar), but the ×d part confused me. Initially I thought it meant "multiply d times", but there is no numeric variable d elsewhere, leading me to think that ×d is meant to be an abbreviation for "multiplied".

Has ×d been used in other works to mean multiplied? Here, it seems to mean that in context (it fits the sentence, at least), but other historical examples would increase my confidence.

A copy of the paper is here. The image is from the bottom of page 29 of the PDF.

  • $\begingroup$ In context, could it by a typo? That is, does it make sense to just be x d with the d not raised? $\endgroup$
    – puppetsock
    Jun 6, 2019 at 19:33
  • 1
    $\begingroup$ Given the effort involved in letterpress printing, that sort of typo is unlikely. Also, using superscript final letters for abbreviations used to be quite a common thing. $\endgroup$ Jun 6, 2019 at 19:52
  • $\begingroup$ I don't think it would make sense, since that would mean multiplied by d, but there aren't any variables d in the paper (except for about 13 pages back, but that refers to a point, not a number). $\endgroup$ Jun 6, 2019 at 19:53
  • $\begingroup$ The first x does not have any raised d. On the same page, clearly x is not the same as the algebraic x also used, and has superscripts which seem to represent powers. $\endgroup$ Jun 6, 2019 at 19:56
  • $\begingroup$ @AndrewLeach It being that convention would make sense, and it seems to be used elsewhere in the paper with the 'multiplied by' meaning. $\endgroup$ Jun 6, 2019 at 20:01

1 Answer 1


There is a transcription of the paper originally from UCLA but now on the WayBackMachine It uses two different "x". The UCLA copy still uses the archaic bar in place of parenthesis.

In modern notation I copy it as:

(n+1) x EX^d

Where the lower case x is multiplication, the upper case X is a variable and ^d is exponentiation.

Upper case X is a variable used many times in that area of the paper.

I think the real answer to this question is "Go and find a different (newer) transcription of the paper and draw your own conclusions."


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