When was the cross-correlation function invented? And what was the motivation behind it? In a previous question I asked about the history of auto-correlation
In this question I'm interested in the discovery process behind cross-correlation.


*

*When was it invented? 

*Was it independently invented multiple times?

*What motivated its invention?

 A: Hard to date an intuitive geometric concept. Maybe starting with the Gramian matrix? The use of the covariance matrix in statistics is very much related 
to the concept of Mahalanobis distances.
A: In my opinion correlation is synonymous with cross-correlation. If you accept that then Galton is your guy circa 1877. If your want the first time the word cross-correlation was used then Thorndike is your guy circa 1920.

In a psychology study published in 1920,
Thorndike asked commanding officers to rate their soldiers; he found
high cross-correlation between all positive and all negative traits.
People seem not to think of other individuals in mixed terms; instead
we seem to see each person as roughly good or roughly bad across all
categories of measurement.

(From Wikipedia on the "Halo effect.")
More on Thorndike

Way back in 1920, just after the first burst of enthusiasm about
then-new IQ tests, psychologist Edward Thorndike created the original
formulation of "social intelligence." One way he defined it was as
"the ability to understand and manage men and women," skills we all
need to live well in the world.
But that definition by itself also
allows pure manipulation to be considered a mark of interpersonal
talent.

Daniel Goleman, Social Intelligence: The New Science of Human Relationships, p. 11.
