I used to keep subject folders for primary materials on agricultural structures, and I have a small one on cisterns.  (Much of this material you can now find online.)  I found a couple of mentions of the use of brick walls to filter water, one apparently vertical, and the other horizontal.

A reader writes to the American Agriculturist in 1856 describing a cistern 8-feet deep and 10-feet in diameter (circular).  After describing how to build it, he adds:  

"If drinking water is desired, divide the cistern into two equal parts, by a 4 1/4 inch brick wall, laid in mortar, one part sand and two parts cement -- (the brick having been first soaked in water some half hour,) into one of these divisions, the water is conducted from the roofs, and it will weep, ooze, and press through the bricks of the wall, as if would through a filtering stone, until level in both divisions, affording limpid, tasteless, pure delicious drinking water, the healthiest and best beverage with which man ever moistened his lips.  --Jno. F. H. / Shepherd's Town, Jefferson County, Va."

"Cisterns," _American Agriculturist_ 12, no. 5, ser. 4 (November 1856): 134.

Another example:

"A correspondent furnishes in substance the following plan for a filtering cistern, recommended by its cheapness and simplicity, and which any mason can make without trouble, and at a cost of a dollar or two additional to any common cistern.  The only drawback is a slight taste of brick for a few weeks at first.  It consists simply of a brick partition built across, through which the water percolates slowly, but quite as fast over such a broad surface as it will be wanted for ordinary use.  As there will be a great pressure of water against this wall, it must be firmly set in the cistern walls with cement, and all built up together; and it must be convex from the pump and towards the entrance spout -- say a curve of six inches in five feet, or one foot in ten.  Without this precaution, the wall will burst by the pressure of the water when it pours in rapidly in a hard rain."

"Cheap Filtering Cistern," _Illustrated Annual of Rural Affairs, for 1870-1-2, vol. 6, J.J. Thomas, ed. (Albany, NY:  Luther Tucker & Son, 1872): pages 150-151.

(Ah.  I found this online, after I transcribed it. 
<https://books.google.com/books?id=3KI1AAAAMAAJ&lpg=RA1-PA150&ots=9m6aWIfZJx&dq=%22cheap%20filtering%20cistern%22&pg=RA1-PA151#v=onepage&q=%22cheap%20filtering%20cistern%22&f=false>

Good luck!

Marty Perdue
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> On May 6, 2020 at 8:48 PM Susan Wlater <[log in to unmask]> wrote:
> 
> 
> Hi All,
> I have a cistern with what appears to be a brick filter inside, on its floor.  The cistern dates to 1900, and is in National City, California.  None of “my” other cisterns had this arrangement.  
> I’d appreciate comments.
> Thanks,
> S. Walter
> 
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