GENERALLY:   This Rider-Remington Rolling Block knock-off was originally based on a patent granted to Theodore Laidley and C.A. Emery in 1866 and was manufactured by the Whitney Arms Company of (big surprise) Whitneyville, Connecticut..  Originally, the Whitney rifle's action had a specially designed cam which locked the breech closed, separate and distinct from the hammer, (which locks the breech in the Remington-Rider system).  Later versions of the Whitney-Laidley rifle are a near exact copy of it's much more successful rival, the Remington.   Whitney also built sporting rifles such as the Phoenix, but these were not successful military contenders.

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PHOTO:  The above picture is of a standard M1872 Whitney-Laidley (also Laidley-Emery) Military rifle, which was part of an 1877 purchase by Mexico directly from Whitney of some 2,000 such rifles.

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DISTINGUISHING CHARECTERISTICS:  Mexican rifles are marked R. DE MEXICO or simply R.  M. (Republica Mexicana) and are sometimes also marked with the "Liberty Cap on Sunburst" design, sometimes called the "Phrygian cap insignia."  As far as I can tell, dimentions, furniture and charecteristics are almost (though not quite) identical to the M1871 Spanish Remington.  The Whitney can also be recognized by the extra lateral screw in the left side of the receiver below what looks like the pin retainer plates (there are actually 2 separate parts locked in by a single center screw) ... and the "pin retainer plates" themselves, which, although they look like cover plates covering retainer pins, are actully part of the retainer pins.

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I expect that examples of the M1868 (71?) Spanish Model Mexican Rolling Block rifle bought by Mexico at the same time would be similarly marked.