Thank you for sharing this wonderful watch.
Unfortunately, I do not have much information to add. As @Modest_Proposal
wrote, the movement is a caliber 19CH, which was Longines' second chronograph movement. As shown above, there are two variants of the movement. Both are based on the time-only caliber 19A. This information comes from Patrick Linder's book on Longines, entitled "At the Heart of an Industrial Vocation".
As for your example, the condition is fantastic. Though I do not recall seeing another example with the same handset, the style looks appropriate for the era. The enamel dial is lovely, with red numbers for the chronograph minute counter and outer scale. I agree with your estimate of circa 1890 as the production or original invoice date. I suppose that the watch was originally sold in France, given the "M" by the stem.
Admittedly, I do not entirely understand how these chronograph movements work. I think that they use some sort of vertical clutch, rather than a horizontal clutch. I wonder if the chronograph is engaged/disengaged via a lever (red arrow) that acts on a vertical pin (green arrow), which is attached to a hidden lever (part number 506, Linder) that extends to the driving wheel (blue lever). In its current position (reset), the tooth of the lever is between columns on the column wheel. Starting the chronograph would cause the lever to pivot down and right, which would presumably move the pin and hidden lever away from the driving wheel.
Anyway, it is a fascinating and uncommon watch. Examples of Longines' first chronograph, the 20H, seem to be more common than examples of the 19CH.
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