You guys are so small arms fixated you can't conceive of other weapons being around.
this is the 3.2 inch M1890 American Field Artillery,
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This is one field artillery unit that Pershing took with him when in 1914 the US invaded Mexico. It is surprising how few know of the siege of Sara Cruz or of this whole debacle.
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Field Artillery around 1922, not that much different from pre WW1
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I expect the field artillery would engage your unit around 7,000 to 10,000 yards out.
This is a copy of a French Howitzer, you can look up the type of howitzers around in the 1890's, typically they were 105mm to 155mm. Maybe their range is a little less than 20,000 yards. But I guarantee, if they could see troop or horse concentrations, lets say 10,000 yards away, they would blast them. If the horizon is seven miles away, given a flat part of the earth, (12,320 yards) then this thing could shoot over the horizon. You think they are worried about rifle shooters hitting their horses?
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Of course these were the bigga badda boomers. Not portable at all. I think they would make 50 foot wide divots in the ground. There were mortars of similar size.
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Why would anyone from the time period be thinking about killing horses with rifles, at lets say, under 1000 yards, when field artillery could blow any visible unit into shreds out to 12,320 yards? And the 12 inch gun would shoot maybe 20 miles?