Hello
1b. Lord Arthur Cecil (The Mount, Lymington, Hampshire), b. 3rd July 1851 ;
First m. 8th January 1874, Elizabeth Ann da. of Joseph Wilson of Woodhorn Manor, d. 11th October 1901 ;
Secondly, 4th November 1902, Baroness Frederica da. of Otto Baron von Klenck [Austria]; and has issue 1c to 2c.
1c. Arthur William James Cecil, Lieut Grenadier Guards, b. 4th April 1875.
2c. Reginald Edward Cecil, Capt. 21st Lancers, born 15th November 1878; m. 1st February 1902, Mary Beatrice da. of Henry Drayton Pilcher ; and has issue 1d.
1d. Margaret Mary Cecil, b. 21st July 1903.
2b. Lady Margaret Elizabeth Cecil (Oakdown, Burwash), b. 30th October 1854.
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Details here, pages 224 & 223
https://archive.org/stream/plantagenetrollo00ruviThe Mount, Lymington, Hampshire was put on the property market by Lady Arthur Cecil, Sale date advertised was 30th October 1919, but I cannot find a photo

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The house was situated 2 miles from Lymington Town and 3 miles from Brockenhurst Junction, (Railway).
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Not the house, but:-
The Mount, Bishopstoke (different address), is a similar style (tall chimneys & Bays), but definitely
not your photo.
Mark