NavList:

  Marq St-Hilaire, Capitaine de frégate, first published his method in the a series of articles published

 in the Revue Maritime et Coloniale :

 Note sur la Détermination du Point,   October 1873, pp 41-58

and

Calcul du Point Observé,  published in two parts:  August 1875, pp 341 -- 376  and September 1875, pp 714 --752.  

 An English translation of these articles appears in the book Line of Position,  by Vanvaerenberg and Ifland, published by Unlimited Publishing of Bloomington, IN in 2003.  The ISBN is 9781588320681. This book,  Line of Position  also contains a reprint of Thomas Sumner's original 1843 publication of his method:   A new and accurate method of finding a ship's position at sea, by projection on Mercator's chart. 

I wrote an article about the connections between these two methods in 2007.  You may view or download a full copy of that paper at https://www.academia.edu/5870349/Circles_of_Illumination_Parallels_of_Equal_Altitude_and_le_Calcul_du_Point_Observé_Nineteenth_Century_Advances_in_Celestial_Navigation

Adoption of St-Hilaire's methods were slow and graduate (in comparison with the rapid adoption of Sumner's methods).

Publications in France praised the nouvelle navigation astronomique  and its new techniques for position finding. [ 1877, 1888].   Adoption in England came more slowly despite early publications in English around 1880 and 1881.  It was introduced into the British Navy in 1886, but students preparing for a career in the English Merchant Navy were not exposed to the preferredhaversine tables and formula until about 1908 and therefore did not use the intercept method.  A similar pattern was followed in the United States -- the United State Navy published a treatise  on Navigation and Nautical Astronomy including the intercept method in 1908 for use as a textbook at the Naval Academy.  But it was the demands of aviators for a more rapid method of position finding that drove further development of the intercept method, includng the development of azimuth tables [HO 120, HO 171 ] and sight reduction tables [H.O. 201, 1919]  (providing both azimuth and computed altitude).  

The above paragraph contains a combination of quotations, condensations, rewordings, simplifications, and amplifications of material drawn from  Line of Postion,  Vanvaerenbergh and Ifland, pp 21--23.  The interested reader should consult the  bibliography given on pp 30--31.