Alphonse Beau de Rochas filed a patent application but failed to pay the second annuity. Thus the patent was deemed abandoned and the French Patent Office did not retain any documents.

After the patent application Alphonse Beau de Rochas published a brochure Nouvelles recherches sur les conditions pratiques de plus grande utilisation de la chaleur et, en général, de la force motrice : avec application au chemin de fer et à la navigation / par Alph. Beau de Rochas. It is handwritten and of course in French. On page 31 Beau de Rochas explains the four phases of his idea to improve the efficiency of gas machines:

  1. aspiration pendant une course entière du piston;
  2. compression pendant la course suivante;
  3. inflammation au point mort haut et détente pendant la troisième course;
  4. refoulement des gaz brulés hors du cylindre au quatrième et dernier retour.
  1. Suction during a full piston stroke
  2. Compression during the next stroke
  3. Ignition at the upper dead point and relaxation during the third stroke
  4. Release of the burnt gases from the cylinder on the fourth and final stroke.

A summary of the Beau de Rochas insights is given in "Gas and Petroleum Engines" by Henry De Gaffigny, translated by A. G. Elliott, London, Whittaker and Co., published 1898. This book is available for free as an ebook in the Gutenberg project. Paragraph 14-16 in Chapter 1 informs us:

 

We have now reached the year 1862, which may be considered a memorable one in the history of the gas engine, for it was in this year that a patent was taken out by M. Beau de Rochas, setting forth from a theoretical point of view the best working conditions for a gas engine. During the forward stroke of the piston the explosive mixture was to be drawn into the cylinder, during the return stroke this volume of gas being compressed; at the dead point at the beginning of the second forward stroke the explosion was to take place, driving the piston forward, the gases being expelled during the second return stroke. The whole principle will be seen to consist of four distinct operations, forming what is known as the Otto cycle, for reasons which we will presently explain.

The peculiar part of the patent was its purely theoretical explanation. Whilst giving all the honour due to the inventor, and recognizing that he fully understood what he was talking about, we must not forget that there was nothing whatever in the patent indicating how the ideas embodied therein might be carried into practice. No drawings were appended to the text, explaining how the gases were to be ignited, or how the exhausted gases were to escape; it contained nothing, in fact, but the plain statement of the most efficient cycle of operation

M. de Rochas did not construct a machine on this principle, and as he omitted to pay his patent fee for the second year, the idea became public property. For these reasons no attention was drawn to it until ten years afterwards, when it came to light during some patent litigation undertaken by Dr. Otto in 1878.