The Siemens engine of 1860 as illustrated in The Theory of the Gas Engine by Dugald Clerk, reprinted from D. Van Nostrand's magazine in 1882. This largely theoretical book on heat and gas contains a discussion section (p83 et seq) in which Dr Siemens discusses his engine and refers to the illustration. The engine never ran successfully and Dr Siemens directed his attentions to other matters.

The mechanism is far from obvious, and Siemens' own description from "The Theory of the Gas Engine" can help.
"With regard to the mechanical arrangement of gas engines, the author (Dugald Clerk) distinguished between three types. In the first, the mixture of gas and air drawn in at atmospheric pressure was exploded. In the second, with which the author (Siemens) had connected his name as that of the first proposer, the combustion was produced gradually ; the gases were ignited as they flowed into the heating cylinder. In the third type, the gases, after being compressed and mixed, were admitted into the working cylinder, and suddenly exploded. With reference to the early engine which Dr. Siemens constructed in 1860, the author (Dugald Clerk) had stated that it combined other elements, which were entirely wanting in the gas engines of the present day."
...
"The combustion of the gases took place in a cylinder without working a piston, and in a cylinder that could be maintained hot, and the gases after having completed expansive action, communicated their heat by means of a regenerator to the incoming gases before explosion took place."

This means of operation can be better understood by studying the Brayton ready-motor.

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