Step 1: Concept
The limit test for Arsenic is based on the Gutzeit test, where arsenic is converted into arsine gas.
Step 2: Meaning
Arsine ($AsH_{3}$) is a gaseous compound produced when arsenic reacts with nascent hydrogen in acidic conditions.
Step 3: Analysis
When arsine gas comes into contact with mercuric chloride ($HgCl_{2}$) paper, it undergoes a chemical reaction that produces a yellow to brown stain. The intensity of this brown color is proportional to the amount of arsenic present in the sample.
Step 4: Conclusion
Therefore, arsine is the specific chemical species responsible for imparting the brown color to the test paper.
Final Answer: (C)