Let's first implement sectional analysis of the text, then we can examine the general meaning of the excerpt. The excerpt begins with the basic rights of governments must form before their people. Then, it follows the performance and the end result of this action. According to this basic idea of fair governance, people have the rights to replace their government if the government is a tyranny. And the substitute have to be a new government which brings safety and happiness to its people.
The general meaning is the justification of a revolt against United Kingdom during that time and the document as this introductory part confirms laid the foundation of this idea to address all the people living in the new ground.
The sentence that contains a participle is the second one - Falling slowly, snowflakes filled the air.
A participle cannot be used as a subject of a sentence, and since <em>Falling </em>in the first example is a subject, it is a gerund, not a participle.
