I would say that General William Hull had two related objectives when he issued his proclamation at Sandwich on July 12, 1812. First, Hull wanted to encourage Canadians to side with the United States in what we now call the War of 1812. Second, if he could not get them to actively support the US, he wanted to cow them so that they would not actively resist his forces. Unfortunately for Hull, neither of these objectives was achieved in any large measure.
At the time of the War of 1812, many Americans thought that Canada was a natural place for the US to expand. They felt that many Canadians would prefer to belong to a democratic country instead of remaining as subjects of the English monarch. Hull’s proclamation makes it clear that he held to this belief. Hull was trying to persuade the Canadians that the US was a more just country than the UK was and that the US could protect Canada from British tyranny.
However, the proclamation also shows that Hull was worried about Canadians who would not voluntarily side with the US. Anticipating that some Canadians might resist, he warned that any resistance would bring down the “horrors and calamities of war” on the Canadians. This statement and others like it are clearly meant as threats to deter the Canadians from opposing Hull’s forces.
Thus, we can see that Hull’s proclamation was meant to persuade Canadians to side with the US and to deter any Canadians who might think of resisting.