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The tiger is an analogy for the pendulum; it gives the impending doom of the movements of the pendulum a slightly more understandable comparison. Of course, not many people have been hunted by a tiger, so it is a rather exotic analogy; but people are probably slightly more familiar with tigers than they are with deadly pendulums, so it serves its purpose.
The narrator is comparing the slow approach of the pendulum to the way a tiger stalks its prey. The pendulum makes slow, steady, and precise movements as it closes in on its prey; just as the tiger crouches low, its eyes never leaving its object of desire as it stalks forward slowly, hiding in the tall grass, waiting for its opportunity to pounce and finish the job.
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