Answer: "Gyrations" refers to circular or spinning movements, often used to describe a rapid, energetic, or repeated series of such movements. It can also be used figuratively to describe sudden or erratic changes in behavior, opinion, or value, much like the erratic movement of a spinning object.
Explanation: In this context, "gyrations" likely refers to sudden, erratic or unpredictable movements, actions, or changes in behavior, particularly in the context of Japanese foreign minister Matsuoka. The passage suggests that Matsuoka was making certain promises to Germany regarding Axis agreements, despite the ongoing talks between the United States and Japan. Eden believed that Hull should be made aware of these "gyrations" - likely indicating that Matsuoka's behavior was unexpected, and perhaps concerning. Hull, in turn, was angry at the implication that he had been deceived by the Japanese and had acted against the interests of the British.