Background -- the Ryukyu Islands had been a tributary state of China since the 14th century. However, in the early 17th century, Satsuma succeeded in making the Ryukyus her vassal. From that time onwards, the Ryukyu kings were subjected to double subordination, regarding China as father and Japan as mother. Officially, the Ching government knew nothing of Ryukyu’s double status, and treated it as her exclusive tributary state.
The situation was advantageous to Satsuma because the trade with the Ryukyus was an indirect means of trade with China. At the same time, Satsuma got sugar from the Ryukyus as part of the tax payments.
With the Meiji Restoration, the Tokyo government continued to treat the islands a Japanese vassal. As such, conflict with China was inevitable. This took place in 1874, one year after the Korean crisis which had split the Meiji leadership.

Taiwan and Ryukyus 1871-4 -- in 1871, a number of shipwrecked Ryukyu sailors were killed by Taiwan aborigines. Japan took the opportunity to protest on behalf of the Ryukyuans to the Ching Court in 1873. By so doing, she wanted the Ching Court to recognize Japan’s claim over the Ryukyu Islands. Chinese officials in the Tsungli Yamen refused to entertain Japan’s protest, and pointed out that the Ryukyus was a Chinese tributary.
Meanwhile, the Japanese decided to take military actions against Taiwan, ostensibly to revenge for the Ryukyuans. In fact, the Taiwan expedition was motivated partly by a desire of the Tokyo government to pacify agitations of the ex-samurai who had unsuccessfully asked for an expedition to Korea. It was also partly motivated by a desire for overseas expansion of the Japanese. Since the Qing Dynasty was a weak neighbour, Japanese leaders thought it worth gambling.
Japan’s military operation in Taiwan was not effectively resisted by the Chinese government which lacked the strength to defend the islands. Negotiations between China and Japan took place in late 1874. With the mediation of the British Minister at Peking, Thomas Wade, an agreement was finally reached. China agreed to pay Japan an indemnity of half a million dollars. In addition, China agreed not to condemn the Japanese action -- a concession which implied recognition of Japan’s claim to sovereignty over Ryukyu.

Effects -- during the crisis, the Qing government revealed her weaknesses in diplomatic manoeuvres and in military strength. She failed to enlist other powers’ assistance in the crisis and to resist Japan’s aggression. As a matter ol fact, she was willing to pay the aggressor (Japan) for being invaded. This, of course, was an invitation to further foreign encroachment. As for Japan, she succeeded in her gamble. In 1879, when China was preoccupied with Russia over the Ili crisis, Japan annexed the Ryukyu Islands and renamed it Okinawa Prefecture. This was her first territorial gain from China.