The first comet discovered by telescope is…

The Dutch are reaping spectacular profits from the opium trade.

Buying opium cheap in India and selling high in Java has gained the Dutch East India Company a four hundred percent profit on shipments in the 1670s.

Opium, moreover, proves to be an essential trade good that attracts Asian merchants to Batavai, by 1681 representing thirty-four percent of the cargo on Asian ships sailing from here.

The remnants of Wu Shifan’s armies are defeated soon thereafter in December 1681 and Wu Shifan commits suicide; Wu Shigui's son-in-law is sent with Wu Shifan's head to Beijing.

The Qing general Zhao Liangdong proposes a three-pronged attack on Yunnan in 1681, with imperial armies from Hunan, Guangxi and Sichuan.

Cai Yurong, Viceroy of Yungui, leads the attack on the rebels together with Zhang Tai and Laita Giyesu, conquering Mount Wuhua and besieging Kunming.

Zhao Liandong's army is in October the first to break through into Kunming and the others follow suit, swiftly capturing the city.

Wu Shifan commits suicide in December; the rebels surrender the following day.

Zheng Jing, driven off the mainland by the Manchu, has retreated to Tainan, where he falls ill and on March 17, 1681, dies of “dissipation”.

Zheng had named as his successor his oldest son, Zheng Kezang; however, Zheng Kezang is quickly toppled in favor of twelve-year-old Zheng Keshuang.

Fyodor III in 1681 recalls the long-exiled Nikon to Moscow, but the former patriarch dies on the journey.

Thököly, aided by the emperor's preoccupation with hostile France, and backed by the Turks and the prince of Transylvania, overruns much of upper Hungary and forces Leopold to restore Hungarian liberties (Treaty of Sopron, 1681) and to recognize his own quasi-sovereignty in north Hungary.

He soon resumes hostilities against the emperor, however, allying himself with the Turks, whose army by 1681 appears very strong, and taking the title of prince over his own dominions.

Greysolon, lured by native stories of the Western or Vermilion Sea (likely the Great Salt Lake in Utah), had reached the Mississippi River via the Saint Croix River in 1680 and then headed back to Fort de Buade, where he had heard that jealous Quebec merchants and the intendant Jacques Duchesneau de la Doussinière et d'Ambault are slandering him.

He is forced to return to Montreal and then France in 1681 to defend himself against false accusations of treason; he will return the following year.

Saint-Domingue's total population by 1681 is estimated to be six thousand six hundred and fifty-eight.

El Paso del Norte becomes the new base for Spanish governance of the territory of New Mexico.

From El Paso, the Spaniards, led by Diego de Vargas, group once again to recolonize the precious Spanish territory that is centered in Santa Fe and stretches from Socorro (New Mexico) to the areas that include Taos.

The Russians, having in 1679 and 1680 repulsed the attacks of the Crimean Tatars, on January 3, 1681, sign the Bakhchisaray Peace Treaty with the Ottoman Empire and the Crimean Khanate.

They agree to a twenty-year truce and accept the Dnieper River as the demarcation line between the Ottoman Empire and Moscow's domain.

All sides agree not to settle the territory between the Southern Bug and Dnieper rivers.

After the signing of the treaty, the Nogai hordes still retain the right to live as nomads in the southern steppes of Ukraine, while the Cossacks retain the right to fish in the Dnieper and its tributaries; to obtain salt in the south; and to sail on the Dnieper and the Black Sea.

The sultan then recognizes Muscovy's sovereignty in the Left-bank Ukraine region and the Zaporozhian Cossack domain, while the southern part of the Kiev region, the Bratslav region, and Podolia are left under Ottoman control.