Medials (介音) are very important in Chinese, there are three medials, namely i, u, ü. Pioneers of Sinology seem to rely heavily upon their own language intuitions while treating these sounds. This short note concerns the most important medial i, which was transcribed as ë in the translation of Peking Gazette, one of the court news bulletin in late Qīng dynasty.
Medial is a sound, syllable, or letter occurring between the initial and final positions in a word or morpheme. In Chinese, these kinds of sound are very important. There are three medial in Chinese, namely in Pīnyīn, i, u, and ü.
Historically, these sounds have been transcribed in variety ways. The sound concerned in this short note is medial i sound occurred in the translation of Peking Gazette, one of the court news bulletin in late Qīng dynasty.
In the issue of 1873 Peking Gazette, the medial i was transcribed as ë, for example:
乾隆 the Emperor K’ëen-lung
喬松年 Këaou Sung-nëen
Ë (or ë) appears in words like French ‘Noël’ and Dutch ‘koloniën’, which is called trema. This letter is used to indicate that the vowel should not be diphthongized. For example, “Noël” is pronounced /noɛl/, whilst “Noel” would be pronounced /nœl/. Likewise, “koloniën” is pronounced /koloniən/, whilst “kolonien” would be pronounced /kolonin/. 
In Chinese, all vowel combinations can be treated as diphthongs or triphthongs, when pronouncing, it starts from the first vowel, and glides to the last, including a rising or falling movement. A group of two or three vowel letters haven’t been yet monophthongized such as French or English has during the evolution of the language. The translators of the Peking Gazette used ë to transcribe the Chinese medial sound [i], put two dots on the of e (e-umulaut) , they seem to try to indicate the ëe combination should not be diphthongized or monophthongized as in English word tree.
Interestingly, in the same document, 天津 was transcribed as Tien tsin, which was the large port city near Peking.
In the paragraph on May 11th (2):
“It is on record that His Excellency the Assis- tant Minister K’hwei-chang and others, formerly prayed the Emperor that ten teachers of foreign drill and two Ensigns might be sent from Tientsin (天津) in the Province of Chili, to the Boundary (Ili) to give instruction to the soldiers there. “
In the paragraph on May 21st (3):
“The Autumn term for the trial of prisoners is now approaching, and the petitioner being at present at Tien-tsin, where he is engaged in regulating matters concerning the foreign merchants, and in receiving the Imperial tribute sent by sea, cannot at present return to his own duties.”
In modern Chinese, medial i and the i as final are treated same, but in Peking Gazette, these two sounds were different. From example, the measure of distance 里 transcribed as Le, and the surname 李 as Le:
In modern Chinese, another sound after initials z c s are written as zi, ci si, same form as the medial but pronounce different.
In contrast with Pīnyīn, Peking Gazette use i sound as a diphthong ei, such as the previous mentioned Hih-lung-këang, and in this name Sëaou Tih-yang, etc.
To sum up, while I am reading these interesting and important documents, I feel that in translating of Chinese documents in early 18th to 19th centuries, the translator didn’t have a systematic method to transcribe Chinese sound system, especially for names of people and places. They seem to rely heavily upon their individual language intuitions.