1. Note that the Tianshan here may or may not refer to the range we know by that name today. The Tianshan or Tängri Tagh both mean ‘Heavenly’ or ‘Celestial Mountains,’ and “form the northern border of the Tarim Basin.” Mallory and Mair (2000), p. 45.
          De Crespigny (1984), p. 43 says that: “In Han times, the Barköl Tagh were known as the Tian Shan, and the steppe country there, Yiwu, was a notable territory of the Xiongnu state.” He gives as his reference (in note 57, p. 465) the commentary of the Qing scholar Shen Qinhan to HHSJJ 23/13, 11a.

2. The kingdom of Pulei 蒲類 [P’u-lei]. The text here on the shifting of the population from Lake Barkol by the Xiongnu is self-explanatory. For further discussion on the formation of this kingdom see Chavannes (1905), p. 557, n. 3 and Stein (1928), p. 542.
          The directions given in the text, “west of the Tianshan mountains,” and 536 km from the residence of Lukchun, are very difficult to follow. There are three main possibilities:

1. If the route ran through the region of Further Jushi (Jimasa), it was probably located somewhere near modern Hutubi, northwest of Urumchi (but see note 2 below).

2. If the distance was measured from Lukchun through Urumchi, it would place it somewhere near modern Hutubi.

3. However, if it was on the route running towards the Wusun, it would probably have been located just east of modern Bayanbulak near the junction of routes running west to Tekes and Yining (and the Wusun), south to Yanqi or Karashahr, and southwest to Kucha. It is impossible to be certain from the information available, but the latter identification seems the most likely to me. 

3. The ninety days ride was to the Kingdom of Awu 阿惡 – not to the new Pulei 蒲類, where some of the escaped prisoners settled. See Stein (1928), p. 542.