The Lyman series of hydrogen was observed by SUMER on SOHO on the north pol
ar limb of the Sun with a total exposure time of more than ten hours. The r
esulting line profiles have been analysed using the technique described by
Marsch et al. (1999). The data analysis corroborates earlier findings on th
e Lyman lines, but also yields phenomena which cannot be fully understood a
t the present time. Firstly, the Line width of the Lyman lines increases wi
th decreasing series or quantum number. Secondly, the hydrogen temperature
gradient in the height range from 12 000 km to 18 000 km is unexpectedly sm
all and does not reveal a steep jump as might be expected from modelling of
the transition region. The average temperature increases only slightly fro
m 1 10(5) K to 2 10(5) K. Possible explanations of these observations are g
iven and models are briefly discussed.