MADE BY CAPTAIN BACK DURING HIS LATE ARCTIC EXPEDITION. 
399 
been made by Captain Back ; after which it was lowered, by as nearly as possible 
the same intervals, to the lowest at which the experiments began ; the temperature 
and time of vibration being similarly determined in all cases. The needle under trial 
being removed, the time in which the trial-needle made 100 vibrations was again 
ascertained. The needle, in all cases, commenced vibrating from the same arc 35° ; 
the time, however, of commencing the vibrations was reckoned from its first passing 
zero, and the time of completing each ten vibrations, at the same point, was noted, 
up to one hundred. 
The following Table exhibits the observations that were made with the needle 
No. II. belonging to Captain Back’s dipping instrument. When under the influence 
of this needle, the time of vibration of the trial-needle was so much increased that 50 
vibrations were performed in nearly the same time as 100 had been made when it was 
uninfluenced : and the vibrations could not have been conveniently counted much 
beyond this number. In all cases, the time was determined by two observations. In 
this Table, Thermometer II. indicates the temperature of the needle No. II., and 
Thermometer N, nearly that of the trial-needle. 
Trial-needle uninfluenced. 
Trial-needle under the influence of the needle No. II. 
First 
obser- 
vation. 
Last 
obser- 
vation. 
Begin- f Therm. II. 
60-0 
o 
46-2 
60-0 
72-6 
84-6 
72-0 
59*8 
46-2 
ning \ Therm. N. 
57-2 
60-2 
58-2 
59-6 
60-0 
61-0 
61-0 
61-0 
60-6 
S 
S 
S 
S 
S 
S 
S 
S 
S 
Time of 100 vibra- ~l 
147-8 
147-8 
'1 ’ime of 50 1 
157-2 
155-6 
153-8 
152-6 
154-0 
155-5 
157-1 
tions J 
148-0 
147-9 
vibrations / 
157-0 
155-7 
154-0 
152-8 
154-0 
155-6 
157-1 
O 
o 
O 
O 
O 
O 
O 
o 
End- ("Therm. II. 
60-0 
47-8 
59-6 
71-6 
82-8 
72-0 
60-8 
47-0 
ing \ Therm. N. 
58-0 
60-2 
59-0 
60-0 
60-6. 
62-0 
61-0 
60-8 
60-4 
,, /Therm. II. 
60-0 
47-0 
59-8 
72-1 
83-7 
72-0 
60-3 
46-6 
Mean j XhernuN 
57-6 
60-2 
58-6 
59-8 
60-3 
61-5 
6l-0 
60-9 
60-5 
Mean time of one 1 
n478'7.'i 
3-142 
3-113 
3-078 
3-054 
3-080 
3-110 
3-142 
vibration . . . . / 
The first observation commenced at l h 0 m p.m. 5th March, and the last concluded at 4 h 35 m p.m. 
If we call the terrestrial force acting upon the vibrating needle, M ; the force with 
which the needle II. acts upon it, at any given temperature, m ; the time of vibration 
of the trial-needle, when acted upon by the terrestrial force alone, T ; and its time of 
vibration, when influenced by the needle II., that is, when acted upon by the differ- 
ence of the two forces M and in , t ; then we shall have 
M ~m _ T 2 
M — &> 
and 
— — i _ — ( 16 .) 
M 1 t 2 y J 
Substituting in this equation the observed times of vibration at different tempera- 
