20 Captain Sabine's experiments to determine the 
in the ratio suggested by Dr. Young, inversely as the square 
root of four diminished by three times the square of the fine 
of the dip, which ratio has been remarkably confirmed in 
dips from 70 to 90 degrees, by the experiments made during 
the late Arctic voyage ; the force acting on the horizontal 
needle, being reduced as the radius to the cosine, becomes in- 
versely as + 3; 5 being the sine of the dip; whence, in 
London, the duration of any number of horizontal vibrations 
would be increased by about -jdoo P art > 011 a reduction of one 
minute in the dip. 
The needle No. 3. of the preceding experiments, sus- 
pended in the manner therein described, and released at an 
arc of 40° from the meridian, will continue to vibrate more 
than forty minutes, making upwards of 400 vibrations, be- 
fore the arcs become so small as to render the completion of 
each vibration indistinct. If the times of commencement and 
conclusion are observed in the method exemplified in the 
experiment with this needle, page 17; the duration of any 
number of vibrations may be readily and accurately determin- 
ed to a part of a second ; if, therefore, 400 be taken as the ex- 
perimental number, and the duration be supposed 42 minutes, 
or 2520 seconds, the reduction of 3 minutes of dip, which 
is presumed to take place annually, would cause an increase 
of two seconds and two-tenths in the time of vibration ; which 
difference may, perhaps, be considered sufficient to encourage 
the experiment, especially if a mean be taken of many obser- 
vations in each year ; in which case it may be advisable to 
compare together observations made at the same season in 
successive years ; and perhaps, also, at the same hour of the 
day ; although the experiments of Messrs. Humboldt and 
