PRINCIPLES OF A NEW SPECIES OF BALANCE. 
419 
the squares of the distances between the threads of oscillation divided by their 
lengths, and that, contrary to the law of torsion as deduced by Coulombe, is as the 
P d 3 
weight of the cylinder P : hence we have n <x — — ; and since the oscillations of the 
cylinder are found by experiment to be isochronous at all angles (4.), we may con- 
clude that n is also proportional to the angle of deflection of the threads, as shown 
by the index P i, fig. 13. 
6. These results were verified experimentally in the following manner : 
Experiment B. — A weight fw as caused to act tangentially to the circumference of 
the cylinder P, fig. 13, by means of a slender filament of silk, f p P, passing over an 
extremely delicate pully p. This pully was attached to a slide and socket u, fixed 
to the circular rim u g i, moveable about the interior block carrying the graduated 
card p g i; hence the line f p P could be exactly set at right angles to the radius of 
deflection in all positions of the index i, and the precise weight determined requisite 
to balance the reactive force of the threads at any given angle, or otherwise by turn- 
ing the whole frame of suspension d s e in a circular socket formed in the transverse 
piece A A' through any number of degrees, as measured by a graduated card n x and 
index x, and preserving always the index P i of the cylindrical weight at zero, we 
arrive at the reactive force of the threads of suspension, at any required angle, in a 
similar manner. 
The results of a series of experiments conducted in this way completely verified the 
above deductions, the weight requisite to maintain the index at an angle of 60° being 
as the weight of the cylinder P multiplied into the squares of the distances between 
the filaments of suspension divided by their length. It was also found to vary accu- 
rately with the angle of deflection, the attendant circumstances being unchanged. 
7. The following Tables, abridged from a greater number of experiments than it is 
desirable to mention here, afford a sufficient practical evidence of the truth of these 
results. In these Tables the unit of weight is 1 grain, the unit of length 1 inch, the 
unit of time 1 second. 
Table I. 
Showing the Rate of Oscillation with different Lengths and Distances of the Threads, 
as in Sect. 4. 
Weight of cylinder = 960 grains. Angle of oscillation 45°. 
Length. 
Distance. 
Oscillations 
in 60 ". 
Time of ten 
oscillations 
by observation. 
Time of one 
oscillation. 
\ 6 
i 0-25 | 
J 1 
28-50 
21 
2-1 
e 24 
14-25 
42 
4-2 
1 6 
1 f 
46 
13-1 
1-31 
jj 12 
>0-4 
32-50 
18-5 
1-85 
24 
J l 
23 
26-2 
2-62 
24 
0-8 
46 
13-1 
1-31 
3 h 2 
