419 
sulphur were converted respectively into iodide and sulphate of potas- 
sium, and estimated in the usual way. 
Calculated. Found. 
S 2 , . 20-13 20-28 
I. . 79-87 79.81 
100 0 100-9 
Though in this note the recomposition is considered as a means 
of preparing the compound halogen S 2 I, it is perhaps of equal 
interest as offering a method for obtaining an organic chloride from 
its iodide, — a problem otherwise difficult and cumbrous in solution, 
albeit its inverse is easy and of frequent occurrence. 
4. Notice of an Expeditious Method (believed to be new) for 
Computing the Time of Descent in a Circular Arc. By 
Edward Sang, Esq. 
In determining the intensity of gravitation from the oscillations 
of a pendulum, and in estimating the directive power of the earth’s 
magnetism from the frequency of vibration of a needle, we have to 
make allowance for the extent of the arc through which the motions 
take place. 
The formula usually given for this purpose contains a series con- 
verging rapidly enough for very 
small arcs, but which requires a 
great amount of labour when the 
angle of deflection exceeds twenty 
or thirty degrees. 
My object is to give notice of 
a process by which the labour 
becomes insignificant. 
Let O be the centre of motion, 
N the lowest point of the curve, 
and AN the arc through which 
the descent is to take place. 
Having drawn the horizontal 
tangent NC, make the angle 
NOC one-fourth part of NO A ; 
through C draw CD perpendicular 
to OC meeting ON produced in D, and inflect the chord NB equal 
vol. v. 3 k 
