CAPTAIN ELLIOT’S MAGNETIC SURVEY OF THE INDIAN ARCHIPELAGO. 321 
To determine the time of one vibration, 360 were observed, and care was taken 
that the vibrations of the deflecting- needle should be limited to an exceedingly 
small arc. 
Formulas for the Determination of m and X. 

Defection . — The value of ^ is found for each distance by the formula 
tan a. 
where 
P= 
rHf tan a^—rf-r^ tan a 
r^^tana^— r^tana ’ 
r and r^ being two distances at which the deflecting magnet is placed, a and a, the 
corresponding angles of deflection. 
Vibration . — From the experiments of vibration. 
where t is the ratio of the circumference of a circle to its diameter, k the moment 
of inertia of the magnet and stirrup, T the time of one vibration. 
To obtain the value of k, a cylindrical brass weight is attached at each end of the 
magnet, 
fp2 
and ^ — rjp /2 rp 2 
where k^ is the moment of inertia of the magnet and attached weights, T the time of 
vibration with the magnet and stirrup only, T the time with the weights attached, 
and . 
in which /=the interval between the points of suspension of the weights, r the 
radius of the brass cylinders, and 2p their weight. 
Determination of the Coefficients. 
In finding the values of m and X, it is necessary to determine certain constants ; 
such as (1) the value of one division of the scale of the suspended magnet ; (2) the 
coefficient of temperature of the deflecting magnet; (3) its moment of inertia; (4) 
the value of P. 
(1.) Value of one division of the scale . — In the Singapore Observatory Declinometer, 
the value of one scale division was determined by the formula 
a'~X3437'-747: 
the results alone are given. 
MDCCCLI. 2 T 
