162 Attempt to facilitate Observations of 
Now, let us suppose two weights to be placed in succession on the southern arm of 
the needle, and let their moments, »’ and »”, be adjusted so as to bring the needle into 
the positions forming half a right angle with the horizon, below and above; the corres- 
ponding values of @ then are +45° and —45°, and substituting, we have the two equa- 
tions following 
nu = o (sindé—cos 0), nw’ =@ a (sin 8 + Cos 0). 
Adding and substracting these equations, we have 
uw +p =2oosind, pb’ —p =296 C08 6. 
from which we obtain, 
‘ tan 8H po V2= yn te (2) 
wu 
Accordingly, to determine the intensity of the terrestrial magnetic force, as well as 
the dip, we have only to find the moments of two counterpoises which will bring the 
needle into the two positions above mentioned ; the sum of these divided by their dif- 
ference is equal to the tangent of the dip, and the square root of the sum of their 
squares furnishes a measure of the intensity. Another set of results might be obtained 
by observing also the moment of the counterpoise which brings the needle to the 
horizontal position ; for it will be easily seen that this moment is equal to the arithme- 
tical mean between the two preceding, or equal to ¢ o sin 6. 
In the practice of this method, it is obvious that a divided circle is not required; it is 
only necessary to place four lines on the frame of the instrument corresponding to the 
inclinations of 45°. It is requisite, however, to have some means of determining the 
moments of the counterpoises with facility. For this purpose I procured a needle fur- 
nished with a small sliding weight, and having a scale on its southern arm, divided to 
the 1-50th of aninch. I had then only to observe the division on the scale coinciding 
with a fixed mark on the sliding weight, when the needle was brought to the two 
required positions. 2 
Simple as this method appears, a few trials were sufficient to convince me that it 
would prove a most inconvenient one in practice. The adjustment of the counter- 
poise, so as to bring the needle to the required inclinations, was found to be a tedious 
and delicate operation, requiring a frequent removal of the needle from its supports ; 
and the repetition of this process, in the various positions of the needle and instrument 
in which an observation of dip is usually taken, multiplies, of course, the difficulty. 
For these, and other reasons, it appeared far preferable to observe the positions 
which the needle assumes with fixed counterpoises, rather than the counterpoises which 
bring it into fixed positions. It will be easily seen, that two such observations are 
sufficient to determine the dip and the magnetic intensity. 
