Analysis of Mr Barlow’s Essay on Magnetic Attractions. £63 
before Mr Barlow attempted to connect these several points with 
each other ? Was the surface formed by the union of those 
points investigated ? Was it known whether this surface was 
a curve or plane ? And what was its position either with reference 
to the bar or to the horizon ; and how did its position change 
in different latitudes ? We believe that no one of those ques- 
tions could have been answered prior to Mr Barlow’s experiments. 
He has first shown, that these several points of no action fall 
in one plane, and that that plane always forms with the horizon 
an angle equal to the complement of the dip. It must there- 
fore, we conceive, be admitted, that, in this determination, he 
has made a considerable step towards reducing to definite laws 
the hitherto apparently uncertain action of unmagnetised iron. 
We have been the more particular in examining this question, 
because it appears, by a letter lately published by the author, 
that some attempts have been made to show that there was no 
novelty in this deduction. 
In order to pursue his inquiries further, Mr Barlow imagined 
the circle cut off by the plane of no attraction, from a ball of iron, 
or any sphere concentric with it, to form an equation ; and 
hence, by means of imaginary circles of latitude and longitude, 
(the first circle of the latter passing through the east and west 
points of the horizon), he was enabled to designate the situation 
of his needle in that sphere, which, together with the distance 
from the centre, answered all the purposes of three rectangular 
co-ordinates, by which positions in space are commonly deter- 
mined. 
Having made the requisite computations for this purpose, he 
caused the compass to be moved round the ball in different 
circles, first, in those in which the longitude was zero, or a con- 
stant quantity, in order to obtain the effect due to latitude only ; 
then in circles of which the latitude was constant, in order to 
obtain the effect due to longitude only, the distances remaining 
constant ; and in this manner he obtained the simple law ex- 
pressed by the following formula, viz. 
Tan. A — A sin. £ a cos. 7. 
That is, the tangent of deviation is proportional to the rectangle 
of the sine of the double latitude and the cosine of the longi- 
tude. 
