84 
Dr. E. Obach on an Improved Construction 
Having then only to deal with a single angle for a particular 
measurement, these products of tangents and secants may be 
calculated beforehand. For this purpose the natural sines are 
sufficient, because tan x sec = &. 
' cos l 
The following Table gives, for easy comparison, the values 
of tangents, secants, and their products at ten and mul- 
tiples of ten degrees. These products, like the tangents, 
range from nil to infinity, but increase more rapidly. 
Table II. 
Angle. 
0° 
10° 
20° 
30° 
40° 
50° 
60° 
70° 
80° 
90° 
tan 
sec 

10 
•176 
1015 
•364 
1-064 
•577 
1155 
•839 
1-305 
1192 
1-556 
1-732 
2000 
2-747 
2-924 
5-671 
5-759 
00 
00 
oo 
tan X sec 

•1786 
•3873 
•6664 
1095 
1-855 
3-464 
8-032 
32-66 
III. Method of Constant Deflection. — Here the coil is each 
time inclined until the needle reaches a certain deflection, say 
26^°, 45°, or 63^°, of which the corresponding tangents are £, 
1, and 2 respectively. This figure then enters the constant, 
giving the simpler formula 
,r = sec<£x const., 
the instrument acting as a secant-galvanometer. For a given 
constant deflection the secant-measurements range between 
unity and infinity, as the above little table shows. This 
method has the peculiarity that the needle occupies a fixed 
position in space during the measurements, which in some 
instances may be found of advantage. 
IV. Method of Constant Inclination. — In this case the coil 
is fixed at a given inclination, and sec <£ enters the constant; 
thus the formula is reduced to that of the ordinary tangent- 
galvanometer, 
^ = tan ax const. 
As compared with other galvanometers proposed for a similar 
purpose, the one here described otters the great advantage 
that the magnetic needle has not to be shifted from one 
measurement to another, whereby the magnetic field may 
sometimes considerably alter; furthermore it does not depend 
