| of a rigid body 35 
the cross-bar. The optical system consists of a lens fixed to the 
arm near the pivot and of a fine vertical wire attached to the 
other end of the arm and adjusted to be in the focal plane of 
' the lens, 
| The spherical pivot is a phosphor-bronze ball attached to the 
base by a fitting which allows the distance between the ball 
and the scale to be adjusted. The ball enters a conical hole turned 
out of a block of brass attached to the arm. ‘This arrangement 
destroys three out of the six degrees of freedom of the arm relative 
tothe base. The other end of the arm carries two brass feet which 
rest upon the cross-bar and thus destroy two degrees of freedom. 
The remaining degree of freedom allows the arm to turn about an 
_ axis through the centre of the ball and perpendicular to the plane 
of the surface of the cross-bar. This design has the advantage 
_ that it is impossible to strain the instrument by lifting it by the 
_movable arm, for the arm at once comes away from the base. 
The scale on the cross-bar is divided into millimetres, and the 
ball is adjusted so that its centre is 40 cm. from the edge of the 
scale. The readings are taken by means of a fine wire passing 
_ across an opening in the arm and stretched by a spring; the wire 
is easily replaced if broken. The scale is engine-divided on white 
metal and is provided with an anti-parallax mirror. For small 
angles, one centimetre along tine scale corresponds to #4) radian; 
b y the scale can be read to ;4, cm., the angle can be read to 
zoo Yadian, or to about -, degree. 
ime The lens attached to the movable arm is achromatic and has 
a focal length of 35 cm. The vertical wire is held in an adjust- 
able frame attached to the arm and is kept tight by a spring, and 
_ this frame is adjusted so that the wire is in the focal plane of the 
lens. The image of a distant point will then fall upon the wire, if 
the arm be properly directed. Ifa plane mirror be placed so that 
_ the lens lies between it and the wire, the image of the wire formed 
by two refractions through the lens and one reflection at the mirror 
may be made to coincide with the wire itself. 
When the goniometer is used in mechanical experiments to 
determine the angle turned through by a body about a vertical 
axis, a plane mirror is attached to the body and the image of the 
_ goniometer wire is made to coincide with the wire itself. If this 
coincidence is restored after the body has turned, the angle turned 
through by the body is equal to that turned through by the 
goniometer arm. To facilitate the adjustment, the short scale 
which is provided with the instrument is fitted into the frame 
holding the wire, the divided face of the scale being turned towards 
| the lens. On looking at the wire in the direction of the lens, 
| an inverted image of the scale (formed by the lens and the 
| plane mirror) will be seen crossing the wire. In this use of the 
| 
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