CRYSTALLOGRAPHY. J 
ment exact, the measurement, with the best instruments, will give the 
angle within 10’. 
Other goniometers have only the second of the two telescopes just 
alluded to, as is the case in the figure on page 11. This telescope gives 
a fixed position to the eye ; and through it is seen a reflection of some 
distant object, which may be even a chimncy-top. For the measure- 
ment the object, seen reflected in the two planes successively, is 
brought each time into conjunction with the hair cross. Exact adjust- 
ment is absolutely essential, and with an instrument having the two 
telescopes, the first step in a measurement cannot be taken without it. 
_ Only small, well-polished crystals can be accurately measured by the 
reflecting goniometer. If, when using the instrument without tele- 
scopes, the faces do not reflect distinctly a bar of the window, the flame 
of a candle or of a gas-burner, placed at some distance from the crystal, 
may be used by observing the flash from it with the faces in succession 
as the circle isrevolved. A ray of sun-light from a mirror, received on 
the crystal through a small hole, may be employed ina similar way. But 
the results of such measurements will be only approximations. With 
two telescopes and artificial light, and with a cross slit to let the light 
pass in place of the cross hairs of the first of the above-mentioned tele- 
scopes, this light cross will be reflected from the face of a crystal even 
when it is not perfect in polish, and quite good results may be obtained. 
B. Structure.—Structure includes cleavage, a characteristic 
of crystals intimately connected with their forms and nature. 
Jt is the property, which many crystals have, of admitting of 
subdivision indefinitely in certain directions, and affording 
usually even, and frequently polished, surfaces. The direction 
is always parallel with the planes of the axes, or with others 
diagonal to these. 
The ease with which cleavage can be obtained varies greatly 
in different minerals, and in different directions in the same 
mineral. In a few species, like mica, it readily yields lamine 
thinner than paper, and in this case the cleavage is said to be 
eminent. Others, of perfect cleavage, cleave easily, but afford 
thicker plates, and from this stage there are all grades to that 
in which cleavage is barely discernible or difficult. The cleav- 
age surfaces vary in lustre from the most brilliant to those that 
are nearly dull. When cleavage in a mineral is alike in two or 
more directions, that is, is attainable in these directions with 
equal facility and affords surfaces of like lustre and character 
or marking, this is proof that the planes in those directions are 
similar, or have similar relations to like axes. For example, 
equal cleavage in three directions, at right angles to one another, 
shows that the planes of cleavage correspond to the faces of the 
cube ; so equal cleavage in two directions, in a prismatic min- 
eral, shows that the planes in the two directions are those of a 
