On the Belgian Whetstones. By Rev. A. Rénard. 273 
may be perceived to be bounded by regular lines, and one may dis- 
cover their lozenge-shaped faces, which are to be referred to the 
rhombo= dodecahedron. The dimensions of these crystals are ordi- 
narily so minute that they are not attacked in the polishing 
process, and thus they are preserved to us in the integrity of their 
form. They are therefore, in general, complete on all sides. It 
is difficult to judge of their optical properties, as they are set in 
a double refractive substance ; but by observing those of larger 
size that protrude on both sides of the micaceous lamin, or those 
isolated at the extremities of the thin sections where the thickness 
is least, they may be seen to be dark between the Nicols’ crossed 
risms. 
i Their perfect isotropism and their crystalline form place them 
amongst the minerals of the first crystallographic system. Seen by 
transmitted light they appear completely devoid of colour, bordered 
by zones of deep black, which diminish in intensity toward the 
centre of the crystal, where the colourless part sparkles with ex- 
ceeding briliancy. I have found these crystals in great numbers 
in all the various kinds of whetstones of the Salm formation. At 
one time they are gathered together at one point, at another they 
form lines or chaplets, and again they are isolated. 
With this ensemble of characteristics one may ask to what 
mineral species we are to refer these globular-formed crystals. 
However strange the conclusion may appear, I refer them to the 
garnet. In support of this I may show that the interpretation 
making it a garnetiferous rock is in no way opposed to any of the 
details of the micrographic description I have given, that it explains 
naturally all the facts that I have mentioned as well as the physical 
properties of the whetstone of Salm. 
The rhombo = dodecahedral forms, or globular crystals, which, 
however, now and then present a rhombic face, point out a mineral 
of the first system. The single refraction on which I before 
insisted now comes to support my interpretation. The high index 
of refraction of the garnet (4 = 1°772) shows itself by the unusual 
brilliancy displayed by the crystals when observed by trans- 
parency. * 
The high specific gravity of the rock (= 3°223) is also 
explained by the density of the garnet, which forms a great part of 
it. The specific gravity of garnet, as is known, reaches to 3°4 and 
even 4°3. Hitherto it has been frequently asked what the sub- 
stance could be that enabled these whetstones to wear even steel, 
and it was the supposition up to the present time that the element 
* To explain this fact, it is to be remembered that luminous rays penetrating 
a refracting body by a point, and forming at the point of incidence a hemispheric 
pencil, form in refraction a cone whose angle at summit is given by the equation 
sin. 7 =—- This angle diminishes in proportion as n increases. 
n 
