1819.] Haviy on the Measuring of the Angles of Crystals, 425 
out, the inclination in question would be 126°52’12”. Hence I 
conclude that this angle is the angle of nature; and the theory 
gives me the value of this small difference of 7’ 48”, which the 
instrument cannot determine. 
When the celebrated Coulomb made his fine experiments, by 
means of which he demonstrated that the electric and magnetic 
forces followed the law of the inverse of the square of the dist- 
ances, the numerical expressions of these forces, deduced from 
the mechanical means which he employed to measure them, 
never represented rigorously the law to which he supposed 
that these forces were subjected; but they approached it so 
nearly that he was authorized to consider the differences as una- 
voidable errors in his experiments. Thus in an experiment 
relative to magnetism, in which the measure of the forces 
depended on the square of the number of oscillations which a 
magnetic needle freely suspended, made in 60”, and placed suc- 
cessively at two different distances from the centre of a magnet, 
the one of which was double of the other, he observed that the 
corresponding number of oscillations were in the one 41, and in 
the other 24 and a fraction. But that the squares of these 
numbers, deducing the square of 15, which represented the 
action of the globe on the needle, should be to each other in the 
inverse ratio of the squares of the distance, it was necessary to 
suppose that the needle in its second position made 24 oscilla- 
tions + 22, very nearly. Thus calculation gave the exact value 
of a correction, which observation left undetermined. Such is 
in general the method of proceeding of the physical sciences ; 
and we have the more reason for considering our experiments as 
decisive, when they give only slight differences with the results 
of our theories. It would be rather surprising if they agreed 
with them precisely. 
In the species whose primitive forms differ more or less from 
those which I have mentioned, and which may be regarded as 
the limits of all the others, the ratios between the lines, which 
enter as data in the solution of the problems, can only be deter- 
mined by observation. But I conceived that these forms were 
assimilated to their limits, as the reports in question ought like- 
wise to be simple, or at least to approach simplicity. 
The method which I have adopted to obtain these ratios 
under the most advantageous form consists in representing under 
radical quantities the two terms which compose them. The 
result is, that among the primitive forms which belong to the 
different species, those which are susceptible of being cut in a 
certain direction, so that the section is a rhomb, possess a 
remarkable property, which belongs likewise to those solids 
which have the characters of limits; namely, that the cosine of 
the small angle of the rhomb is a rational number. Different 
rhomboidal prisms, the section of which is an oblique parallelo- 
gram, in which the sides are only equal two to two, possess the 
