428 Haiiy on the Measuring of the Angles of Crystals. [Junx, 
the sign of which would be D ; we shall have for the incidence 
of N on N, 142° 13’ 22”, which differs from the corresponding 
angles of the two preceding dodecahedrons 2° 7’ 4” and 
2°20 32”. 
For the incidence of N on N’ 105° 15’ 14”. Diff. 36’ 34” and 
58’ 16”. 
For that of N on N”, 137° 5’ 56”. Diff. 6° 14’ 30” and 
4° 6’ 28”. 
We see that there remains still a certain latitude for the appre- 
ciable differences of other dodecahedrons approaching still more 
and more to the metastatic; but which can only be regarded as 
hypothetic ; because the law on which they would depend would 
deviate more and more from the simplicity of the ordinary laws, 
15 
a 
than that represented by D, the possibility even of which may 
be questioned. 
I return to the measurements of angles taken by the reflecting 
goniometer. Mr. Phillips acknowledges that this instrument is 
very delicate, and requires great attention in the choice of the 
crystals to be measured. He mentions one which gave him 
successively for the inclination of two of its faces 92° 55’ and 
93° 20’, or even 93° 25’, which makes a difference of 30’. He 
speaks of another kind of difficulty which comes from the inequali- 
ties of reflexion on the different faces. Having undertaken to deter- 
mine the angles of the crystals of oxide of tin, he no doubt had at 
his disposal the most perfect which the county of Commwall could 
furnish; and he has himself furnished the touchstone of his 
results, by indicating the measures, which may be considered as 
given @ priori, or which depend geometrically on each other. 
We have seen that some of the differences which had prevented 
him from being of accord with himself, were equal to those 
which exist between the primitive angles indicated by his gonio- 
meter, and those which correspond with the limits which I have 
adopted, and that there is even one which goes a great deal 
further ; namely, to 26’. 
Without venturing to pretend that the simple ratios on which 
these limits depend are the true ratios of nature, as seems to me 
to have been the conclusion of philosophers of distinguished 
merit, I think at least that the results just stated are insufficient 
to demonstrate the contrary. But I will suppose, if you please, 
that the reflecting goniometer, employed with all the requisite 
skill on crystals possessed of the greatest perfection, gives appre- 
ciable differences from the angles deduced from the ratios of 
which I have spoken, and that these differences may amount to 
half a degree. 
To render the new angles obtained in this way capable of 
being employed in the applications of the theory, we must deduce 
