504 NATURE 
[JuLy 18, 1912 
” 
ness of packing of the nodes or “points” of the 
space-lattice or point-system) along the planes of 
the principal faces. 
of equal symmetric value) of greatest reticular 
density are those of most fundamental importance 
to both the internal structure and the correct set- 
ting, and those which, given ideal conditions of 
development and equal chances of growth all round, 
grow most slowly and are consequently the best 
developed, a fact proved conclusively by Wulff. 
The setting, therefore, which corresponds to 
primary faces of maximum reticular density is 
regarded by Prof. von Fedorow as the only correct 
one on which comparisons should be made. 
He has next prepared with consummate trouble 
a table of the elements and morphological con- 
stants of all the hitherto goniometrically measured 
crystalline substances, arranged in regular pro- 
gressive order, and calculated on the lines just 
explained for the correct setting in each case. It 
will doubtless be with some astonishment that 
chemists will learn that no fewer than ten thousand 
erystalline substances of definite chemical constitu- 
tion have been measured adequately enough to be 
included in this table. Prof. von Fedorow then 
proceeds to show that if a few measurable crystals 
of any one of these substances be subjected, by 
an observer trained in his method and to whom 
the name or formula of the substance is not given, 
to a short goniometrical investigation on the theo- 
dolite goniometer, occupying at most two or 
three hours and possibly only a few minutes, it 
is possible by a reference to the table of elements 
and constants to discover and recognise immedi- 
ately the substance of which the crystal is com- 
posed. In other words, provided a chemical sub- 
stance has once had its crystals measured by a 
trained crystallographer, it is possible to detect 
it at any time by merely making a few brief 
measurements so as to be able to calculate the 
elements—by a shortened process, partly graphical, 
which Prof. von Fedorow has perfected—and then 
searching the table for the substance there re- 
corded as possessing these constants. The con- 
stants being arranged progressively in the table, 
and according to their systems of symmetry, the 
search occupies but a moment of time, the table 
being practically an index. 
In order to test this new mode of chemical 
analysis, which has the great advantage that the 
substance is not destroyed or even injured in the 
process, the crystals remaining as perfect at its 
conclusion as they were before it was undertaken, 
Prof. von Fedorow invited the cooperation of a 
number of co-workers in crystallography in various 
countries of Europe and the United States, and 
the gratifying result has been that a considerable 
number of well-crystallised substances, which had 
been the subject of careful investigations, were 
sent to him in bottles marked with only a distin- 
guishing number and no name or formula label. 
In all cases—except a very few in which the 
erystals had either deteriorated, or where the 
substances were not included in the ten thousand 
recorded in the table (owing mostly to too recent 
NO. 2229, VoL. 89| 
For the forms (sets of faces | 
publication of the results concerning them), or in 
which they were indistinguishable from an iso- 
morphous substance owing to the faces not being 
sufficiently perfect to enable the measurements to 
be trustworthy to within a few minutes of arc— 
Prof. von Fedorow has identified them with the 
greatest facility. 
Among these test substances were a number 
which had been sent out by the writer, and 
had been for the first time investigated by him, 
and in every one of these cases the substance (often 
an organic compound of some complexity) was 
identified by Prof. von Fedorow without hesitation. 
Several of these cases are described at length by 
Prof. von Fedorow in his’ memoir, and it is 
interesting that in nearly all of them, and also in 
some of the sulphates and double sulphates in- 
vestigated by the writer and also examined as un- 
known substances by Prof. von Fedorow, faces not 
actually observed during the latter’s brief examina- 
tion for the purposes of identification, but found 
by him, on calculation, to be important faces with 
respect to the ideal development and setting, had 
been observed by the writer in his detailed in- 
vestigation some years ago. Some of the crystals 
sent by the writer had, in fact, been measured 
no fewer than twenty-two years ago. They were 
dispatchéd, unlabelled except by numbers, with 
the aid of Mr. T. V. Barker, of Oxford, who had 
spent some months with Prof. von Fedorow in 
his laboratory at St. Petersburg, and had kindly 
undertaken to collect and send out the contribu- 
tion of British crystallographers and chemists to 
this interesting test. 
Even at so early a date in the development of 
this surprising method of crystallochemical 
analysis, Prof. von Fedorow undertakes that at 
least three out of every four analyses shall be suc- 
cessful, and when the table is further extended this 
proportion will be materially raised. Moreover, if 
an analysis is not successful, it is usually because no 
result can be arrived at, owing to malformation of 
the crystals; in no case is an inaccurate result 
obtained, except, perhaps, in the few cases of iso- 
morphous compounds so closely equiangular that 
the degree of perfection of faces present is possibly 
inadequate to enable the observer to distinguish 
between them. But in these cases an optical deter- 
mination of refractive index would amply suffice 
to effect the distinction. Also, of course, the 
method fails in its simple form in the cases of cubic 
crystals, in which the angles are always the same; 
but again an optical test is successful where that 
of symmetry, elements, and angles fails. 
Sufficient will have been said to show that we 
have in this new mode of chemical analysis a most 
striking testimony to the value of crystallography 
to the chemist, and a further imperative reason why 
the crystals of every well-crystallised substance 
should not fail to be measured. It forms another 
stage in the development and the rapid march of 
this now highly important science. If any readers 
of Nature should be further interested in the sub- 
ject, they will find a remarkably correct account of 
it in English, written eighteen months ago from 
———EEE 
