[Reprinted from American Chemical Journal, Vol. XIII, No. 8.] 
SOLID FORMULAE; MODELS FOR USE IN 
TEACHING ORGANIC CHEMISTRY. 
By Arnold Eiloart. 
In lecturing on stereochemistry I have found models similar to 
those here described very helpful, and believe that they will prove 
useful also in general lectures on organic chemistry, elementary 
as well as advanced. These models do not pretend to represent 
any new conception as to the space-relations of atoms, but merely 
conveniently to represent established conceptions; further, they 
are not intended to supersede existing models, but to supplement 
them, for if only one sort of model be used there is danger that 
what is accessory may be considered essential; but when the same 
idea is represented by a variety of models it is seen that the essen- 
tial is common to all, while variation of the accessories makes 
plain their non-essential nature. 
That which is common to all models representing the space- 
relations of radicals attached to a carbon-atom is the prominence 
of four equidistant points; for although different radicals probably 
place themselves at different distances from the central carbon, 
they are for convenience represented as equidistant from it and 
from one another. Thus Van't Hoff used a regular tetrahedron, 
of which the centre and the four corners represented the relative 
positions of a carbon-atom and the radicals attached to it, a carbon- 
atom attached to unlike radicals being represented by a tetrahe- 
dron with the corners of different colors. The essence of the 
present device is the use of letters instead of colors at the corners 2 
of the tetrahedra. As by means of caps fitting over the tetrahe- 
dron corners Van't Hoff could change their colors, so can the 
letter-symbols be changed by exchanging one cap for another. 
In addition, means are provided for supporting the tetrahedra so 
that the caps may be readily changed, for holding the cap on the 
corner it covers, for connecting the tetrahedra by one or by two 
corners, and for easy transition from the single to the double 
connection as well as vice versa. • 
The figures (see Plates) show the arrangements.1 It will 
be seen that when the tetrahedra are joined at one corner only 
the hinged connecting rod remains straight, because it sinks just 
so far into the lower tetrahedron that the hinge is covered. To 
convert the corner-connection (single-bond) into the edge-connec- 
tion (double-bond), a pin is placed in the middle of that edge of 
the lower tetrahedron which is to be joined to the upper one, the 
latter is slightly raised, the little finger of the hand which raises it 
is used to lift the hinged rod till the hinge is free, and now any 
free corner of the upper may be made to touch the proper corner 
of the lower tetrahedron, and the pin will make the connection 
secure. This pin fits into the lower tetrahedron so tightly that it 
remains there when the edges are separated for restoration of the 
single-bond. These manipulations take a few seconds only. To 
test the durability of the arrangement by which the caps are held 
in place, some of them have been put on and off many times, one 
of them 300 times; all those tested work as well as when first 
used. To put a cap on and off takes less than a second. 
The Use of the Models for illustrating General Organic 
Chemistry. 
It is true that.in using the models for this purpose our instruc- 
tions are liable to become permeated with ideas as to the relative 
positions of atoms, ideas which we have not hitherto allowed to 
exert much influence on such teaching. But it is also doubtless 
true that an analogous statement could at one time have been 
made with regard to the introduction of structural formulae. 
These, however, have long since emerged from the study of the 
investigator who, to make plain to himself his own conceptions, 
first used them, and now cover our blackboards. Similarly 
stereochemical models which already find a place on the study- 
1 The upright rods on which the models are supported have been omitted from the plates. 3 
tables of the few, must sooner or later cover our lecture-tables. 
Solid formulae will partially supersede structural formulae, as 
these have partially superseded empirical formulae, and the gam 
in our power of concise and rapid thinking, similar in origin, will 
possibly be comparable in degree. As structural formulae are 
more cumbersome to use than empirical, so are solid more cum- 
bersome than structural formulae; but in each case the more ample 
formula best stenographs our thought. And when a solid formula 
is once arranged it takes no more time to alter it, by exchanging 
one cap for another, than to turn to the blackboard and make the 
alteration in a written formula; in manipulating the models we 
have, too, the advantage of always facing the audience. 
As to the dangers which are incident to the use of all formulae, 
the history of stereochemistry shows that we must especially 
guard against proceeding faster than our knowledge warrants in 
the allotment of formulae; on the other hand, the danger of cramp- 
ing rather than stimulating thought is perhaps less formidable in 
the case of solid than of other formulae. 
It is well, however, in discussing the advantage of using solid 
formulae, to consider particular cases. For instance, the fact that 
it is matter of indifference which hydrogen-atom in methane be 
exchanged for a given radical has been illustrated by means of the 
models of Kekul£ / the solid formulae are equally effective, and 
with them we may illustrate the replacement of hydrogen by any 
given radical, and this without straining the memory to connect 
H, Br, CHs, etc., with the particular color assigned to it. Next, 
the cap marked CHs, which has represented methyl acting as an 
element, may be replaced by a block with three caps marked H; 
with the aid of this double means of representation the conception 
of a compound radical is readily imparted; similarly we may 
H H H 
develop -C2H5 to-C - CH, or to-C-CHs. The deriva- 
H H H 
tion of the series CH4, C^Hs, etc., and of the general formula 
CnHan + a is clearly seen; the tendency to ring-formation and the 
stability of rings of five or six carbon-atoms are explained at 
once.2 Further, we may show the double- and the triple-link- 
ing of carbon-atoms; the diminution in the number of atoms 
bound by carbon-atoms so linked is represented by the impossi- 
1 See, however, Le Bel: Bull. Soc. Chim. [3] 3, 788. 
2 See Plate in the report on Stereochemistry. 4 
bility of covering by caps those of the tetrahedron corners which 
are in contact, and the formulae CnH2n and CnH2n -2 are deduced. 
Some of the facts mentioned might be represented by plane struc- 
tural formulae; but the representation of all the facts in the same 
way strengthens their connection in the mind. 
The Special Use of the Models in Stereochemistry. 
For a general explanation of the isomerism of compounds of the 
type CR'R2R3R4, the models of Kekul€ or those of Van't Hoff 
may be used; it is when we have to deal with particular com- 
pounds (such, for instance, as the lactic acids) that we find the 
use of the models with letter-symbols desirable if not indis- 
pensable. 
We may also not only show the general relations of radicals 
attached to two carbons singly-linked, the effect of the relative 
rotation of these carbons and of the inclination of the axes round 
which the two sets of radicals are ranged, but we may give solid 
formulae to any compound of the type CsR'RsRsR^^R6; we may 
show, side by side, the three solid formulae for tartaric acid, how 
two of these together represent racemic acid, and how this acid is 
necessarily the product of the addition of four hydroxyl groups to 
two molecules of fumaric acid, while it is mesotartaric acid that 
must result from similar treatment of maleic acid. The solid 
formulae of fumaric and maleic acid render Van't Hoff's theory as 
to their isomerism at once clear, and all the transformations 
attributable to their different configuration are traced with ease by 
means of the models. There are, in fact, but few configurations 
known to the stereochemistry of carbon which cannot be thus 
represented. 
An objection to the particular form of model here described is 
yet to be noticed. The configurations of Wunderlich perhaps 
more nearly represent the truth than do those of Van't Hoff, and 
the former, it may be urged, should be taken into account in any 
attempt to extend the use of stereochemical models. Unfor- 
tunately, Wunderlich's configurations would require the use of 
transparent models in order that the formulae of the radicals 
attached to the carbon-atoms might all be visible at once. 
Besides, the models described may be used to illustrate the gen- 
eral nature of the theories of Wunderlich, and they represent 
after all the four points equidistant in space about which Wun- PLATE I. 
Separate parts of model. 2. Methane. 3. Acetic acid. 4. Propionic acid 
PLATE II. 
5. Lactic acids (right and left-handed). 
6. Tartaric acids (right and left-handed), j. Tartaric acid 
inactive. 
8. Fumaric acid. 
PLATE III. 
g. Maleic acid. 5 
derlich's figures for the form of the carbon-atom are described. 
To illustrate further the theories of Wunderlich and Skraup1 two 
large round-bottomed flasks may be used. The necks serve as 
handles, and four equidistant points on the outside of each flask 
are marked with colors or letters. 
Details of Constrzcction. 
The dimensions given need not be followed exactly; but for 
every model the dimensions should be the same, so that the parts 
may be interchangeable. 
The tetrahedra, 13 cm. (5 in.) in the edge, are cut from a long 
triangular prism of white wood 13 cm. in the side. At each corner 
is bored a hole of 0.5 cm. in.) in diameter and 4 cm. (i^ in.) 
deep. Lining this and firmly fitted into it is a brass tube of 0.4 cm. 
in.) internal diameter, projecting only about 0.1 cm. Slight 
variation in the length projecting, in order to correct inequality in 
the length of the edges, is permissible. In the middle of each 
edge is bored a hole 0.5 cm. wide at the mouth and tapering to 
0.3 cm. in.) at 0.3 cm. from the mouth; the hole then continues 
3 cm. (1^ in.) deeper, the diameter of this part being adjusted to 
that of the rod which is to support the block. (A bill-file with 
loaded foot may be used.) In the middle of one face is bored a 
similar hole to fit the rod ; no enlargement at mouth. If many 
connected blocks are to be supported it is well to make in the 
middle of one face a hole large enough to receive the rod of a 
retort-stand having three feet. 
The position of the grooves on the tetrahedron-faces is marked 
by drawing a line along the free edges of a cap pushed home on 
one of the tetrahedron-corners. The groove, which at its widest 
part is about 0.3 cm. across, slopes downwards towards the curve 
so described, where its depth is greatest-not more than 0.08 cm. 
in.) Six blocks suffice for most purposes, but for benzene- 
derivatives more will be necessary. 
The cafts are made of tin-plate about 0.5 mm. in.) thick, and 
measure about 6.3 cm. (2i in.) in the edge; fitted on to a block, 
a cap then comes within about 0.5 cm. Q in.) of the centre of the 
block-edge. The cap is painted black, and on each of its three 
sides the symbol of the element or group for which it stands is 
1 Monatsh. Chem. 13,146. 6 
stencilled in white or gold.1 It is well to have about forty caps, 
six marked H, four Cl, four Br, four I, four OH, two CHs, two 
CaHs, two CsHs, four COOH, and some caps unlettered for mark- 
ing with chalk at will. 
The hinged rods have each limb 3.5 cm. (1^ in.) long, and are 
0.3 cm. in.) thick, so that they slide freely in the brass tubes of 
the corner holes. 
The pins are 2.5 cm. (1 in.) long, 0.5 cm. in.) thick in the 
middle, and taper down to 0.3 cm. at the ends. A pin pushed into 
one of the holes in the edge-centres must sink in a little more than 
half way ; the part left outside the hole will then not fit a similar 
hole too tightly, so that another block may be put on and removed 
without disturbing the pin; that this may be done without allowing 
too much side-play to the blocks joined by the pin, care in adjust- 
ing the dimensions of the pins and holes is necessary. 
The dimensions given are those of the models used by me; for 
a very large lecture-room larger blocks and caps would be neces- 
sary in order that the letters might be written larger; but blocks 
15 cm. (6 in.) and caps 7.5 cm. in the edge would answer every 
purpose. 
The work connected with this paper was done at Cornell 
University. I take this opportunity of expressing my thanks to 
Mr. Lester J. Young, instructor in Architecture, without whose 
valuable aid in word and deed it would have been hardly possible 
to bring the models to their present state. 
New York, October, 1891. 
1 To protect the letters two small knobs of solder are placed on each face, one near each end 
of its free edge. The caps may then be packed one inside another without injury. This 
addition had not been made when the photographs were taken.