From the American Journal of Science and Arts, Second Series, Vol. V. 
ON THE LIMIT OF 
SUBDIVISION BY TRITURATION AND SOLUTION, 
AND THE 
PRINCIPLES ON WHICH THE LIMIT MAY BE JraDEFINITELY EXTENDED. 
BY B. F. JOSLIN, M.D 
Of New York. 
If any coarse and dry substance is triturated by itself, it will 
continue to be permanently divided and subdivided to a certain, 
but limited extent. For beyond that, the blow would either 
leave the parts so near each other, that they would instantly re- 
unite by the power of the cohesive forces and again become one 
solid body, or would drive these newly separated parts against 
others or against each other, and effect their union by bringing 
them within the sphere of cohesion. 
If a flint stone were pulverized in a mortar, it would at length 
become so fine, that some of the finest of these invisible flint 
stones would, after any farther division, be soon reunited. All 
that would be necessary for their reunion and the restoration of 
their previous hardness, would be, to bring the parts or their mu- 
tually attractive poles, as near to each other as they had been be- 
fore their separation; for the strength of their cohesion depends 
on the degree of their proximity. The approximation and union 
of some of these smaller than microscopic pebbles, would be pro- 
moted by the pressure of the pestle : the same blows that severed 
some, would unite others, so that the average size of the parts 
would remain unchanged. 
I have referred to poles, believing that the cohesion of all at- 
oms and of all groups sufficiently small, depends on polarity and 
is a crystallizing force, and probably magnetism itself in its most 
elementary form. But similar principles apply to my theory of 
comminution and similar language may be employed, whether 
we regard the cohesive force as residing on all sides of the groups, 
or only at certain poles. For if a group were surrounded by ma- 2 
On Subdivision by Trituration and Solution. 
ny others within its sphere of cohesion, some of their poles would 
be in a position favorable to union, and others be brought into 
that position by rotation, as would be the case with a multitude 
of small magnets thrown together promiscuously. 
In experiments with the solar microscope, twelve or fifteen 
years since, I saw and exhibited to the Senior class of Union Col- 
lege, thousands of instances of rotation, attraction, and induction, 
in the crystals of camphor formed from the tincture placed on a 
small plate of mica and exposed to solar radiation. When the 
sky was very clear and the radiation intense, the phenomena be- 
came confused by the rapidity of the crystallization, and it was 
necessary to dilute the saturated tincture with about five times its 
bulk of alcohol, in order that these phenomena might be exhibit- 
ed in all their distinctness and beauty. Thin clouds permitted 
, the use or the undiluted tincture, and intermediate states of the 
sky required intermediate degrees of dilution. A description of 
these interestingIphenomena wTas given in the “Report of the 
Regents of the University of the State of New York, for the year 
pp. 207 to 209, and an abstract in this Journal, vol. xxv. 
I here refer to them as evidence of the polarity of minute groups. 
In resuming the consideration of pulverized flint, let us sup- 
pose the powder had attained such an extreme degree of fine- 
ness as can be given to it by a process which I shall describe, and 
let us suppose that it could be separated from other substances 
and subjected in mass to the blows of the pestle; the effect 
would be like that of pounding a quantity of clean leaden shot: we 
should stick them together in large masses. If we had a suffi- 
cient quantity of such a powder confined in a cylinder and press- 
ed by a piston, we could probably unite it all into one flinty rock, 
perhaps defective in hardness at some points, from want of the 
requisite position of the poles. 
I have taken an extreme case, in order to enable the reader 
more easily to conceive of the principle on which the limitation to 
comminution in the ordinary process of pulverization depends. 
The powder of any substance, pounded or rubbed by itself in a 
mortar, would attain a limit of fineness, beyond which its sub- 
division could not be carried by the combined labor of all man- 
kind operating in the same way through all ages. 
A sliding motion of the pestle enables us to go a little farther 
before we reach this limit, not only because it subjects small iso- 
lated masses more directly and efficiently to the dividing force, 
but because it allows fewer opportunities for the reuniting force of 
cohesion to come into play, by keeping the newly divided parts 
at a greater distance from others already divided. But in this 
mode of operating also, the limit will be as surely reached as in 
pounding. For when a certain degree of fineness has been effect- 
ed by this rubbing process, the stratum of powder beneath the On Subdivision by Trituration and Solution. 
3 
pestle will either be so thin as to elude its dividing action, or so 
thick that the number of parts which are pressed against each 
other by its strokes and reunited, will equal the number divided 
by the same strokes. At this stage, the comminution will cease ; 
and the trituration, ever so skillfully conducted, and carried on 
forever, could not reduce the powder to any greater degree of 
fineness. 
Is there any way in which this limitation may be obviated, 
and the fineness of the powder indefinitely increased? Yes: it 
may be done by successive mixtures with some other substance, 
using thorough trituration after adding each portion. This meth- 
od is of universal application; yet for the sake of convenience 
and precision, I shall assume particular substances and a particu- 
lar proportion. Suppose a flint powder to be rendered as fine as 
it is possible to make it by rubbing it per se; and suppose one 
grain of this to be triturated with ninety-nine grains of ordinary 
loaf-sugar, or of the harder—and therefore better—non-medicinal 
substance, sugar of milk. Suppose, by means of stirring with 
a spoon or spatula, the flint powder be intimately mixed with 
the pulverized sugar, so as to be uniformly distributed through it, 
before the trituration is commenced. [This is not requisite in 
practice, but simplifies the investigation.] Then each of the mi- 
croscopic flint stones is surrounded by ninety-nine times its weight 
of sugar, which keeps them at nearly five times their former dis- 
tance from each other, as estimated from centre to centre. What 
is the consequence, if trituration be commenced under these cir- 
cumstances ? A new and far more minute division must result. 
The sugar serves two purposes, viz. first, to divide the flint, 
and secondly, to keep it divided ; it contributes both to effect and 
preserve the division. It serves the first of these purposes in 
more than one way. First, it aids division by mechanical collis- 
ion, when driven against the flint by the pestle. It in this way 
aids the fracture ; as the stroke of one body may often be made 
to break another though harder than itself. Thus a quartz peb- 
ble can be crushed between two large pieces of marble, and a still 
smaller one between two large pieces of sugar of milk. The ad- 
vantage given by magnitude, suggests that the sugar employed 
will be more effectual if selected in a state coarser than that of 
the harder powder which it is employed to comminute. In later 
stages it will necessarily have this advantage. Secondly, the su- 
gar may aid the division by its affinity, its attraction for the flint. 
Thus whilst some of the pieces of hard sugar are acting as ham- 
mers and wedges, and tending to separate an intermediate piece 
of flint into two pieces, other pieces of sugar, situated in the line 
in which the fragments of flint when divided tend to move, may 
by their affinity draw the fragments in the direction in which the 
other pieces of sugar push them, and thus both kinds of force 
conspire to effect their separation. 4 
On Subdivision by Trituration and Solution. 
Having hitherto considered the direct agency, I now proceed 
to the indirect; viz. the promotion of farther division by keeping 
separate the parts already divided. The sugar favors comminu- 
tion by keeping the pieces of flint at a distance from each other, 
and thus preventing that reunion which would be continually 
taking place in the parts of the pure flint powder pressed against 
each other by the pestle. The parts when once divided, are by 
the interposition of the sugar prevented from again coming within 
the sphere of mutual cohesion, until the subdivision has been car- 
ried to a much greater extent than would have been practicable 
in triturating the flint by itself. 
A limit will, however, be ultimately reached, even under these 
circumstances. As the subdivision continues, the mutual dis- 
tance of the pieces of flint diminishes, and some portions are ulti- 
mately brought again within the sphere of cohesion, and made to 
unite by the same strokes of the pestle which divide others. 
When the number united by each stroke equals the number divi- 
ded by the same, the fineness can no longer be increased by con- 
tinuing the friction. 
The only way in which the fineness can be increased, is by 
another mixture. If a grain of this powder is mixed and tritura- 
ted with ninety-nine grains of hard sugar, like that previously 
employed, a still more minute division of the flint is effected ; 
but, for the same reasons as in the preceding case, we ultimately 
reach the limit, beyond which it is impossible to pass without a 
new mixture or dilution. By the continued repetition of opera- 
tions similar to those above described, an inconceivable degree of 
comminution may be effected. 
We may not be able to determine theoretically the number of 
subdivisions which are practicable at each stage. But if subdi- 
vision did not affect the intensity of cohesion, and if the division 
were already carried so far, that the magnitude of each piece was 
so small compared with the magnitude of its sphere of cohesion, 
as to produce no sensible influence in the estimate, then it would 
appear from the theory above given, that the maximum commi- 
nution at each stage would be in the ratio of one hundred to unity. 
So that flint, silex. gold, mercury, or any other substance prepared 
in this way with sugar or saccharum lactis—or some other suit- 
able substance—would, at each succeeding stage of the process, 
be divided into parts, all of which would be one hundred times 
as numerous, and each of which would be the one hundredth 
part as large as the parts in the preceding stage. This increase 
in the number, however, supposes that every grain of the preced- 
ing one hundred is subjected to a similar operation. If, as before 
supposed, only one grain at each stage is taken from the hundred 
and subjected to this operation, then the parts of each trituration 
will be equally numerous, but increase in fineness at each stage On Subdivision by Trituration and Solution. 
5 
in the ratio of one hundred to one; and a grain of the thirtieth 
trituration of gold would contain as many minute pieces as a grain 
of the third trituration. 
But I am convinced that the intensity of some properties of 
substances is greatly increased by comminution. If the sphere of 
cohesion is thus increased, the maximum comminution will fall 
below the above estimate. I believe that in practice the commi- 
nution will fall below it, not only for the above reason, but also 
because the trituration, though continued sufficiently long to 
bring most of the parts to the maximum size, will be discontinued 
before every part is equally reduced. 
Hence microscopic observations are liable to lead to erroneous 
conclusions. Dr. Mayerhofer has seen scores of millions of pieces 
of metal in a single grain of the sugar with which it had been 
triturated to form the third trituration. The number varied with 
different metals. From the considerations which I have above 
stated, as well as from others, I am convinced that the number of 
invisible pieces far exceeded the number of visible ones. Those 
only were seen which had escaped the full effect of the dividing 
forces. The minimum groups in the third trituration are not ob- 
jects of microscopic vision. From the wide range of magnitude 
in the visible pieces, as well as from the appearance, on close in- 
spection, of pieces at first invisible, Dr. M. justly concluded, that 
in the first trituration of precipitated gold, “ the metal is divided 
into particles so small as to be invisible under a glass magnifying 
14,000 times.” He u examined the fourth trituration by a power 
magnifying 90,000 times, and it was evident that the diminution 
of the particles progressively increased; the smallest gold mole- 
cules appeared yellow, and the metallic lustre was not to be mis- 
taken.” The diminution here refers to the visible ones. As the 
conclusions which I have drawn in regard to the facility of re- 
union, the limit of comminution, and the intensity of properties, 
refer to those more numerous groups which are so small as to be 
invisible by the most powerful microscope, it would be impossi- 
ble either to establish or refute them by microscopic observations. 
The above method of trituration has great advantages for 
effecting a minute division of substances. I have shown, that in 
order to triturate a substance to powder of a certain degree of 
fineness, it is necessary to mix it with a sufficient quantity of 
some other substance; and that the requisite quantity of this ad- 
mixture increases with the fineness required. Such a degree of 
fineness can be specified, as would render the labor of comminu- 
ting a single grain impracticable, even if the requisite amount of 
material for the admixture could be obtained. The labor of the 
whole human race operating through all ages since the creation 
of man, could not thoroughly triturate a single grain of one sub- 
stance with a decillion grains of any other substance. Yet the 6 
On Subdivision by Trituration and Solution. 
same degree of fineness as would be effected by such an opera- 
tion may be effected by one man in thirty hours, and with 
scarcely three thousand grains of auxiliary material. If we sup- 
pose him to commence with one grain of the substance to be 
comminuted, and allot one hour to each of the thirty stages, the 
resulting powder would contain a portion of the original grain, in 
a state of fineness equal to that in which the whole grain would 
have existed in a deciilion grains equally well triturated. 
The above theory is original; but this process of trituration is 
not. Most persons who have practiced it, have not considered 
the only direct object of it to be comminution; and if any have, 
they have not explained, on physical principles, the mode in 
which it is effected, nor the limit which we encounter by the 
ordinary process, nor the peculiar advantages of this process in 
avoiding that limit. 
I shall not here state particularly the effect and ultimate object 
of the comminution effected by the above process. In my opin- 
ion it must develop a species of magnetism, and the minutest 
pieces thus obtained must be intensely magnetic. As a branch 
of physical inquiry, this subject has especial interest at the pres- 
ent tune, when the attention of philosophers is becoming more 
and more directed to molecular forces, and the peculiar properties 
of small masses. The recent experiments of Sir G. C. Haughton 
have afforded new evidences of the identity of molecular magnetism 
and cohesion, and new proofs that all bodies are magnetic when 
they are rendered sufficiently small.* What intensity of mag- 
netism may not be expected in bodies as minute as those which 
can be suspended fifty or a hundred miles above the earth’s sur- 
face, in air so rarified as to be incapable of reflecting any sensible 
quantity of solar light! I believe this intensity to be far more 
than sufficient to compensate for the reduction of the quantity of 
ponderable material, and to be adequate to the production of the 
most brilliant aurora borealis. In this case there is probably a 
crystallization, a change from the fluid or aeriform state to that of 
minute solids, whose magnetism ultimately becomes latent after 
aggregation in larger masses. 
I believe it to be a general law of nature, that certain proper- 
ties possessed by small groups of molecules, are marked or ren- 
dered latent by the proximity of a sufficient number of similar 
groups ; and that, conversely, properties or powers are developed 
by the division of substances. 
It would seem that bodies rendered so inconceivably minute 
as they can be by the process of trituration above described, 
must possess a most intense magnetic state, although their cir- 
cumstances are evidently such as to preclude the application of 
* Lond. and Edin. Phil. Jour., for June, 1847. On Subdivision by Trituration and Solution. 
the ordinary tests. As the examination of any known mode of 
testing the power of such preparations would involve physical 
and professional considerations, I shall do nothing more than sub- 
mit the mechanical explanation of the comminuting process to 
the consideration of natural philosophers, trusting that they will 
consider the subject interesting as a branch of physical investi- 
gation. 
Similar principles are applicable to subdivision by solution. 
It is generally believed, that the simple solution of a substance 
effects the minutest division of it which is practicable. In call- 
ing in question the correctness of this notion, [ am aware of the 
strength of the prejudices to be encountered—prejudices both of 
the senses and intellect. For deciding such a point, there is no 
adequate delicacy in human vision nor in the instruments of 
physical research; nor is the human mind so constituted, as to 
be capable of any adequate conception of the minuteness of ulti- 
mate atoms, or of the infinite diversity of magnitude existing 
among infinitesimals. 
The following are the views which I take of solution, and 
which I am desirous of submitting to the consideration of natu- 
ral philosophers. In a saturated aqueous solution of any salt, I 
consider the molecules of the salt as existing in hard solid groups 
or masses of the salt, suspended at equal distances in the water, 
which exceeds the salt in quantity. Each mass of salt consists 
of innumerable particles. It is impossible to make these groups 
smaller, either by the affinity of the water or by any mechanical 
force, as long as the quantity of water remains the same. If 
they were sundered, they would instantly reunite. For, any 
division of the solids into smaller groups would diminish their 
mutual distance, and consequently increase their mutual attrac- 
tion ; whilst the quantity of water which surrounds each mass 
is diminished in quantity, and hence possesses less attractive force 
for resisting the reunion of the solids, than it had when they 
were in larger masses; even then this affinity was but just suffi- 
cient to keep them separate. Therefore any division would be 
followed by instantaneous reunion, both on account of an increase 
in the cohesive forces, and a diminution of affinity. The ultimate 
molecules are not separately invested with the water, but united 
in hard and complex masses, which cannot remain suspended 
within a given mutual distance. 
How can this limitation be obviated, and the size of these 
complex molecules be progressively and indefinitely diminished ? 
This may be effected by successive dilutions. To select the 
same proportion as in trituration, suppose one drop of the satura- 
ted solution to be put into ninety-nine drops of water. This 
water exerts its affinity as an antagonist to the cohesion of the 
solid groups of salt, and effects their dismemberment to a far 8 
On Subdivision by Trituration and Solution. 
greater extent than was practicable in the saturated solution. 
Brisk agitation favors uniform diffusion and rapid dismemberment, 
and more promptly in a vessel but partly filled. But the process 
of disintegration commences instantly, before the diffusion is 
complete. To simplify the investigation, let us suppose the drop 
to be uniformly diffused before any disintegration of the groups 
commences. The groups would be at nearly five times their 
original distance, and each mass or group of salt would be sur- 
rounded by one hundred times as much water as in the saturated 
solution. This state of things could not remain a moment; es- 
pecially if the disruptive power of the affinity of this increased 
quantity of water, were aided by a mechanical succussion, as 
strong as that to which the saturated solution had been subjected. 
For the equilibrium, before existing between cohesion and affin- 
ity, will be disturbed by that increase of the latter which results 
from the increase of the liquid; and the suspended solids will 
each be sundered into numerous smaller solids. But the salt is 
not divided into its smallest particles; nor could it be by the 
most violent succussion. The vibrations caused by jars, tran- 
siently increase the distance of some particles of each group, and 
approximate them to the liquid, and thus give affinity a prepon- 
derance over cohesion. In this way succussion aids division. 
But to carry division by this means beyond a certain point, 
effects no permanent change; as the particles will instantly re- 
unite by the preponderance of cohesion over affinity. 
If a drop of this solution is shaken with ninety-nine drops of 
water, a new subdivision of the molecules takes place, on the 
same principle. By repeating this process, the groups may be 
rendered inconceivably small, and this magnitude progressively 
and indefinitely diminished. I doubt whether those who have 
practised it have understood its immediate object, or the mode in 
which it is attained. 
New York, July 23d, 1847.