842 
NATURE 
~ [June 23, 1923 

however, as it does to Dr. Kammerer, the most likely 
explanation; and as the male is frequently smaller 
than the female, this may lead to a deeper embedding 
of his hand in her flank and a larger area of contact, 
and thus to an extension of the callosities. 
Since the pad only appears on males in the third 
generation after they have begun to pair in water, 
and then in the same place as it appears in Pelodytes 
and Bombinator, to suggest that it is not a functional 
adaptation but a chance mutation throws a singular 
light on what I may term the constitution of the 
Mendelian mind. 
Turning now to Mr. Cunningham’s letter in NaTuRE 
of May 26, I find that he criticises Dr. Kammerer’s 
experiments on Salamander and Ciona. Taking his 
remarks on Salamander first, he has misunderstood 
Dr. Kammerer’s reference to the ovary of the Sala- 
mander as being enclosed in a membrane, while that 
of the bird is not. It really does not assist in the 
controversy for Mr. Cunningham to accuse Dr. 
Kammerer of childish mistakes which would disgrace 
a first-year student in biology. Translating Dr. 
Kammerer’s statement into modern technical lan- 
guage, it reads thus: ‘‘ The ovary of the Salamander 
is completely invested by peritoneum and suspended 
to the back by a mesentery ”’ (a fact which I have 
verified), ‘‘ whereas the ovary ofa bird is covered only 
on its ventral surface by peritoneum and is largely 
retroperitoneal, and therefore more difficult to remove 
in its entirety.” 
Next, Mr. Cunningham refers to Dr. Kammerer’s 
Mendelian experiments with naturally and artificially 
striped Salamanders and the “ forma typica.’”’ It is 
indeed disquieting to find so sound a Lamarckian as 
Mr. Cunningham so much under the influence of 
what I may term Mendelian dogmatism as to suggest 
that because the artificially-striped Salamander does 
not ‘‘ Mendelise’’ when crossed with “ typica,”’ 
therefore the character is not gametic or hereditary ! 
Truly a vicious circle of thought: the test as to 
whether a character is hereditary or not is surely 
whether or not it can be transmitted to the offspring. 
I agree with Mr. Cunningham that Dr. Kammerer’s 
results in Mendelising and in ovarian transplantation 
are extremely unexpected, and I may add that Dr. 
Kammerer himself did not expect them, and frankly 
admits that he has been unable to frame an explana- 
tion for them which is satisfactory to himself. I will 
not waste space by attempting to suggest an explana- 
tion, but I will refer Mr. Cunningham to Dr. Kam- 
merer’s long paper, where full details are given. I 
think he will find that the results are such that it 
would be difficult for mistakes to be made, and 
therefore, unless Dr. Kammerer is to be charged with 
deliberate bad faith, they must be accepted. 
Dr. Kammerer regarded his experiments on Ciona 
as affording the clearest proofs of the inheritance of 
acquired characters. He showed photographs of his 
results. Mr. Cunningham objects that no photo- 
graphs of the controls, z.e. of ordinary adult specimens 
of Ciona, were shown, in spite of the fact that Dr. 
Kammerer stated at the meeting that the experi- 
ment had been conducted on roo specimens, and 
that, of course, controls had been made—that, indeed, 
the establishment of controls was the A B C of experi- 
mental science. I think that Mr. Cunningham, on 
reflection, will see that by this attitude he is joining 
the ranks of those who seek to escape from the 
inevitable deductions to be drawn from Dr. Kam- 
merer’s results by accusing him of deception, and 
this is an attitude with which none of us who had the 
pleasure of meeting Dr. Kammerer and seeing his 
specimens and discussing matters with him would 
have any sympathy. E. W. MacBriveE. 
NO. 2799, VOL. IIT] 


Law governing the Connexion between the Number 
of Particles and their Diameters in grinding 
Crushed Sand. 
THE discovery of a simple law relating to continuity 
of particle size in fine grinding (or the breaking up 
larger into smaller particles) has long been a matter 
of scientific and technical importance. By means of 
experiments extending over some years, the British 
Portland Cement Research Association has definitely _ 
ascertained that, so far as a crystalline substance 
such as “‘standard sand”’ is concerned, a definite law 
does undoubtedly exist, which may be defined 
mathematically as follows : 
In a given weight of W of finely crushed sand, if 
N be the number of particles of diameter x and if N 
and % be considered as variables, then in every case 
so far tested 
N= aes Sha . sh CE) 
where a and b are two constants characteristic of the 
particular sample tested. 
Differentiating (1) we obtain: r 
ae b.ae**= —-b.N. 
ag eae = ee Pepe t 62) 
In other words, the vate of increase with decrease of 
diameter, of the number of particles present of any given 
size is proportional to the number of particles of that 
size. 
It is therefore possible to calculate the number of 
particles of any given diameter without going through ~ 
the laborious process of sieving. 
Another result of this law is that it now becomes 
possible to calculate exactly the theoretical amount 
of work required to produce powders of different 
degrees of fineness, and in that way do for the art 
of grinding what has long since been done for steam 
and electricity, namely, reduce grinding to an exact 
mechanical science. In other words, just as the 
engineer knows the amount of electrical energy or 
steam necessary to perform a given amount of work 
under definite conditions, so also he will in future be 
able to estimate the amount of work required to 
reduce a given material to a given degree of fineness 
under given conditions. It will thus be possible 
to deduce the efficiency of any grinding machine. ~ 
These and other matters will be gone into in a paper 
now in preparation, in which the experimental details 
will be fully described. 
The physical significance of this law is simple. © 
Consider a set of sand particles A (Fig. 1), By 
grinding, each of the particles A gives rise to the same 
number & (in our illustration k =2) of smaller particles 
B, each of which in its turn gives rise to the same 
number # of still smaller particles C, and so on all 
down the scale so fay as we can pursue the matter by 
means of the microscope, with the ultimate production 
of colloidal particles. 
The law is probably the expression of the fact that 
crystals have a definite and fixed structure, and conse- 
quently break up when subjected to percussion or 
pressure in a regular and definite manner, which 
follows a definite mathematical law when the number 
of particles considered are sufficiently numerous to 
allow of the application of the law of probability. 
The subject is of great scientific interest. For 
example, there is an obvious thermodynamical con- 
nexion between the work done in grinding (i.e. 
producing small particles from large ones) and the 
amount of heat required theoretically to gasify the 
material. For—considering the simplest possible 
case—in gasifying a homogeneous solid material 
(without passing through the intermediate liquid 
. 

