\ 
6 

and the fact that the contents of each pollen grain have to pass 
through the coats, both of the pollen tube and of the embryonic 
sack.” (I extract these latter addenda from Mr. Darwin’s letter.) 
I do not much complain of having been sent on a false quest 
by ambiguous language, for I know how conscientious Mr. Dar- 
win is in all he writes, how difficult it is to put thoughts into 
accurate speech, and, again, how words have conveyed false im- 
pressions on the simplest matters from the earliest times. Nay, 
even in that idyllic scene which Mr. Darwin has sketched of the 
first invention of language, awkward blunders must of necessity 
have often occurred. I refer to the passage in which he supposes 
some unusually wise, ape-like animal to have first thought of 
imitating the growl of a beast of prey so as to indicate to his 
fellow monkeys the nature of expected danger. For my part, I 
feel as if I had just been assisting at such a scene. As if, having 
heard my trusted leader utter a cry, not particularly well articu- 
lated, but to my ears more like that of a hyena than any other 
animal, and seeing none of my companions stir a step, I had, 
like a loyal member of the flock, dasheddown a path of which I 
had happily caught sight, into the plain below, followed by the 
approving nods and kindly grunts of my wise and most-respected 
chief. And I now feel, after returning from my hard expedition, 
full of information that the suspected danger was a mistake, for 
there was no sign of a hyena anywhere in the neighbourhood. I 
am given to understand for the first time that my leader’s cry had 
no reference to a hyena down in the plain, but to a leopard some- 
where up in the trees ; his throat had been a little out of order 
—that was all. Well, my labour has not been in vain ; it is 
something to have established the fact that there are no hyenas 
in the plain, and I think I see my way to a good position for a 
look out for leopards among the branches of the trees. In the 
meantime, Vive Pangenesis. FRANCIS GALTON 
The Hylobates Ape and Mankind 
THE readers of Mr. Mivart’s communication in NATURE for 
April 20, on the affinity of the Hylobates genus of ape to the 
human species, may be interested to learn that the fact was well 
known to the author of the Ramayana, the earliest Sanscrit epic, 
probably contemporaneous with the Iliad. In this poem the 
demigod Rama subdues the demon Ravana, and regains his 
ravished bride Sita by the assistance of a host of apes, which may 
be identified with Ay/obates Hoolook. The human characteristics 
of these semi-apes, their gentleness, affection, good humour, sa- 
gacity, self-importance, impressionability, and proneness to 
melancholy, are portrayed with the most vivid strokes, and evi- 
dently from careful observation. See Miss Frederika Richard- 
son’s charming volume, ‘‘ The Iliad of the East,” a selection of 
legends drawn from the Ramayana. (Macmillan and Co., 1870.) 
April 27 R. G. 
Tables of Prime Numbers 
WHEN a number is given, and it is required, without the aid 
of tables, to find its factors, there is not, I believe, any other 
method known except the simple but laborious one of dividing it 
by every odd number until one is found that measures it, and if 
the number should be prime, this can only be proved by show- 
ing that it is not divisible by any odd number less than its square 
root. Thus to prove that 6966007 is prime, it would be neces- 
sary to divide it by every odd number less than 2639, and even if a 
table of primes less than 2639 were at hand, about 380 divisions 
would be requisite. 
On the other hand, there are few tables which are more easily 
constructed than tables of divisors, and it is the extreme facility 
of asystematic tabulation compared to the labour of isolated 
determinations, which has led to the construction of such elaborate 
tables on the subject as have been produced. 
The principal tables are Chernac’s, which give the factors of 
numbers from unity to a million; Burckhardt’s, which extend as 
far as three millions, and Dase’s, which form a continuation of 
Burckhardt’s, and extend to ten millions. 
The mode of formation of these tables was extremely simple. 
By successiveadditions, the multiples of 3, 5, 7, 11, 13,17 . + . 
were formed up to the limit to which the table was intended to ex- 
tend; this gave all the numbers having these numbers for 
factors, and the primes were recognised from the fact of their not 
occurring as multiples of another prime less than themselves. 
Practically the work was rendered even simpler by mechanical 
means; thus, forms were printed containing, say, a thousand 
NATURE 

[May 4, 1871 

squares, and in these were written consecutive thousands of odd 
numbers in order ; one number in each square, room being left 
for its divisors, if any, in the square. A pair of compasses was 
then taken and opened a distance corresponding to the prime 
whose multiples were to be obtained ; for example, in marking 
the multiples of seven, the compasses were opened the width of 
seven squares, and then ‘‘ stepped ” along the lines starting from 
7, thereby marking the numbers 7, 21,35 . - . and the number 
7 was written in each of thesquares in whicha leg of the com- 
passes fell, When the factor was large it was more convenient 
to form a separate table of its multiples, and enter it in the 
square corresponding to the latter Many simplifications were 
introduced in the details of the construction ; for instance, Burck- 
hardt hada copper plate engraved with 77 (=7 x11) squares 
one way and So the other; by this arrangement the multiples 
7 and 11, which were of the most frequent occurrence (for all 
multiples of 2, 3, and 5 were rejected from the tables), occupied 
the same place on each sheet, and he was thus enabled to en- 
grave the numbers 7 and 11 on the plate, so that these numbers 
were frinfed in all the squares containing the numbers they 
measured. 
Dase, who originally applied himself to the construction of the 
tables at the suggestion of Gauss, left behind him in manuscript 
at the time of his death, in 1862, the seventh and part of the 
eighth million complete, besides a considerable portion of the 
ninth and tenth millions. The seventh, eighth, and ninth mil- 
lions were completed by Dr. Rosenberg, and published by a 
committee at Hamburgh. In the preface to the ninth million 
(1865), which is the last I have seen, it is stated that the tenth 
million, which was nearly ready, was the last the committee 
intended to publish. 
My object in writing this letter is not only to call attention to 
a most valuable series of tables, which seem to have scarcely 
excited so much interest as they deserve, but also to ask if any 
of your readers can inform me if the work is being continued, 
or if there is any chance of its continuation. It is not often that 
tables are so indispensable as in the present case, or that a want 
so pressing can be supplied with such comparative ease ; and the 
cessation of the tables would be a real calamity. The tenth 
million has, I presume, been published. 
At the British Association Meeting at Dundee in 1867, a list 
of 5,500 large prime numbers was communicated to Section A 
by Mr. Barrett Davis. A short discussion took place on the 
“reading” of the paper, in the course of which it was stated 
that Mr. Davis’s table was unaccompanied by any explanation of 
how the numbers had been obtained, or on what grounds they 
were asserted to be prime ; it was also asserted that Mr. Davis 
wished to keep his method secret. 
Perhaps some reader of NATURE can say whether Mr. Davis’s 
numbers have been printed. If they exceed Dase’s limit, their 
publication (if they have not yet been published) is very desi- 
rable; and even supposing they are given in Dase’s tables, it 
would be valuable to know how far the latter have been verified 
by them. ‘The statement about Mr. Davis’s method being secret 
was probably founded on some mistake, and no doubt Mr. Davis 
would not object to explain it. J. W. L. GLAIsHER 
Trinity College, Cambridge, April 29 
Units of Force and Energy 
THE best root for the name of a unit of force is d¥vauis. There 
is, therefore, no ground for Mr. Muir’s complaint (NATURE, vol. 
iil. p. 426), and I now venture to propose that the name dyze be 
given to that force which, acting on a gramme for a second, 
generates a velocity of a metre per second. A thousand dynes 
to make one 4z/odyne, and a million dynes one megadyne. 
Borrowing a hint from Mr. Muir, I would point out that the 
kilodyne may also be defined as the force which, acting on a 
kilogramme for a second, generates the velocity of a metre per 
second, or, as the force which, acting on a gramme for a second, 
generates a velocity of a £z/cmetre per second. 
The Aint, or pound-fcot-second unit of force, is about 138} 
dynes. Very roughly expressed in terrestrial gravitation mea- 
sure, the kinit is the gravitating force of half an ounce, the dyne 
of about 14 grains, the kilodyne of about } of a pound, and the 
megadyne of 2 cwt., the approximation being much closer in this 
last case than in the others, so that within one part in 400 we 
haye 10 megadynes = the force of terrestrial gravity on a ton. 
I have often felt the want of a name for an absolute unit ot 
energy, or, what amounts to the sam¢ thing, an absolute unit of 
