424 
Japan fully four years ago, but most uf the copies 
of it were destroyed in a fire, and reprinting has 
been delayed through the author’s absence and 
pressure of other work. It is now available to 
students of archeology in this country, and they 
will find much in it which affords an opportunity 
for the comparative study of archeology in Japan 
and other countries in the East and the West. 
It is interesting to note that there are now a 
considerable number of Japanese workers in the 
field of archeology, and to them Dr. Munro gives 
thanks for assistance in his work. The Imperial 
University of Tokyo and the Imperial Museum 
have now very interesting collections, and many 
valuable papers on anthropology appear in the 
Tokyo Anthropological Magazine, the Archaeo- 
logical World, and in the Transactions of the 
Asiatic Society of Japan. Dr. Munro has taken 
full advantage of these, but his book is no mere 
compilation, but owes a great deal to his own 
investigations. It treats of the Paleolithic phase, 
the Neolithic sites, habitations, implements and 
utensils, weapons, ceramic art, diet, dress, and 
social relations, in each of which a great deal of 
interesting information is given. The earliest 
forms of religion in Japan are discussed, and 
many suggestions occur to students of compara- 
tive religion. 
The concluding chapter deals with the pre- 
historic races, and shows that these, as certain 
remains testify, formerly possessed the west and 
the south, but were compelled to retreat by the 
pressure of the alien Yamato, and they are now 
represented by the Ainu, the sole survivors of the 
primitive inhabitants. The Japanese people, 
according to Dr. Munro, are a mixture of several 
distinct stocks. | Negrito, Mongolian, Palasiatic, 
and Caucasian features more or less blended, 
sometimes nearly isolated, are met with every- 
where. The book may be regarded as a cultural 
history of the Ainu and of their conquerors, and 
it forms a very valuable supplement to the many 
popular books about Japan which have appeared 
in recent years. 
LETTERS TO THE EDITOR. 
[The Editor does not hold himself responsible for 
opinions expressed by his correspondents. Neither 
can he undertake to return, or to correspond with 
the writers of, rejected manuscripts intended for 
this or any other part of Nature. No notice is 
taken of anonymous communications.] 
Forced Vibrations. 
WHEN a system capable of natural vibrations is 
acted upon by forcing influences, it is usually sup- 
posed that the amplitudes of forced vibration will be 
greatest when the forcing influences are in tune with 
the natural vibrations. If there is no damping or 
corresponding loss of energy this is correct, but when 
there is such loss of energy it is incorrect. 
I do not know if this has been talken into account 
in spectrum analysis, or with what care measurements 
have been made in comparing the bright lines of a 
gas with the dark absorption lines of the same gas. 
In wireless telegraphy the tuning of the antennz 
ought to be readjusted when the sender becomes the 
receiver. 
NO. 2226, VoL. 89] 
NATURE 
[JUNE 27, 1912 
Simplest mechanical example. A body of mass M 
vibrates at the end of a spring of yieldingness h; 
there is a force of friction b times the velocity. 
Two methods of forcing vibration may be taken. 
The other end of the spring may have a varying - 
displacement y from its mean position; or y being 
0, the body may be acted on by a varying force F, 
Let y be y, sin qt, or let F be F, sin qt. The equation 
of motion is, using the letter @ for d/dt and x for the 
displacement of the body, 
24 66+ = or F 
M621 +602 aes ra E. 
Using 2f for b/M and n* for 1/hM, we have 
Ox + 2/01 4+ 2-x% =77 yp sin gt or pa sin g/. 
The frequency of the natural vibration is q!/27, 
where 
The forced motion is 
fisis Fo \ 
(7 Vy OY ew) gt 
oa 
6+ 2f8+n? 
Using qi or q\ —1 for @, we see that the amplitude is 
greatest when (n*—q’)?+4f?q* is least, or 
SEE ool oogio clols'c (2) 
The second case is the electrical analogue of the 
mechanical one. If L is the inductance, R the re- 
sistance of a circuit closed on itself in which there 
is a condenser of capacity K; if v is the voltage 
across the condenser and c is the current, and if there 
is a varying E.M.F. e in the circuit. 
c= — Kév=(v —e)/(R+L86), so that 
(R+L6)K6+1;v=e. Using 2/ffor K and 2 for <a 
(67+ 2f/0+n"*)v=e/KL. 
Making e=o, the frequency of the natural vibration 
is q'/27, where 
Ql n/ia felon «een nee (3) 
If e=e, sin qt, the amplitude of v in the forced case 
is greatest when 
flO So OG gi Oeo-0 oc (4) 
Working out the equation for c we find that the ampli- 
tude of c is greatest when 
(SP 55500065 50 - (5) 
If instead of being closed upon itself this part of a 
circuit containing R, L, and K has the voltage v 
established between its ends, and if v=v, sin qt, the 
current amplitude is greatest when 
(0[= 10. a0 OO Oe Bro OO < (6) 
Let us take another case. Between a point A and 
a point B we have a coil of resistance R and 
inductance L, and there is a condenser K parallel 
with the coil. A current C proportional to sin qt 
enters the system at A and leaves at B, dividing into 
the two parts c, through the coil, and c, through 
the condenser. We have C/c,=KL(6?+2f0+n7?). 
This is a minimum when 
Q = Nis Bago wt» o) eee (7) 
A more complex condition makes C/c, a minimum. 
If we regard c,—c, as a circulating current, it may 
be important to make C/(c,—c.), or (c,+c.)/(c,—¢,), @ 
minimum, and for this we find 
RH py. 1515) 0) CAMEO. oO. c (8) 
Other simple interesting examples may be given. In 
every one of these we look for a critical value of q; 
