506 
NATURE 
| March 17, 1870 
history the idea not only of sequence, but of the lapse of how 
long before and how long after, can be mastered. The attempt 
to fathom the geological past with our short historical sounding 
line has up to the present time resulted merely in estimates, 
varying according to the assumed basis in each by thousands of 
centuries, that have been about as valuable in geological theory 
as Archbishop Usher's chronology has been found in Biblical criti- 
cism. The problem is hedged in by innumerable difficulties, 
which cannot be overcome in the present state of science. 
W. Boyp Dawkins 
On the Diffraction Spectrum and Wave Lengths 
Ture letter which I wrote about the diffraction spectrum has 
called forth several inquiries. I have been asked how it is that 
in that spectrum the position of a line depends only on its 
wave-length, and I may take the opportunity of answering these 
questions through your columns. First, however, let me state 
that the numbers given in the table in my letter of February 9 
are copied, including the obvious errors, verbatim: from the trans- 
lation of Mossotti’s memoir in vol. v. of Taylors “Scientific 
Memoirs.” I attach no importance to such analogies. Any 
analogy between these lines and interdependent notes of music 
must, I expect, be entirely accidental. ‘The latest experiments 
made by Mr. Lockyer have shown that the lines given ont by a 
gas vary according to temperature and pressure, and if these be 
caused by vibrations of the particles of the gas, whether atomic 
or molecular, the periods of these vibrations must be dependent 
on the temperature and pressure. A distinct numerical state- 
ment of this interdependence is a great desideratum in this part 
of science with a view of affording the materials for making and 
testing a mechanical theory of that interdependence, ‘These are 
the great problems which demand our attention, as I take it, 
with respect to the fixed lines, and our ability to correlate light 
with other modes of force. 
If a beam of homogeneous light be admitted through a small 
hole into a dark room, and fall on the opposite wall, it will illu- 
mirate only the portion of the wall directly opposite it. But if 
a series of fine parallel wires, or a fine grating be put across the 
hole, there will be seen ranzed in a line perpendicular to the 
grating a series of nearly equal distant spots, or rather streaks 
of light. ‘This is because the wires of the grating shut out those 
waves of light which at these points would destroy the other 
waves. To understand this more clearly, suppose Aa, Bd, &c., 
&e., ta be a number of consecutive and equidistant points in the 
front of a wave coming through a small hole, Aa, &c. These may, 
by the principle of Huyghens, be regarded each as the origin of 
a new wave, together having the same effect as the original 
A 
qr 
PPS ? 
awe 
ee c= 
wave, all starting in the same phase. There is darkness at 
every point on an opposite wall, except directly opposite the 
hole, because of the interference of these elementary waves, 
which destroy one another everywhere except exactly in front. 
This is owing to the shortness of the waves and the number of 
sources. Let P bea point on the wall which we shall suppose 
sufficiently far from the hole in order that the lines PA, Pa, PB, 
Pb, &c., may be regarded as all sensibly parallel. On that 
account also each of these lines exceeds the one next it by the 
same amount. Now, generally, when the waves from A, a, &c. 
arrive at P, the wave from @ will not entirely blot out that from 
A, but a residue will be left, which will be blotted out by other 
similar residues. But there will be certain points along the wall 
at which the waves will blot one another out in a peculiarly 
regular way. We shall suppose P to be one of these points, 
namely, that each of the distances A P, a P, &c., exceeds the 
one next it by exactly some odd multiple of the length of half a 
waye—say in this instance half a wave’s length. Then in this 
ease the disturbance originating at @ will arrive at P exactly half 
a wave’s length in advance of that from A, and the wave from A 
will be exactly blotted out, so to speak, by that from a, simi- 
larly that from B will be exactly blotted out by that from é ; and 
soon. So that if I were to put wires at a, 6, ¢, &c., so as to stop 
up the waves entering there, the waves from A, B, C, &c., would 
fall at P each undestroyed and assisting one another, each dis- 
turbance being an exact wave-length behind the other, and 
therefore all in the same phase. ‘Thus light would be restored 
at P. And similarly at other points where the difference be- 
tween A P, a P, &c., is three, five, &c., semi-wave-lengths. Light 
would be restored in the same way at no other places because 
the elementary waves do not at other points destroy one another 
in this peculiar alternative manner. Supposing a, 4, ¢, &c., to be 
the centres of the wires, A, B, C, &c., to be the centres of the 
spaces between, a more refined consideration shows us that the 
position of P does not depend on the space A @ being equal to 
the space a B, but only on the total length A B(or@d). Hence 
we have a very accurate method of determining the wave-length 
from the position of P. For if @ be the angle between the line 
drawn from the hole straight forward in the direction of the ray 
and the line drawn to P, then the difference between A P and 
B P, which is a wave-length, is also A Bsin @, So that to get 
the wave-length all that we have to do is to measure @ and A B. 
A B may be very accurately got by ruling the grating on glass 
with a machine, and counting the whole number of rules given 
and the total space which they occupy. Adaptations of this 
method may be made to suit circumstances, as for instance the 
grating may be attached to the object glass of a telescope 
used for measuring the angle @. It is by such a method 
that the wave-lengths haye been found for the principal fixed lines 
in the solar spectrum, and the waye-lengths of all other lines are 
determined from these by some formula or other which may best 
suit the views of the calculator ; the constants of the formula 
being determined so as to constrain the formula to satisfy the 
truth at those fixed lines whose wave-lengths are got directly from 
the refraction spectrum. Uncertainty, therefore, prevails about 
all wave-lengths thus obtained, although, of course, the uncer- 
tainty must, from the method of calculation and the number of 
lines whose waye-lengths have been obtained from the diffraction 
spectrum, lie necessarily between narrow limits. These latter 
are the only wave-lengths, however, which have the recommenda- 
tion of being due to direct observation; and the method of 
obtaining the wave-length by observation from the diffraction 
spectrum is one capable of such accuracy, that I haye sometimes 
considered that the waye-length thus determined might be used 
as an absolute and recoverable standard of linear measure. 
Of course, the preceding investigation must not be considered 
to be perfectly exhaustive in giving the whole character of the 
phenomena, which are explained by a more refined investigation, 
in which the space between each wire is regarded, not as the 
source of one, but of an infinity of wayes, so that the application 
of Huyghens’ principle becomes rigidly correct. By this means 
the difference of the spaces oceupied by the wire and the opening 
is found to have no effect on the position of P, but a certain 
effect on the brightness there, which, under certain circumstances, 
causes one of the spectra entirely to disappear ; an experimental 
result which, being thus deducible from the theory of undulations, 
gives a striking proof of the power of that theory to account for 
phenomena. JAMES STUART 
Trinity College, Cambridge, March 2 
The Valuation of Liquid Town Sewage 
Ir there is one thing that is more to be deprecated than an- 
other, it is the unnecessary importation of personalities into a 
scientific discussion, or indeed into any serious matter of business, 
and fortunately this is not now a common proceeding in this 
country. It was therefore with a feeling of unqualified disap- 
pointment that I read Dr, Paul’s personal attack on myself in 
your columns. 
Whenever I hear or read an opinion or statement which I 
believe to be erroneous, I endeayour to point out its fallacy, and 
shall always continue to do so. It is the undoubted right, as it 
is in some degree the duty, or every man to do this. But 
opinions may be criticised and condemned without any reflection 
on the man who holdsthem. ‘Thisis all I did in Dr. Paul’s case, 
and I certainly endeavoured to do it good-naturedly ; at all 
events I not only made no reflection whatever on Dr. Paul’s 
character, but I did not even mention his name. He had, in 
his article, hazarded an opinion on a question of practical 
farming, of which, so far as I know, he does not profess to 
have any personal knowledge or experience whatever, This 
opinion I knew from experience to be utterly erroneous, although 
