April 12, 1883 | 
mispronunciation. An instance of this occurred within 
the lecturer's experience at Marlborough School not long 
ago: one stammering member of a certain form having 
communicated his defect to several of his schoolfellows. 
(4.) Bad teaching, and inattention to faults in their 
nascent condition. Many mothers think fit to accommo- 
date their speech to favourite children by mutilating and 
defacing it ; keeping two vocabularies, one for the draw- 
ing-room, another for the nursery. This is a fatal source 
of imperfections, the more so as it is to be remarked that 
stammering never comes on till about the age of five 
years or more. 
Lastly come peculiarities of an unconscious character 
akin to stammering—clucking, coughing, the reiterated 
interpolation of otiose syllables such as ‘‘er er,” ‘‘ta ta”; 
even of definite words or sentences such as “ you know,” 
or the coarse expletive adjectives of habitual swearers. 
The lecturer cited a case within his own remembrance 
where an estimable clergyman had acquired the singular 
trick of unconsciously interlarding all his remarks with 
the involuntary phrase, “ What a pity ! what a pity !” in 
defiance of all sense and context. 
Methods of cure were then adverted to. Probably no 
human infirmity had been the object of such diverse or 
such blundering and unscientific treatment. Even so good 
a surgeon as Diefenbach cut wedges out of the tongue of 
the patient ; Itard made them speak holding a gold fork 
in their mouth; Serres advised a waving motion of the 
arms during speech; Bertrand caused them to regulate 
the words to a rhythmical motion of the fingers, or to 
keep time to a stick as in the orchestra. He also placed 
substances in the mouth. This had been done centuries 
before by Demosthenes, according to that unveracious 
gossip, Plutarch. These might be termed mechanical 
attempts at cure. 
Next to them came musical methods, and foremost 
among them singing; it being well known that many 
confirmed stammerers sing with perfect articulation. 
Secondly, a so-called secret method, which consisted in 
either whispering or speaking in a gruff unmelodious 
tone. Thirdly, the very opposite of this as recommended 
by Marshall Hall, namely, chanting or monotoning. 
Fourthly, preceding all abrupt and consonantal sounds by 
a vowel such as E, recommended by Arnott. Fifthly, the 
plan of running all the words of a long sentence into one, 
and thus acquiring as it were an articulatory momentum. 
Intellectual or rational methods brought the lecture to 
a close. First among these is pausing and deliberate- 
ness. The stammerer may be compared mechanically to 
a steamship which overruns her screw, and treated 
similarly. Secondly, the imitation of good models, by 
reading in unison with an articulate speaker. Thirdly, 
and perhaps best of all, prefacing every sentence by a 
deep breath, which relaxes all the muscles of speech, and 
enables them to start fairly one against another. Fourthly, 
a plan was suggested which had succeeded admirably in 
the lecturer’s experience, namely, that of learning a new 
language. For this purpose none was better than French. 
Its pronunciation is so thoroughly different from that of 
English, that it requires and establishes a totally new 
coordination of muscles. Moreover its mode of habitual 
acquirement is entirely different from that of English. 
Any one who will watch a French child just rising out of 
infancy must notice that whereas the character of an 
English child’s incipient speech is “smudging” and 
confusion, the other’s is slow, pompous, and deliberate. 
It is not till later in life that the French acquire that 
lightning-like rapidity of speech which is the terror of 
foreigners ; while young they speak well and slowly. The 
third lecture ended with a few directions how to proceed 
in a case of stammering, and some suggestions as to the 
prospects of cure. As to the former, it is obviously de- 
sirable to examine carefully for the exact seat and the 
exciting cause of the defect; most of the systems in 
NATURE 
359 
vogue having erred by exaggerating a particular treat- 
ment to the exclusion of others equally admissible. As 
to the latter, there is no doubt that stammering can be 
cured. This was proved by such instances as Demos- 
thenes, Wilberforce, and Kingsley, But it was equally 
proved by the three names thus enumerated that to 
conquer the vicious habit required no usual amount of 
patience, ability, and determination. 
DISTRIBUTION OF ENERGY IN THE 
SPECTRUM 
ia 
the reaction against the arbitrariness of prismatic 
spectra there seems to be danger that the claim to 
ascendency of the so-called diffraction spectrum may be 
overrated. On this system the rays are spaced so that 
equal intervals correspond to equal differences of wave- 
length, and the arrangement possesses indisputably the 
advantage that it is independent of the properties of any 
kind of matter. This advantage, however, would not b> 
lost, if ins ead of the simple wave-length we substituted 
any function thereof; and the question presents itself 
whether there is any reason for preferring one form of the 
function to another. 
On behalf of the simple wave-length, it may be said 
that this is the quantity with which measurements by a 
grating are immediately concerned, and that a spectrum 
drawn upon this plan represents the results of experiment 
in the simplest and most direct manner. But it does not 
follow that this arrangement is the most instructive. 
Some years ago Mr. Stoney proposed that spectra 
should be drawn so that equal intervals correspond to 
equal differences in the frequency of vibration. On the 
supposition that the velocity of light in vacuum is the 
same for all rays, this is equivalent to taking as abscissa 
the veciprocal of the wave-length instead of the wave- 
length itself. A spectrum drawn upon this plan has as 
much (if not more) claim to the title of zorvma/, as the 
usual diffraction spectrum. 
The choice that we make in this matter has an im- 
portant influence upon the curve which represents the 
distribution of energy in the spectrum. In all cases the 
intensity of the radiation belonging to a given range of 
the spectrum is represented by the area included between 
the ordinates which correspond to the limiting rays, but 
the form of the curve depends upon what function of the 
ray we elect to take as abscissa. Thus in the ordinary 
prismatic spectrum of the sun, the curve culminates in 
the ultra-red, but in the diffraction spectrum the maximum 
is in the yellow, or even in the green, according to the 
recent important observations of Prof, Langley. If we 
wish to change the function of the ray represented by the 
abscissa, we can of course deduce by calculation the 
transformed curve of energy without fresh experiments. 
To pass from the curve with abscissz proportional to 
wave-length to one with abscisse proportional to reci- 
procals of wave-length, we must magnify the ordinates of 
the former in the ratio of the square of the wave-length, 
and this will give us an energy curve more like that ob- 
tained with a prismatic spectrum. 
There is another method of representation intermediate 
between these two, which is not without advantage. In 
the diffraction spectrum the space devoted to a lower 
octave (if we may borrow the language of acoustics) is 
greater than that devoted to a higher octave. In Mr. 
Stoney’s map the opposite is the case. If we take the 
logarithm of the wave-length (or of the frequency) as 
abscissa, we shall obtain a map in which every octave 
occupies the same space, and this perhaps gives a fairer 
representation than either of the others. To deduce the 
curve of energy from that appropriate to the diffraction 
spectrum, we should have to magnify the ordinates in the 
ratio of the first power of the wave-length. 
My object, however, is not so much to advocate any 
