406 
NATURE 
[ Feb. 17, 1870 
tion, that “ the drainage of the Cazembe’s country is all into the 
Nyanza on the east.” 
“The Nile of Egypt, in thus having its source at the opposite side 
of the continent of Africa, within a short distance of that ocean 
into which it does o/ flow, only follows an almost general law of 
Nature. In the A/heneum of July 22nd, 1865, when commenting 
on Sir Samuel Baker’s announcement of his discovery of the 
Albert Nyanza, I compared the Nile and its Lakes with the Po 
and its Lakes, pointing out how the two rivers have some of 
their sources in szowy mountains, not at the extremity but at the 
side of their respective basins. Dr. Livingstone’s present dis- 
coveries seem to establish the fitness of this comparison, and to 
extend it. For as the Po, whose exit is in the Adriatic, has its 
head sources in the Cottian and Maritime Alps, within a few 
miles of the Gulf of Genoa ; so, in like manner, the Nile, which 
flows into the Mediterranean, has its head on the Mossamba 
Mountains, within 300 miles of the Atlantic Ocean. 
‘he spot which I have thus discovered to contain the hitherto 
hidden Source of the Nile, and so to reveal! 
—fluori causas per szcula tanta latentes, 
Ignotumque caput, 
is the most remarkable culminating point and water-parting 
of the African Continent, if not of the whole world; for, 
within the space of a degree east and west (between 18° and 19° E. 
long.) and half as much north and south (between 11° 30 and 12° 
S. lat.) it includes not only the head of the mighty Nile, which 
runs northwards over one-eighth of the entire circumference of 
the globe, but likewise those of the Kuango, (Congo), the 
Kuanza and the Kunene flowing westwards ; those of the Kuivi 
and the Kubango running to the south ; and that of the Lunge- 
bungo haying its course eastward and forming the head stream 
of the Zambesi. It is, in fact, what I have been endeavouring to 
determine since 1846, ‘‘the great Aydrophylacium of the con- 
tinent of Africa, the central point of division between the waters 
flowing to the Mediterranean, to the Atlantic, and to the Indian 
Ocean” (Fournal of the Royal Geographical Society, vol. xvii. 
p. 82), as likewise to Lake Nyami, or some other depression in 
the interior of the continent. 
Bekesbourne, Feb. 2 CHARLES BEKE 
Analogy of Colour and Music—Supernumerary 
Rainbows 
In what I saw of a recent discussion in your paper as to the 
analogy between the colours of light and musical notes, I did 
not observe any reference made to an analogy on this subject, 
published, I believe, in 1845, by Prof. Mossotti, of Pisa, The 
analogy is pointed out at the end of a paper concerning the dif- 
fraction spectrum. ‘This spectrum, the disposition of the colours 
in which depends solely on the wave-lengths, has its point of 
maximum brightness in the middle, which in this spectrum is 
occupied by a shade of colour rather nearer to the line E than 
TD. Fig. 1 represents the positions of the lines in the diffraction 
spectrum ; and fig. 2 represents the spectrum formed by refrac- 
tion through a certain flint glass prism which belonged to Fraun- 
hoffer. The ordinate of the curve which is drawn above each 
spectrum represents the intensity of the light at each place of 
that spectrum. ‘The curve drawn above fig. 2 is that due to 
lraunhoffer’s actual observations with the prism above referred 
to. The intensity of the light in the neighbourhood of the prin- 
cipal lines is given by him by the following numbers :— 
B 
"032 
D 
(e EF He 
094 108 70056 
These intensities were determined by comparison with the light 
of alamp placed at various distances. It is hard to say, however, 
E 
“48 
G 
“O31 
what physical and physiological facts are included in these numbers. 
The curve given in fig. I is constructed by Mossotti analyti- 
cally, on a principle which amounts to this :—He takes hold of 
the spectrum in fig. 2, and shifts it so that the fixed lines come 
into the positions of fig. 1, and decreases or increases the ordi- 
nate representing the brightness in the neighbourhood of each 
fixed line in exactly the proportion that the spectrum has been 
expanded or contracted in the neighbourhood of that line. The 
change of place of portions of colour not in the immediate 
neighbourhood of one of these lines is regulated by a formula 
founded on a certain physical investigation of Mossotti’s as to 
the dependence of the refraction index upon the wave-length, 
which formula has its constants determined by the method of 
least squares, so as to represent with sufficient accuracy the truth 
at the fixed lines. 
Following a method similar to that adopted by Newton, 
Mossotti supposes the spectrum in fig. 1 to be bent round the 
complete circumference of a circle, and he finds that if x be the 
wave-length in millionths of a millimetre at a point distant by 
an are whose circular measure is x, from the brightest portion of 
the spectrum, then x is given for the fixed lines with sufficient 
accuracy by the formula 
x = 553°5 + 184°5% 
extending this formula to the ends of the spectrum, it constrains 
the longest wave-length to be 738, and the shortest 369 millionths 
of a millimetre. ‘This result Mossotti regards as sufficiently 
near the actual wave-lengths of the extremities of the spectrum. 
The longest and shortest wave-lengths taken in conjunction 
with the wave-lengths of the brightest part of the diffraction 
| spectrum and of the fixed lines BC DEFGH form ten wave- 
lengths, which Mossotti thus compares with the notes of the 
diatonic scale ;— 
; wp © 5 4 Zeya 3} pie 25) 2 
25 8 4 3 18 2 3 3 
I I y Le eae , I me . I ak pod I 
738 688°3 656 590 553'5 53f 492 443 393°5 309 
738 688 656 589 553°5 526 484 429 303 369 
— B Cc D _ E F G Tre — 
The first line represents the number of vibrations necessary to 
produce the notes of the diatonic scale. The numbers in the 
second line have the same ratio as the numbers in the first, and 
therefore the denominators of these fractions represent the wave- 
lengths of the respective notes. The third line represents the 
lengths in millionths of a millimetre of the waves corresponding 
to the lines respectively placed under them, 
I need not here give any opinion as to the utility or inutility of 
such analogies, but I shall be glad if this letter should call the 
attention of any of your readers to the remarkable syminetry of 
the diffraction spectrum, which is in fact Nature’s own graphical 
method of exhibiting the numerical wave-lengths which corre- 
spond to each part of the spectrum, 
Trinity College, Cambridge, Feb, 9 JAMES STUART 
IN your journal of January 20th Mr. Grove has honoured my 
little note on ** Colour and Music” by a letter on the subject, in 
which attention is directed to a rainbow, or series of rainbows, 
within the primary. Mr. Grove asks if a description of this 
phenomenon has been published, and whether the effect may 
not be a repetition of the colours of the spectrum after the 
manner surmised by Sir John Herschel. I will endeayour as 
briefly as possible to reply to these inquiries, 
So far as I can trace, the mention of inner or ‘‘ supernumerary” 
bows first occurs in the Phil. Trans. for 1722, p. 241. It is 
there described by a Dr. Langwith,who had seen the phenomenon 
no less than four times in the course of that year. On one occa- 
sion it was so favourably seen, and lasted so long, that he is able 
to give the following careful description, Under the usual 
primary bow, Dr. Langwith says, ‘‘was an arch of green, the 
upper part of which inclined to bright yellow, the lower to a 
| more dusky gieen; under this were alternately two arches of 
reddish purple and two of green, under all a faint appearance of 
another arch of purple, which vanished and returned several 
times so quick that we could not readily fix our eyes on it.” 
