April 28, 1870 | 
NATURE 
653 
sidering them as representing separate notes, and arranging them 
in regular order, counting the original generator as No. 5, we 
get the following scale—major, minor, and chromatic—of FG, 
or green :— ' (Tonic) : 
SI 0 1) 20 TG Bie 52 P30 nesh rah habe 95 
CD) DE EB FG Ay AD Bp B.C 
Grey. Laven- Violet. Indigo. Blue. Green. Red. Orange.Chrome, Yel- Lemon, White. 
der. low. 
= undies is, I think, a misnomer: it should be purple between blue and 
et. 
On the same system it is easy to construct an enharmonic 
scale on the principle employed by M. Chevreul. The double 
flats and sharps sometimes give ternary compounds. For 
example, 4a equals green+ red + red, and its inversion 599 
would give red+green+green. Some of the neutral greys, 
olives, slates, browns, &c., which would not appear in a table 
so constructed and calculated at a normal pitch, are produced 
by lowering the diapason. 
From the above very brief explanation of the system of in- 
versions, the following results may be suggested :— 
1. That a table of colours of all gradations, with their com- 
plementaries, may be musically expressed in numerical notation 
with the greatest exactitude. 
2. That, contrary to scientific opinion, it does not follow that 
because the red ray has the lowest degree of refrangibility, &c. 
&c., or perhaps because it happens to be at the bottom of the 
series of prismatic colours, it should necessarily be the initial 
note on the tonic ofa scale. 
3. Even if the red ray be the tonic, it does not follow that the 
scale of the spectrum should be major, as is too frequently 
given in elementary works on optics. By the system of inver- 
sions of numbers here presented, the scale of the spectrum 
appears, by disjoining the conjunct tetrachords, to consist of 
one tetrachord major and one minor, corresponding to the de- 
scending minor scale in use, of FY minor, supposing CJ to 
represent the normal pitch of the dominant No. 5 corresponding 
to any given intensity of white light. Moreover, one conjunct 
tetrachord of the spectrum appears in ascending and one in 
descending, both tetrachords converging on the tonic. 
4. If the analogy be true so far, there is only one colorific 
key. Modulation through a series of colorific keys, as in »zoder7 
music, is impracticable. The reasons I have not space to 
explain. — J. G 
Mr. SEDLEY TAYLOR has, itseems to me, written his criticism 
on my letter published in NATuRE, Feb. roth, far too hastily. 
I do xot compare the diameter of the rings with one another, but 
their cubes, otherwise we should be led in establishing the musical 
I 
analogy to the absurd equation $4/*=}. It would perhaps have 
been better to have said, that the ratios of the spheres described 
on the diameters of the rings, taken successively from red to 
violet, two and two together, the Ist to the 2nd and the 2nd to 
the 3rd, &c., give a series of fractions identical with those ex- 
pressing the relative lengths of the musical chords from D to C, 
ascending and taken in like manner. As Mr. Taylor doubts 
Prof. Zannotti’s accuracy, I will quote the following passage 
from Biot’s ‘‘ Precis Elémentaire de Physique,” 3rd Ed., Vol. 11. 
Paris, 1824, p. 400, ef seg. Speaking of Newton, **Tl mesura 
les diamétres des anneaux simples de méme ordre, dans la partie 
intérieure et dans la partie extérieure de leur périmetre, et en les 
considérant successivement aux limites des diverses couleurs du 
spectre a commencé par le violet extréme. Suivant sa methode 
constante, il prit soin de lier ces resultats par une loi mathéma- 
tique qui les représentat avec une suffisante exactitude. I] trouva 
ainsi que les diamétres, soit intérieurs, soit extérieurs, étaient 
sensiblement entre eux comme les racines cubiques des nombres 
4, +, 3 3, 4 % & 1, lesquels representent les longueurs que 
doit avoir une corde de musique pour produire toutes les notes 
dune gamme mineure; c’est-a-dire, que si l’on représente par I 
le diamétre intérieur d’un certain anneau, lors qu il est forme par 
les rayons rouges qui composent la partie la plus extreme du 
spectre, *\/3 exprimera le diamétre intérieur du méme anneau, 
quand il sera formé par les rayons qui sont la limite du rouge et 
de Vorange, et ainsi de suite jusqu’ a %s/} qui représentera le 
diamétre intérieur du méme anneau quand il sera formé par les 
derniers rayons violets pris 4 l’autre extrémité du spectre.” 
I can only add, that if Mr. Taylor doubts also the accuracy of 
M. Biot, he can easily refer to Newton’s own treatise on colour. 
Rome, March 16 W. S. OKELY 
The Barlow Lens 
~I HAVE found the addition of a double concave lens to 
my telescope and microscope of so much service that I am 
anxious to call the attention of your readers to this simple appli- 
cation for increasing and improving the working power both of 
telescopes and microscopes. The application consists in the 
introduction of a biconcave lens in the adapter, which holds the 
eye-piece of the telescope, at a distance of two or three inches 
from the field-lens; as the focal length of the instrument is 
thereby increased, it is necessary to adjust the distance of the 
lens from the eye-piece according to the length of the adapter, 
so that the latter still admits of being drawn out sufficiently for 
focussing. A friend procured me several lenses of different 
powers at the ridiculous price of a shilling a-piece from an 
optician and spectacle-maker at Brighton, which answer ad- 
mirably. 
The chief advantage obtained by the use of this lens is the 
great increase of magnifying power without a corresponding loss 
of light. This is a great desideratum in looking at a planet, 
but it is equally important in separating double stars. With a 
low eye-piece of 60, my refractor (one of Cook’s with a 3hin. 
object glass, and the addition of the Barlow lens) shows the 
Companion of Rigel beautifully. 
I first became aware of this useful application many years 
ago, in reading Admiral W. H. Smyth’s ‘‘ Cycle of Celestial 
Objects.” In page 343, vol. i., he states: ‘‘On receiving it, I 
directed the telescope upon a watch-plate fixed on a distant 
chimney, which quickly proved the power of the lens in enlarge- 
ment, with scarcely any obscuration of light. While the image 
expanded under each progressive eye-piece, I was surprised at 
the additional advantage of its simultaneously flattening the 
whole field of view ; and though the magnifying power became 
double on distant objects, the apparent magnitude of the spider- 
lines diminished in an equal ratio: a property which, with all 
powers above three hundred, is of considerable benefit to 
operations upon close double stars, and the finer micrometric 
desiderata. I afterwards raised the discs of the Satellites of 
Jupiter, and examined several double stars, with equal facility 
and advantage, the definition being quite distinct, and the stray 
light rather subdued than increased. After a little practice, I 
came to the conclusion that the achromatic concave lens will 
render the instrument to which it shall be applied equal to two 
telescopes for particular cases; for if a set of observations be 
made with it and another set wthowt it, the errors of vision will 
be in some degree neutralised, or even done away with.” 
In spite of this strong recommendation I never gave it a trial 
until a few weeks ago, when a paper in the Polish language by 
Prof. Piotrowsky passed through my hands. It remains to this 
Ath 
Fig. 1. 2 c, object glass; ef, Barlow Fig. 2. a4, object ; cd, image, with 
lens; @ g, foci of Sc, with and 
without Barlow lens. 
day a sealed book to me, but the two annexed figures taken from 
it leave no doubt in my mind that the paper treats on the same 
subject of which Admiral Smyth speaks so favourably. The 
result of my own trial made me regret having foregone for many 
years an advantage which I have every reason to congratulate 
myself on now possessing; but this circumstance it is also 
which induced me to ask for a small corner in NATURE for these 
remarks, when other more interesting subjects are less \pressing 
than usual. 
Walham Groye 
convex lens alone; ¢/, image, with 
Barlow lens. 
F, dA. 
