OPTICS. 
lar image or fpedtrum is caft, and PT the image itfelf; 
whofe Tides, towards v and w, are rectilinear and parallel, 
and ends, toward P and T, femicircular.. j/KHP and 
xLIT are two rays; the firft of which comes from the 
lower part of the fun to the higher part of the image, and 
is refraCted in the prifm at IC and II; and the latter 
comes from the higher part of the fun to the lower part 
of the image, and is refraCted at L and J. Since the re¬ 
fractions on both Tides the prifm are equal to one ano¬ 
ther, that is, the refraCtion at IC equal to the refraCtion at 
I, and the refraCt'on at L equal to the refraCtion at H, fo 
that the refractions of the incident rays at K and L taken 
together, are equal to the refraCtions of the emergent 
rays at H and I taken together; it; follows, by adding 
equal things to equal things, that the refraCtions at K 
and H taken together are equal to the refraCtions at I 
and L taken together; and therefore, the two rays, being 
equally refraCted, have the fame inclination to one ano¬ 
ther after refraCtion which they had before; that is, the 
inclination of half a degree, anfwering to the fun’s dia¬ 
meter. So then, the length of the image PT would, by 
the rules of vulgar optics, fubtend an angle of half a 
degree at the prifm, and by confequence be equal to the 
breadth vw, and therefore the image would be round. 
Since then it is found by experience that the image is not 
round, but about five times longer than broad, the rays 
which, going to the upper end P of the image, fuffer the 
greateft refraCtion, mull be more refrangible than tliofe 
which go to the lower end T. 
“ The image or fpectrum PT was coloured, being red 
at its leaft-refradted end T, and violet at its mofl>re¬ 
fraCted end P, and yellow, green, and blue, in the inter¬ 
mediate fpaces.” 
To fiiow that the unequal refrangibility of the rays in 
this experiment is not accidental, or owing to any new 
modification produced by the medium through which 
they pafs, fir Ifaac Newton refraCted the rays of each 
colour feparately, and found that they ever after retained 
both their colour and peculiar degree of refrangibility. 
Nearly in the fame manner, it may be Ihown, that com¬ 
mon day-light confifts of rays which differ in colour and 
refrangibility. For, if the round hole in the fhutter re¬ 
ceive only light from the clouds, and the eye be applied 
to the prifm, the image is obferved to be oblong, and 
coloured, as in the former cafe. 
Sir Ifaac Newton, with the alfillance of a perfon who 
had a more critical eye than himfelf, diltinguifhed the 
fpeCtrum into feven principal colours, proceeding from 
the lefs to the more refrangible rays, in the following 
order: red, orange, yellow, green, blue, indigo, violet; 
of which the yellow and orange were found to be the 
mod luminous, and the next in iirength were the red and 
green ; the darker colours, efpecially the indigo and vio¬ 
let, affeCled the eye much lefs fenfibly. 
If, by any method, the prifmatic colours be again 
united in the proportion which they have in the fpec¬ 
trum, they compound a white fun-light; and, by the 
mixture of different forts of rays, in different proportions, 
various colours are produced, according to the quantity 
and nature of the rays united. Thus, a mixture of red 
and yellow produces an orange; yellow and blue form a 
green, &c. 
From what has juft been faid, we may conclude, that, 
if a ray of white light be refradted through a medium 
contained by parallel planes whofe diftance is inconfider- 
able, it will not, as to fenfe, be feparated into diftindt co¬ 
lours. For the ray of each particular colour emerges 
parallel to the incident white ray; confequently, the 
emergent rays of different colours are parallel to each 
other; and, fince the thicknefs of the medium is incon- 
fiderable, they emerge nearly at the fame point, and there¬ 
fore excite only the fenfation of whitenefs. Thus it hap¬ 
pens, that objects feen through common window-glafs do 
not appear coloured. 
The fame may be faid, if the emergent rays, after fe- 
659 
veral refradtions, be parallel to the incident white ray, and 
the points of emergence nearly coincide. 
Prop. II. The more refrangible rays are more reflexible. 
A ray of light cannot, confiftently with the general 
law of refradtion, pafs out of a denfer medium into a 
rarer, when the fine of incidence exceeds the limit deter¬ 
mined by this proportion, Sin. refradtion : fin. incidence 
:: radius : fin. incidence, which is the limit fought; 
therefore, the greater the ratio of the fine of refradlion to 
the fine of incidence, the lefs will this limit be; and, con¬ 
fequently, the fooner will the rays be refledted. 
Prop. III. If a fmall cylindrical beam of white light pafs 
nearly perpendicularly out of common glafs into air, 
the difperfion of the differently-coloured rays is about 
•j- 2 ^ of the mean refradtion. 
Let a fmall beam of the fun’s light be refradted by a 
glafs prifm, in the manner deferibed at Prop. I. and let 
PT, fig. 3. reprefent the fpedtrum, divided by lines which 
are perpendicular to its parallel Tides, and drawn through 
the confines of the feveral colours. Alfo, let ab, be, cd, de, 
ef, fgy be the fpaces occupied by the red, orange, yel¬ 
low, green, blue, indigo, and violet, rays, refpedlively; 
then, if the whole length ah be reprefented by unity, ab 
is found to be f, ac=%, ad=z±, ue—\, a/=ag= =■§■; and 
thefe are nearly proportional to the differences of the 
fines of refradtion of the differently-coloured rays to a 
common fine of incidence. (Between the divifions of the 
fpedtrum, thus made by the different colours, and the 
divifions of the monochord by the notes of mufic, Newton 
conceived that there was an analogy, and indeed an iden¬ 
tity of ratios; but experience has fince fhown that this 
analogy was accidental, as the fpaces occupied by the dif¬ 
ferent colours do not divide the fpedtrum in the fame 
ratio, when prifms of different kinds of glafs are em¬ 
ployed.) 
Now, when the rays pafs out of glafs into air, if the 
common fine of incidence be reprefented by 50, the fines 
of refradtion of the extreme red and violet rays are found 
to be 77 and 78 refpedlively; therefore, the fines of refrac¬ 
tion of the other rays are 77f, 77^, 77$-, 774, 77I, 77$. 
That is, the fine of incidence of any red ray is to the fine 
of refradtion in a ratio not greater than that of 50 : 77, 
nor lefs than that of 50 : 77^; but varying, in different 
ftiades of red, through all the intermediate ratios. In the 
fame manner, the fines of refradtion of all the orange rays 
extend from 77-^ to 77^, &c. the rays which are in the con¬ 
fines of the green and blue have a mean degree of refran¬ 
gibility, and the fine of incidence of thefe rays is to the 
fine of refradtion as 50 to 77J. 
When the angles of incidence and refradtion are fmall, 
they are nearly proportional to their fines; and, confe¬ 
quently, if the common angle of incidence be reprefented 
by 50, the deviation of the violet rays is 78—50, or 28; 
the deviation of the red rays is 77—50, or 27 ; therefore 
the difference of thefe, or the angle through which the 
rays of different colours are difperled, is of the devia¬ 
tion of the red rays, of the deviation of the violet rays, 
and —, or — of the deviation of the rays of mean re- 
275 . 55 
frangibility, from their original courfe. 
The angle through which all the red rays are difperfed 
is £ of -^5-, or of the mean refradtion, &c. 
In general, if the fines of refradtion of the red and violet 
rays, in their pafl'age out of any given medium into air, 
be i-j-m and i+», to the common fine of incidence 1, 
then, when the angles of incidence and refradtion are 
n—711 
fmall, the difperfion of the rays is an ———tli part of the 
refradtion of the red rays; and, fince m and n are invari¬ 
able, this expreffion may be properly taken as the mea- 
fure of the difperjing power of the medium. 
Whillt the refradting mediums are the fame, a given 
refradtion 
