TRANSACTIONS OF THE SECTIONS. ll 

lens, the power of which is equal to the semi-sum of the reciprocals of the focal 
_ lengths in the two principal planes, combined with an astigmatic lens, the power of 
which is equal to their semi-difference. 
If two plano-cylindrical lenses of equal radius, one concave and the other convex, 
be fixed, one in the lid and the other in the body of a small round wooden box, with 
a hole in the top and bottom, so as to be as nearly as possible in contact, the lenses 
will neutralize each other when the axes of the surfaces are parallel; and, by merely 
turning the lid round, an astigmatic lens may be formed of a power varying con- 
tinuously from zero to twice the astigmatic power of either lens. When a person 
who has the defect in question has turned the lid till the power suits his eye, an 
extremely simple numerical calculation, the data for which are furnished by the 
chord of double the angle through which the lid has been turned, enables him to 
calculate the curvature of the cylindrical surface of a lens for a pair of spectacles 
_ which will correct the defect of his eye. 
On the Determination of the Wave Length corresponding with any point of 
the Spectrum. By Professor Sroxes, M.A. 
__ Mr. Stokes said it was well known to all engaged in optical researches that Fraun- 
hofer had most accurately measured the wave lengths of seven of the principal fixed 
lines in the solar spectrum. Now, he found that by a very simple species of inter- 
polation, which he described, he could find the wave lengths for any point interme- 
diate between two of them. He then exemplified the accuracy to be obtained by his 
method by applying it to the actually known points, and showed that in these far _ 
larger intervals than he ever required to apply the method to the error was only in 
the eighth, and in one case in the seventh place of decimals. By introducing a term 
depending on the square into the interpolation still greater accuracy was attainable. 
The mode of interpolation proposed depended upon the known fact, that, if sub- 
stances of extremely high refractive power be excepted, the increment Ay of the re- 
fractive index in passing from one point of the spectrum to another is nearly pro- 
portional to the increment Aa—? of the squared reciprocal of the wave length. Even 
in the case of flint-glass, the substance usually employed in the prismatic analysis 
of light, this law is neariy true for the whole spectrum, and will be all but exact if 
Testricted to the small interval between two consecutive standard fixed lines. Hence 
we have only to consider y% as a function, not of a, but of A—2, and then take pro- 
portional parts. 
On examining in this way Fraunhofer’s indices for flint-glass, it appeared that 
the wave length (Ba) of the fixed line B was too great by about 4 in the last, or 
eighth, place of decimals. It is remarkable that the line B was not included fin 
__ Fraunhofer’s second and more accurate determination of the wave lengths, and that 
the proposed correction to (BA) is about the same, both as to sign and magnitude, 
as one would have guessed from Fraunhofer’s own corrections of the other wave 
lengths, obtained from his second series of observations. 

On Professor Quetelet’s Investigations relating to the Electricity of the Atmo- 
sphere, made with Peltier’s Electrometer. Communicated by Professor 
Wueatstone, F.R.S. 
Of all the meteorological conditions of the atmosphere its electrical state is per- 
haps among the most important. Yet in the various observatories established in 
different parts of the world in connexion with the great magnetic inquiry now in 
progress, and in the establishment of which the British Association has taken so 
_ prominent a part, no provision has been made for regular observations relating to 
‘this important subject. It thus happens, that while we possess a most valuable ac- 
cumulation of periodical records, made with great accuracy and regularity at widely 
different points of the earth’s surface, relating to the magnetism of the earth, and 
‘to the barometric, thermometric, hygrometric, and anemometric conditions of the 
- atmosphere, we have no simultaneous electrical observations with which to compare 
them. 

