TRANSACTIONS OF THE SECTIONS. 3 
points at infinity in the otherwise unknown figure are given in addition (as regards 
the content) to a certain constant termed the homographic determinant. 
* Professor Rankine threw out a suggestion as to the possibility of a practical 
> oe of the preceding theory to the stability of structures standing to each 
other in a certain simple relation of homography. 
On the Conditions of the Resolvability of Homogeneous Algebraical Polynomials 
into Factors. By J.J. WAtkER. © 
In this communication a commencement was made of a systematic investigation 
of the conditions of resolyability of homogeneous polynomials of ” variables into 
factors, and it was shown that in the case of the polynomial of the second degree 
the conditions are that every n—3rd “minor” of a symmetrical determinant, whose 
constituents are the coefficients of the polynomial, should vanish. It was also 
‘shown that the coefficients of the factors are roots of certain quadratic equations, 
and the general theory was illustrated by geometrical applications. 
ASTRONOMY. 
On the Augmentation of the Apparent Diameter of a Body by its Atmospheric 
Refraction. By SrepHen ALEXANDER. 
Professor Challis, in the Report of the Association for 1862, stated that there 
would be reason to expect, in a solar eclipse, that a slender band of the sun’s disk 
immediately contiguous to the moon’s border would be somewhat brighter than the 
other parts, and advised that especial attention should be directed to this point on 
the next occurrence of a solar eclipse. 
The phenomenon thus ingeniously shown by Professor Challis to be in place has 
itself been frequently observed. 
The author first noticed it in February 1831, at Berlin, Maryland, during the 
progress of the annular eclipse (Transactions of the Albany Institute, vol. ii. p. 85). 
It is mentioned in his notes as haying been seen “during the first hour of the 
eclipse, with (at one time and another) different telescopes and screen glasses of 
different colours.” 
It has, almost without exception (perhaps with no exception), been seen by him 
in some seven or eight solar eclipses which he has since observed. jt gai atten- 
tion was directed to its observation in this country in 1854; and its observation is 
recorded by Profs. Frazer and Kendall at Philadelphia in that year (Proc. of Amer. 
Phil. Soc. vol. vi. p. 41), also among his own observations of that eclipse at 
Ogdensburg, New York (Astronomical Journal, No. 75, p. 17). See also his 
Report of Observations in Labrador, July 1860, made to the Superintendent of the 
United States Survey (Report of the Superintendent for 1860, Appendix 21). 
The daguerreotype impressions of the eclipse of 1854 (taken in New York) 
distinctly show the narrow bright band; and it can also be seen in the photogra- 
phic impressions taken in July 1860, in Labrador. A careful inspection will, he 
presumes, reveal it in the instance of any good vousliga impression of 
the partially eclipsed sun; especially where the dark limb of the moon is pro- 
jected on a part of the sun’s disk sufficiently near to the border of the same. The 
phenomenon is thus the most conspicuous when the eclipse is quite small or when 
it is very large. 
On the Selenographical Relations between the Chain of Lunar Mountains the 
Alps with the Mare Imbriwm and the Mare Frigoris. By W. R. Brrr, 
F.R.AS. Communicated by Dr. Ler, F.RS. 
The mountains on the lunar surface known as the Alps extend from the Caucasian 
range bordering the N.E. portion of the Mare Serenitatis to the dark-floored crater 
Plato, approaching nearly to the summit of its western rim, From the ae 
