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PROCEEDINGS OF SOCIETIES. 
similar kind made by other astronomers, acquire an importance far be¬ 
yond that belonging to their immediate object; opening up, in fact, a 
new field of astronomical inquiry, and new motives to diligence and ac¬ 
curacy in the arduous labour of mapping the stars. 
I have said nothing of the manner in which Mr. Cooper’s work has 
been performed, or of the excellence of the observations themselves. This 
is a point upon which none but practical astronomers can form a judg¬ 
ment. Eut we have the strongest external evidence, in the way of pre¬ 
sumptive proof, that the observations are of the highest value for their 
accuracy and excellence; not only from the known scientific zeal and 
devotion of the accomplished director and proprietor of the Markree Ob¬ 
servatory, the perfection of the costly instruments which his enlightened 
liberality has provided, but also from the high astronomical character 
and ability of Mr. Graham, his first assistant, under whose superinten¬ 
dence the observations were made. I may add also, that the instrument 
employed was the great Markree Equatorial, the eye-piece of which was 
furnished with a micrometer of a peculiar construction, devised by Mr. 
Graham; and that the same magnifying power was used throughout the 
whole series of observations. 
II. The chief merit of Mr. Salmon’s “ Treatise on the Higher Plane 
Curves” is the clear and full exposition of all modern improvements in 
the methods of analytical research which it contains. The author does 
not profess to have made any new discoveries, or to suggest new methods 
of investigation, but he has done both; and this new matter is introduced 
with so little parade, or, I should rather say, generally without any notice 
at all, that it requires considerable knowledge of the subject to distin¬ 
guish the discoveries of Aronhold, or Pliicker, ofPoncelet, or Joachims- 
thal, from the new and highly interesting propositions introduced whilst 
giving an account of the investigations of those authors, and connected 
with their researches, but due altogether to Mr. Salmon. 
The method of investigating the properties of conic sections by refer¬ 
ence to two tangents and the line joining their points of contact, and 
the analogous method applied to cubics of the third class; the applica¬ 
tion of the theory of determinants to the discovery of the properties of 
curves, particularly to finding the reciprocals of curves of the third and 
fourth degrees ; the investigation of the focal properties of cubical biqua¬ 
dratic curves, and many other new properties of conics,—may be men¬ 
tioned as original, the result of Mr. Salmon’s genius and research. Eut, 
however valuable and interesting these additions to what previous writers 
had discovered, the great practical value of the work is, that it arranges 
in a clear and connected system all the important geometrical discoveries 
hitherto published, so that, to use the author’s own words, “ each new 
student, who wishes to devote himself to original investigation in any 
branch of mathematics, may have his 1 energies brought to bear upon the 
undiscovered part of the science.” Such a student, with the aid of Mr. 
Salmon’s book, without the labour of searching the scattered papers in 
scientific journals, or transactions of societies, will at once see what has 
been already done, and will escape the danger of wasting his abilities by 
rediscovering what others had discovered long before. 
