240 Notices respecting New Books. 



hence , 2inr tttt + W ~M 



w = • • — • 



Sr Xt T 



From this, taking into account the correction arising from the 

 deadener as being made up of several windings, and the correc- 

 tion for the elasticity of the thread, we find from the above 

 observations 



^<;' = 1898•10 8 . 



[To be continued.] 



XXX. Notices respecting New Books. 



An Elementary Treatise on Trilinear Coordinates, the Method of Reci- 

 procal Polars, and the Theory of Projections. By the Rev. N. M. 

 Ferrers, M.A., Fellow a?id Mathematical Lecturer of Gonville and 

 Cuius College, Cambridge. Cambridge: Macmillan and Co., 1861. 



IN the researches of the ancient geometers a problem presented 

 itself to them in an almost tangible shape ; the eye was a most 

 important auxiliary to the brain ; and, without questioning the truth 

 of the old French definition, " La geometrie est une science par 

 laquelle on raisonne droit sur des figures faites de travers," there is 

 no doubt that a well-drawn figure would often suggest a property or 

 method of investigation which might otherwise have escaped ; and 

 at any rate the ancients never contemplated reasoning on symbols 

 which bore no resemblance whatever to the figure. The moderns, 

 however, without any loss of distinctness of conception, have, by the 

 introduction of symbols, gained important advantages. Among 

 others, they have freed themselves from the necessity of verifying 

 their results in every variation of case arising from a mere change 

 of position in the data of a problem, and they have acquired an 

 almost unlimited power of generalization. 



The coordinate geometry was one of the first grand steps in this 

 direction ; but many important additions have been made since Des- 

 cartes ; and of late years new methods of investigation have been 

 pursued which bid fair to carry science onwards with a speed and 

 safety hitherto undreamt of. 



The book before us makes known in a simple and intelligent 

 manner the characteristic features of these new methods ; it seems 

 especially prepared with reference to the wants of students in the 

 University of Cambridge, and will prove a valuable complement to 

 the works now in use there as text-books. In his preface, the 

 author says that his object in writing on the subject of trilinear co- 

 ordinates has mainly been to place it on a basis altogether indepen- 

 dent of the Cartesian system ; but as several results of that system 

 are assumed, as, for instance, in the definition of a conic, p. 33, and 

 in the means of determining the centre of a conic, p. 35, it is ob- 

 viously not intended to be throughout a perfectly independent work 

 which may be studied without any previous knowledge of any other ; 



