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LI. Notices respecting New Books. 



An Elementary Treatise on the Differential Calculus, containing the 

 Theory of Plane Curves, with numerous Examples. By Benjamin 

 Williamson, A.M., Fellow and Tutor, Trinity College, Dublin. 

 Second Edition, Revised and Enlarged. London: Longmans, 

 Green, and Go. 1873. (Pp. 367.) 



WE noticed the first edition, of this book, shortly after its pub- 

 lication, about a year and a half ago (April 1872). There is 

 therefore no need to say much on the present occasion. The revi- 

 sion to which the work has been subjected consists partly in a change 

 of arrangement of some of the articles (e.g., the chapter on La- 

 grange's Theorem, which was Chap. 20 in the first edition, is Chap. 7in 

 the second), partly in the addition of articles here and there through- 

 out the volume (e. g. the articles on Linear Transformation, Nos. 

 292-294 added to the chapter on Change of the Independent Va- 

 riable), partly in the insertion of additional Examples. The total 

 number of changes is considerable, and the result of the whole 

 is to increase the volume by 24 pages ; still the changes do not make 

 what can be regarded as a substantial alteration in the work. 

 It only remains, therefore, to congratulate the author on the rapid 

 sale of the first edition, and to express a hope that his very useful 

 book will continue to find many readers. 



LI1. Proceedings of Learned Societies. 



ROYAL SOCIETY. 

 [Continued from p. 326.] 



May 1, 1873. — "William Spottiswoode, M.A., Treasurer and 

 Vice-President, in the Chair. 



HPHE following communication was read : — 

 ■*• " On the Effect of Pressure on the Character of the Spectra 

 of Gases." By C. H. Steam and G. H. Lee. 



The variations in the spectra of gases which accompany changes 

 of density have been studied by Plucker and Hittorf, Frankland 

 and Lockyer, Wiillner and others. 



It appears to us that one cause to which these changes may be 

 due has been overlooked, and that many of the observed variations 

 are entirely independent of the density of the gas. If a Leyden jar 

 be placed in the circuit, and the current from an induction-coil be 

 passed through a Pliicker's tube containing nitrogen with the traces 

 of hydrogen generally present, the following well-known pheno- 

 mena are observed. 



When the gas is near atmospheric pressure, the line-spectrum 

 of nitrogen is brilliant, and the F line of hydrogen is broad and 

 nebulous. As the pressure is reduced, the lines of nitrogen gra- 

 dually fade out, and the band-spectrum appears, while at the same 



