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LXY. Notices respecting New Books. 



A Treatise on the Integral Calculus. — Part I. Containing an 

 elementary account of Elliptic Integrals and applications to Plane 

 Curves, with numerous Examples. By Ralph A. Robebts, M.A. 

 Dublin: Hodges, 1S87; pp. viii + 368. 



1YTR- ROBERTS, who has written a number of papers on subjects 

 -^-*- intimately connected with the Calculus, has now embodied some 

 of these results, with the necessary elementary details, in the present 

 treatise. He has not seen fit to introduce his work to his readers 

 with any forewords, so we are left to infer that he considers such 

 a work is required to meet a want not met by existing treatises. 

 The contents, so far, do not differ materially from those of Dr. 

 Williamson's treatise, but the treatment is different, and the illus- 

 trations and examples are very full and important. The main 

 difference is in the amount of space (Chapter v.) devoted to the 

 discussion of Elliptic Integrals ; here our author is specially strong. 

 We have noticed but few typographical or other errors, and as the 

 whole discussion is admirably conducted throughout, we need only 

 append the headings of the chapters. These are : — Elementary 

 Integrals, Integration of Rational Eunctions, Integration by Ration- 

 alization, Integration by Successive Reduction, Elliptic Integrals, 

 Definite Integrals, Areas of Plane Curves, and Rectification of 

 Plane Curves. Erom the titlepage we gather that at least another 

 volume is to follow. The book is of handy form and clearly 

 printed. 



LXYI. Intelligence and Miscellaneous Articles. 



INFLUENCE OF MAGNETISM ON THE THERMOELECTRIC BEHAVIOUR 

 OF BISMUTH. BY DR. GIOVANNI PIETRO GRIMALDI. 



H^HE remarkable influence which magnetism exerts on the elec- 

 •*- trical resistance of bismuth led me to suppose that it would 

 not be uninteresting to investigate whether the thermoelectric be- 

 haviour of bismuth in the magnetic field was different to what it is 

 usually. 



In this preliminary note I give the results hitherto obtained. 

 The experiment was made as follows : — A cylinder of bismuth, 5 

 centim. in length and 1 centim. in diameter, with copper wires sol- 

 dered at the ends, was placed equatorially between the poles of a 

 Earaday's electromagnet. The solderings were immersed in two 

 baths of such a form that they could be close to the poles of the 

 magnet. One of the baths was full of melting snow, and the other 

 of water at the ordinary temperature, which flowed from a large 

 reservoir. 



The bismuth-copper couple was introduced into a circuit of cop- 

 per wire of about 2 millim. in diameter, which remained constant. 

 In this circuit two copper- wire couples of about the same E.M.E. 

 as the couple under experiment were arranged in opposition. The 

 circuit also contained a Wiedemann's galvanometer (Edelmann's 



