Notices respecting New Books. 61 



bodies, and those of Braiily on the absolute measure of electro- 

 motive force. The phenomena of thermo-electric circuits, though 

 occupying much space, are not treated in so satisfactory a manner 

 as their importance demanded, the researches of some recent 

 writers on the subject (<?. g. Prof. Tait) not being even alluded to. 



Clausius's hypothesis respecting the electromotive force in a 

 thermoelectric circuit almost disposes of itself. Clausius en- 

 deavoured to apply Carnot's theorem (relative to heat-engines) to 

 the quantities of heat absorbed or disengaged at the two junctions 

 in a closed circuit of two metals, and showed as a result that the 

 electromotive force must be proportional to the difference of tem- 

 perature. It is fouucl, however, experimentally that this propor- 

 tionality does not hold except within very narrow limits of tem- 

 perature. Prof. Mascart says : — " Carnot's theorem is only true for 

 those heat-engines which are reversible; and thermoelectric currents 

 do not present any character of reversibility which justifies 

 Clausius's calculation." 



A Treatise on the Trisection of an Angle of thirty degrees, and of any 



other plane Angle. By Bernard Tindal Bosanquet. London : 



Effingham Wilson, Koyal Exchange. 1876. (Pp. 20.) 



It is well known that the problem of the trisection of an angle 



is not simply to divide an angle or circular arc into three equal 



parts, but to effect the trisection by means of the straight line and 



circle only. Mr. Bosanquet would probably not have published his 



tract if he had distinctly understood this simple fact. As it is, 



his work consists of two parts : in the former he proposes a 



method of trisecting an angle of 30° by means of the straight line 



and circle ; in the latter he gives a method of trisecting any angle 



hj means of a hyperbola. 



The first of these methods is as follows : — Draw a circle, and at 

 its centre B place an angle CBD of 120° ; draw a radius BE 

 parallel to the chord CD ; bisect BE in G and draw GH at right 

 angles to BE to meet in H a tangent to the circle at C ; with 

 centre H and radius HG, describe an arc of a circle to cut the cir- 

 cumference of the first circle in K ; join BK, GK. Mr. Bosanquet 

 asserts that GHK - 3 GBK=2° 30' ; and if it be so, an angle of 10° 

 can then be constructed. He expresses (Preface, p.iii) a well-founded 

 doubt as to the exactness of this solution. In fact, as GHK is 

 slightly greater than 10°, and GBK very slightly greater than a 

 quarter of GHK, the result 2° 30' must be nearly right ; but the 

 only evidence produced for its exactness is that, when the angles are 

 calculated Trigonometrically, the result comes to 2° 30' within a 

 second — which, of course, is not the sort of evidence required; 

 and, besides, we believe, as a matter of fact, that it is about 1" 

 short of 2° 30' ; so that our author may be held to have failed in 

 the first part of his work, in which he observes the restrictions 

 implied in the problem. In the second part he effects the trisec- 

 tion of any arc of a circle by means of a hyperbola ; but as it was 

 already well known that the solution could be effected by Conic 



