1893.] Presents. 371 



this point on one of the known harmonic polars, the remaining two 

 points hi which the harmonic polar meets the cubic are found by a 

 quadratic construction, and triangular symmetry completes the de- 

 termination of the cubic ; the inflexional tangents to the Hessian 

 and the cusps on the Cayleyan are found by linear constructions ; 

 and the pairs of points in which these curves are met by the har- 

 monic polar, by quadratic constructions. Any coincidence among the 

 points so found indicates some special cubic whose properties may 

 thus be investigated ; among these special cubics are the equian- 

 harmonic cubics, whose properties present themselves very simply by 

 means of the preliminary constructions. These special cubics are the 

 critical ones when we follow out the variation in the Hessian and 

 Cayleyan, which, depending directly on the variation in the original 

 cubic, expresses itself by the change in the relative position of the 

 points determined as above. This variation is shown in a series of 

 diagrams exhibiting the cubic, its Hessian, and Cayleyan ; and, finally, 

 ihe results being compared with those derived from analysis, the 

 variation is represented graphically by means of a single diagram. 



VI. "Alternate Current Electrolysis." By J. HoPKiNSON, D.Sc., 

 F.R.S., E. WILSON, and F. LYDALL. Received November 2, 

 18 ( J3. 



[Publication deferred.] 



Presents, November 23, 1893. 

 Transactions. 



Batavia : Bataviaasch Genootschap van Kunsten en Weten- 

 schappen. Notulen. Deel XXX. Aflev. 34. 8vo. 

 Batavia 1892-93; Tijdschrift voor Indische Taal-, Land- eu 

 Volkenkunde. Deel XXXV. Aflev. 56. Deel XXXVI. 

 Aflev. 23. 8vo. Batavia 1893. The Society. 



Berlin : K. Preussische Akadernie der Wissenschaften. Sitzungs- 

 berichte. Nos. 2338. 8vo. Berlin 1893. The Academy. 



Birmingham : Mason College. Calendar. 1893-94. 8vo. Bir- 

 mingham 1893. The College. 



Brighton : Brighton and Sussex Natural History and Philosophical 

 Society. Abstracts of Papers and Annual Report for the year 

 ending June, 1893. 8vo. Brighton 1893. The Society. 



Brisbane : Queensland Branch of the Royal Geographical Society 

 of Australasia. Proceedings and Transactions. Vol. VIII. 

 8vo. Brisbane 1893. The Branch. 



Brussels : Academic Royale de Medecine. Memoires Couronnes. 

 Tome XII. Fasc. 2. 8vo. Bru.celles 1893. The Academy. 



