126 Royal Society. 



the above-named organs with the vital or organic changes which 

 take place in them. 



In consequence of the secondary actions which occur at the elec- 

 trodes some difficulty is experienced in ascertaining the true or 

 normal result in the roots. Combining however the facts obtained 

 by means of the galvanometer with analogical evidence, the author 

 considers that they tend to establish the conclusion, that, during the 

 changes which occur in the leaves and in the roots of plants, current 

 electricity is manifested. 



2. ** On the relation of Cardioids to Ellipses." By Joseph 

 Jopling, Esq. 



The object of this communication is to point out the relation of 

 Cardioids to Ellipses, and that the former as well as the latter are 

 related to and deducible from the cone. 



The author remarks that the motions of the common trammel show 

 most beautifully the mechanical relation of ellipses and cardioids, and 

 that they are thus reciprocals of each other ; that an ellipse, as is 

 well known, is a plane section, or a projection of a plane section of a 

 cone upon any other plane, the limits being the circle and the right 

 line ; and a cardioid is also a projection from a cone ; the difference 

 being that the cardioid is obtained from a curved section, formed by 

 the intersection of a sphere or other curved solid with a cone. 



After referring to properties of the sections of cones by spheres 

 depending on the magnitude of the vertical angles of the cone, the 

 author states that these and many other new curves, their relations, 

 and new properties of the cone and the sphere are made most clearly 

 manifest, and numerous practical results are very readily obtained by 

 the application of a double scale of sines to the rays of the cone — 

 distributed equally on the plan — correspondingly on the elevation, and 

 on the developed surface, or on any other projection of the cone. 



He considers that it is of great importance that some method 

 should be devised to give appropriate names to these new curves, 

 especially those so evidently and intimately related to old ones. 

 Thus the curved intersection of a cone and a sphere, from which the 

 cardioid is projected on the base, and which has then the cusp turned 

 symmetrically inwards, by another projection on a vertical plane 

 gives a symmetrical line with the cusp turned outwards, having 

 other distinct points of change in the curvature. 



As ellipses are related to cardioids, so it is stated are hyperbolas 

 in a similar way related to conchoids ; conchoids to their mechani- 

 cal reciprocals ; and parabolas to cissoids ; amongst the vast number 

 of curves, any of which can conveniently be derived by scales prac- 

 tically from the cone. 



By this method it is considered that not only projections of curved 

 sections of cones, spheres, &c. are obtained with ease, but also by 

 means of scales, ruled papers, hollow cones and diagrams, the plane 

 sections of cones, and all projections from them are greatly facilitated. 



In conclusion the author remarks, that if this subject can be en- 

 tertained by the Royal Society, he will make copies of a series of 

 diagrams to illustrate what he has here stated in reference to scales 

 applied to cones to obtain cardioids, &c. 



