Januaey 16, 1903.J 



SCIENCE. 



109 



and lower culmination, either by means of 

 the meridian or the vei-tical circle. A plan 

 was then suggested by which the constant 

 might be secured by proper groups of stars 

 in pairs, observed in the prime vertical. 



A Development of the Conic Sections hy 



Kinematic Methods: John T. Quinn, 



Warren, Pennsylania. 



The paper is an abstract of a more gen- 

 eral system of kinematic geometry whereby 

 not only the conic sections, but nearly all 

 the higher plane curves are developed by 

 kinematic methods. The following defini- 

 tion will give some idea of its scope : 



Kinematic geometry treats of the prop- 

 erties of the areas and curves regarded as 

 functions of the spacial and angular veloc- 

 ities of lines, which move in accordance 

 with some fixed law. 



With reference to the conic sections (as 

 those are the curves in which we are at 

 present interested) , the originality of their 

 development consists in the introduction of 

 an auxiliary circle, called the directing 

 circle; and the conditions subject to which 

 the intersecting lines are assumed to re- 

 volve. The lines are pivoted in an axis 

 and conceived to revolve and move at such 

 rates that certain angles are constantly 

 equal, then the locus of their intersection is 

 a conic section. 



That this mode of development makes 

 manifest more than anj' other the essential 

 unity of the curves, and their dependence 

 upon the same law of generation, is evi- 

 denced by the general definition of a conic 

 in this system, referred to a common prop- 

 erty. 



A conic section is a curve the ratio of the 

 distances of whose points form a fixed 

 point and a directing circle is equal to 

 unity. For the ellipse and parabola, the 

 fixed point (a focus) is in the diameter of 

 the directing circle, for the hyperbola, in 

 the diameter produced. 



The problem of constructing tangents to 

 either of the ciirves from external points 

 in their plane is solved in an extremely 

 simple manner. The mode of procedure is 

 essentially the same for each of the curves. 

 This problem is facilitated by the directing 

 circle, which becomes the directrix of the 

 parabola when the circle becomes infinite. 



The point on either of the curves which 

 is common to the tangent through the ex- 

 ternal point is located by drawing only two 

 lines. 



The normal to a curve always is parallel 

 to one of the generating lines. Conse- 

 quently, as a problem in construction it 

 presents no difficulty whatever. 



To construct asymptotes to the hyperbola 

 we have only to describe a circle, upon the 

 line as a diameter, which is limited by the 

 center and the focus. It intersects the di- 

 recting circle in two points, which, with the 

 center, determine the direction and posi- 

 tion of both lines. 



Time Beterininations at the Wasliburn 

 Observatory : Professor Geoege C. Com- 

 STOCK, Madison, Wisconsin. 

 This was a discussion of methods em- 

 ployed in the time service of the Wash- 

 burn Observatory, with especial reference 

 to the advantages to be obtained by a re- 

 versal of the instrument upon each star. 



Determination of Time iy Reversing on 

 Each Star: Professor Charles S. Howe, 

 Case School of Applied Science, Cleve- 

 land, Ohio. 



Complete determinations of time were 

 made on several nights by the usual 

 method with clamp west and also with 

 clamp east. On the same nights deter- 

 minations of time were also made by re- 

 versing on each star. The clock errors 

 were compared with those found with the 

 almucantar. A table of azimuths, clamp 

 west and clamp east was given, and it 



