On the Curves situate on a Surface of the Second Order. 35 

 wanting. The horseshoes show the direction of the wind cur- 

 rent : thus, ~^> means wind /ro?h the west. An included spot 

 3£>, orline ~^>, or cross ^+>, respectively signify that the wind 

 is gentle, moderate, or strong ■ where neither dot, line, nor cross 

 are inserted, the force of the wind is unknown. Thermometrical 

 data are expressed by figures, printed below the wind symbols. 

 The first two figures of each set stand for the height of the ordi- 

 nary thermometer, and the last figure (in a different type) for 

 the difference between this and the thermometer with a wetted 

 bulb. To save confusion of figures, barometer heights are not 

 inserted on the face of the present map : but lines of equal baro- 

 metric pressure have been deduced from the existing observations, 

 and the places where lines corresponding to each integral one- 

 tenth of an inch cut the marginal columns, have been marked. 

 -Thus a straight line joining the pair of figures, 29*7, is approxi- 

 mately the line of that pressure. 



I do not consider the types here employed as forming a com- 

 plete series. An additional shade for cloud is especially wanted. 



It will be observed that no space would be lost by this mode 

 of representation, supposing we possessed observations corre- 

 sponding to every type space of the map. 



42 Rutland Gate, S.W. 



VI. On the Curves situate on a Surface of the Second Order. 

 By A. Cayley, Esq.* 



A SURFACE of the second order has on it a double system 

 of generating lines, real or imaginary ; and any two gene- 

 rating lines of the first kind form with any two generating lines 

 of the second kind a skew quadrangle. If the equations of the 

 planes containing respectively the first and second, second and 

 third, third and fourth, fourth and first sides of the quadrangle 

 are x = 0, y = 0, z=0, iv = 0, and if the constant multipliers 

 which are implicitly contained in x, y, z, w respectively are suit- 

 ably determined, then the equation of the surface of the second 

 order (or say for shortness the quadric surface) is xw — yz=0. 



Assume - — o -= -, then ^-, -, or say (A,, p, v, p), may be 



regarded as the coordinates of a point on the quadric surface ; 



we in fact have x :y : z : w= 1 :^ : -'• £— , or what is the same 

 y \ p Xp 



* Communicated by the Author. 

 D2 



