Mr. A. Cayley on the Cubic Centres of a Line. 433 



rate means of estimation should not be adopted in regular obser- 

 vatories. The most unexceptionable rain-gauge would consist 

 of a sheet of metal, many feet square (for instance 10 feet), 

 spread flat upon the ground in an open place, with a fiat col- 

 lecting vessel in the centre connected by a pipe with a sunken 

 reservoir or recording apparatus. The edges of the collecting 

 vessel should not be higher than an inch, so as to present no 

 appreciable obstacle or hollow space to the wind. At the same 

 time nothing would be lost by splashing, as the splashes within 

 and without the vessel would be equal. 



29. My conclusions, shortly stated, are: — 



(1) An increase of the rainfall close to the earth's surface is 

 incompatible with physical facts and laws. 



(2) The individual observations on this subject are utterly 

 discordant and devoid of law when separately examined, and the 

 process of taking an average under such circumstances gives an 

 apparent uniformity which is entirely fallacious. 



(3) When daily measurements of rain, or even monthly totals, 

 are examined with reference to the strength of the wind at the 

 time, it becomes obvious that there is a connexion. 



(4) Wind must move with increased velocity in passing over 

 an obstacle. It follows demonstratively that rain-drops falling- 

 through such wind upon the windward part of the obstacle will 

 be further apart, in horizontal distance, than where the wind 

 is undisturbed and of ordinary velocity. 



London, August 28, 1861. 



LV. On the Cubic Centres of a Line with respect to Three Lines 

 and a Line. — Seond Note. By A. Cayley, Esq.* 



ON referring to my Note on this subject (Phil. Mag. vol. xx. 

 pp. 418-423, 1860), it will be seen that the cubic centres 

 of the line \x + py + vz =0 



in relation to the lines x = 0, y = 0, z — 0, and the line x + y 4- z = 0, 

 are determined by the equations 



_ 1 _1_ 1 



where 6 is a root of the cubic equation 



J^ + J_ + J: ?_o. 



or as it may also be written, 



^ 3 -%v+vX + V) - 2 \pv = 0. 

 * Communicated by the Author. 



