44 Mr. J. J. Sylvester 07i the Rotation of a Rigid Body 



The growth is the most rapid iu dry hot weather, and in a dusty 

 room. The Unes are quite opake ; when breathed on, however, 

 they become swollen, and, from the moisture imbibed, semi- 

 transparent ; after the moisture is dried up, the lines no longer 

 have their original shai"])ncss. 



I have called these figures electrical, because I conceive their 

 growth is chiefly due to the chfferent electrical states of the par- 

 ticles of dust floating in the atmosphere and the glass. This suppo- 

 sition is, howe\er, insufficient, since I have never seen these figures 

 upon any other than jo/«/e-glass ; and I conceive, therefore, that 

 the attraction of the particles of dust and the formation of the 

 figures is connected with the fine strife formed in polishing the 

 glass. The attraction of a particle of dust to a point upon one 

 of these stri?e may become a point of attraction for another par- 

 ticle, and so the continuous curved Imes may be formed : the 

 dotted lines seem, however, also to indicate a repulsive action 

 between some of the particles. It has been remarked that the 

 curves rarely or never come into absolute contact ; this may be 

 due to the fact, that the strife last formed, in crossing the others, 

 will i-aise a small ridge at the crossing, as we see in making- 

 streaks in sand. It has also been remarked that the particles of 

 dust easily imbibe moisture; if, when thus swollen, the figures were 

 exposed to frost, we should have the same traceiy in frost work : 

 such frozen figures I actually observed last winter on the outside 

 of the plate-glass of a shop-window in Princes Street, Edinbm-gh. 



I may remark, in conclusion, that I imagined at one time that 

 these figures were analogous to the growth oliserved between 

 the lenses forming the object-glasses of telescopes : upon a careful 

 examination of both I am inclined to believe that they are wholly 

 different ; the lines of the growth are at times i-ounded, and they 

 cross one another like the branches of a plant ; but the lines of 

 these figures are quite flat, and apparently never cross. The 

 process of the formation of the figures has reminded me of that 

 of some of the finer filamentary cirrhous clouds. 



Paris, December 1850. 



VII. Explanation of the coincidence of a Theorem given by Mr. 

 Sylvester in the December Number of this Journal, ivith one 

 stated by Professor Donkiu in the June Number of the same. 

 By J. j; Sylvester, M.A., F.R.S. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



I "WISH to state, without loss of time, that in the theorem 

 given by me for the composition of two successive I'otations 

 about different axes, I have been anticipated by Prof. Donkin in 

 the June Number of your Joui'nal. 



