444 Intelligence and Miscellaneous Articles. 



the Auxiliary circle, and are concisely and clearly exhibited. We 

 have come across a few errata, which, however, the student will, 

 we believe, easily be able to correct. 



Exercises in Analytical Geometry. By J. M. Dyek, M.A., Senior 

 Mathematical Master in the Classical Department of Cheltenham 

 College. With Illustrations. Macmillan and Co. 1881. Pp.152. 

 The bare title of this book by no means does it justice. It is 

 certainly not a heterogeneous collection of examples, were it nothing 

 more ; bat besides an excellent progressive arrangement and group- 

 ing of exercises under the different sections of Analytical Greometry, 

 there are some most valuable hints for solving the difficult problems 

 interspersed among the answers, together with a number of figures. 

 As a supplement to the best and well-known modern treatises on 

 Coordinate Greometry, it will be useful to both beginners and more 

 advanced students. 



LY. Intelligence anal Miscellaneous Articles. 



AN AMUSING EXPERIMENT WITH LIQUID FILMS. 

 BY J. PLATEAU. 



T HAVE sought to derive a little amusement from thin liquid 

 J- films. I have had constructed of iron wire of about 0-5 millim. 

 thickness the outline of a flower with six petals of oval form; these 

 are each 24 millim. in length, and 19 millim. in their greatest 

 width. The central ring, made of the same iron wire, to which 

 they are attached, has a diameter of 14 millim. ; it is supported 

 beneath by a little fork, which is fastened to a thicker iron wire, 

 forming the stalk of the flower ; this last is implanted in a small 

 board which serves as a support. All the petals are in the same 

 plane ; and when the board rests on the table the flower is hori- 

 zontal. 



The whole contour of the flower was first slightly oxidized by 

 keeping it for a few moments in dilute nitric acid ; then, after 

 washing it, it was immersed horizontally in the glycerine liquid, 

 but only to a very little depth, in order to avoid the formation of 

 a film in the fork ; it was drawn out again, also horizontally, and 

 was then turned up and the board placed upon the table. Finally 

 the whole was covered over with a glass bell, to shelter the films 

 from the slight agitations of the air. The apparatus was placed 

 before a window so that the sky was seen by reflection from the 

 films. 



I thought that the petals would soon present uniform tints, 

 which would gradually change, in accordance with the attenuation 

 of the films ; but it was not so. During the first moments the 

 flower of course appeared colourless ; then, upon each petal and 

 the central circle, shades of rose and green of the last orders were 

 seen to appear, which gave place to irregularly distributed bands 

 and spots presenting tints of higher orders. The appearance was 

 then that of a flower streaked with the most lively colours. These 



