196 



NA rURE 



[June 28, 1900 



give a lucid explanation of the principles governing the 

 various processes, which may be understood by readers 

 not necessarily acquainted with photographic manipu- 

 lation. 



The opening chapters introduce the elementary ideas 

 of the nature of colour and the undulatory theory of 

 light. Following these is a chapter on the Lippmann 

 process, this being the only direct process having a 

 purely physical origin. 



The fourth chapter deals with the principles of colour 

 vision, showing how the colour curves of red, green and 

 blue sensitiveness are employed in deciding the screens 

 used in the three-colour photographic process ; two pro- 

 cesses of this type, founded by Ives and Joly respectively, 

 being then fully explained. 



The work is brought up to date by descriptions of 

 Wood's diffraction grating process, and later improve- 

 ments on the Joly process. A chapter is also devoted 

 to three-colour photomechanical processes, and another 

 to the method developed by Sanger Shepherd and others 

 of producing lantern slides in three colours. 



Lecons nouvelles stir les applications geomdtriques du 

 calcul diffdrentiel. Par W. de Fannenberg, Professeuf 

 k la Facultd des Sciences de I'Universite de Bordeaux. 

 Pp. 192. (Paris : A. Hermann, 1899.) 



The geometrical applications of the differential calculus, 

 which are usually given in English treatises on the cal- 

 culus, are mostly confined to plane curves. In these 

 lessons, on the contrary, the author begins by assuming a 

 knowledge of elementary analytical geometry of three 

 dimensions, and proceeds at once to deal with subjects 

 which occur in the latter part of an English text-book 

 on solid geometry, in chapters on the general theory of 

 curves and surfaces. 



Thus we have sections on the descriptive properties 

 of tortuous curves and curved surfaces, followed by sec- 

 tions on the metrical properties of tortuous curves, of 

 ruled surfaces, and of surfaces in general. 



The author's treatment of his subject is exceedingly 

 clear and elegant, and there is considerable freshness of 

 method. We may notice, in particular, the early employ- 

 ment of the six co-ordinates of a line ; the use of the system 

 of moving axes formed by the tangent, the principal 

 normal and the binormal at a point on a curve ; the 

 systematic application of Gaussian curvilinear co-ordinates 

 in developing the properties of the several classes of 

 curves that may be traced on a surface. 



In fact, a student will find here in small compass a 

 pleasant introduction to some of the most powerful 

 methods of modern analysis as applied to geometry, 

 and if he proceeds afterwards to the " Lemons sur la 

 theorie generale des surfaces," by Darboux, his study 

 of that great classic will have been much facilitated. 



Elementary Illustrations of the Differential and Integral 

 Calculus. By Augustus De Morgan. New Edition. 

 Pp. viii -1-142. (Chicago : The Open Court Publishing 

 Company. London : Kegan Paul and Co., Ltd., 1899.) 



It is nearly seventy years since De Morgan first pub- 

 lished this tractate in the Library of Useful Knowledge. 

 It was afterwards bound up with his large treatise on the 

 differential and integral calculus, but the very inferior 

 typography detracts much from the pleasure of perusing 

 it there. In the present issue we have a very attractive 

 reprint. Although there has been in recent years almost 

 a superabundance of elementary treatises on the calculus, 

 some of them not lacking excellent illustrations of the 

 fundamental principles and processes of the subject, it 

 may still be said that De Morgan's effort at popularisa- 

 tion remains the greatest of its kind, and far above all 

 others in the philosophic spirit which animates it. 



NO. 1600, VOL. 62] 



LETTER TO THE EDITOR. 

 [Tie Editor does not hold himsetf responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Naturr. 

 No notice is taken of anonymous communications.'^ 



A Surface-Tension Experiment. 



If an unbroken vertical jet of falling water is allowed to 

 impinge normally on a smooth circular disc, whose diameter is 

 rather greater than that of the jet, then a phenomenon, illus- 

 trated by the accompanying photographs, is observed. These 

 are one-ninth natural size. 



A disc about 7 mm. in diameter was supported on the upper 

 end of a knitting-pin, which was held vertically in a clamp. 



A jet of water proceeding from a tube of 6 mm. internal 

 diameter was directed downwards, so as to strike the disc 

 centrally. 



If the initial velocity of the jet is high, then an umbrella- 

 shaped sheet is formed, which breaks up into a shower of drops 

 at its margin. On diminishing the rate of outflow, the broken 



Fig. I. 

 4000 c.c. per min. 



Fig. 2. 

 3000 c.c. per 1 



edge of the sheet gathers itself together and closes inwards until 

 it reaches the upright supporting the disc, thus forming a com- 

 pletely closed pear-shaped surface (Fig. i). The surface-tension 

 of the falling sheet thus drags in the water radially, for if it were 

 in separate drops these would describe parabolic paths. 



On further restricting the water supply there is, in general, a 

 tendency for the surface to elongate and at the same time to 

 contract laterally, thus becomint^ more spindle-shaped (Figs. 2 

 and 3). In this condition the figure is remarkably steady and 

 well defined. 



With a still slower stream of water (Fig. 4), the spindle 

 reaches a certain critical length at which it first begins to 



P i^^m ■■I 



Fig. 4- 

 1600 c.c. per min. 



1000 c.c. per mm. 



oscillate vertically and to pulsate, and then a sudden constriction 

 occurs causing the division of the spindle into two bubbles, one 

 of which rushes down and the other up the vertical support. 



The latter bubble persists as a small conical figure imme- 

 diately beneath the disc (Fig. 5). | *■•-*' 



Since there is an almost instantaneous transition from Fig. 4 

 to Fig. 5, it was not found possible to photograph any of the 

 intervening conditions. 



