Nov. 2, 1S71] 



NATURE 



"ripples " (as I have called them), seen in advance of a 

 body moving uniformly through water ; also a passage 

 quoted by Russell from a paper of date, Nov. 16, 1829, by 

 Poncelet and Lesbros,* where it seems this class of waves 

 was first described. 



Poncelet and Lesbros, after premising that the phe- 

 nomenon is seen when the extremity of a fine rod or bar 

 is lightly dipped in a flowing stream, give a description of 

 the curved series of ripples (which first attracted my atten- 

 tion in the manner described in the preceding letter). 

 Russell's quotation concludes with a statement from which 

 I extract the following :—...." on trouve que les rides 

 sont imperceptibles quand la vitosse est moyennement au 

 dessous de 25c. per seconde." 



Russell gives a diagram to illustrate this law. So far 

 as I can see, the comparatively long waves following 

 in rear of the moving body have not been described either 

 by Poncelet and Lesbros or by Russell, nor are they shown 

 in the plan contained in Russell's diagram. But the curve 

 shown above the plan (obviously intended to represent the 

 section of the water-surface by a vertical plane) gives these 

 waves in the rear as well as the ripples in front, and proves 

 that they had not escaped the attention of that very acute 

 and careful observer. In respect to the curves of the 

 ripple-ridges, Russell describes them as having the 

 appearance of a group of confocal hyperbolas, which 

 seems a more correct description than that of Poncelet 

 and Lesbros, according to which they present the aspect 

 of a series of parabolic curves. It is clear, however, from 

 my dynamical theory that they cannot be accurate hy- 

 perbolas ; and, as far as I am yet able to judge, Russell's 

 diagram exhibiting them is a very good representation of 

 their forms. Anticipating me in the geometrical deter- 

 mination of a limiting velocity, by observing the angle 

 between the obhque terminal straight ridge-hnes stream- 

 ing out on the two sides, Russell estimates it at 8J- inches 

 (2ii centimetres) per second. 



Poncelet and Lesbros's estimate of 25 centimetres per 

 second for the smallest velocity of solid relatively to fluid 

 which gives ripples in front, and Russell's terminal velocity 

 of 21?. centimetres per second, are in remarkable harmony 

 with my theory and observation which give 23 centimetres 

 per second as the minimum velocity of propagation of wave 

 or ripple in water. 



Russell calls the ripples in front "forced," and the 

 oblique straight waves streaming off at the sides " free " 

 — appellations which might seem at first sight to be 

 in thorough accordance with the facts of observation, as, 

 for instance, the following very important observation of 

 his own : — 



" It is perhaps of importance to state that v/hen, while 

 these forced waves were being generated, I have sud- 

 denly withdrawn the disturbing point, the first wave 

 immediately sprang back from the others (showing that 

 it had been in a state of compression), and the ridges be- 

 came parallel ; and, moving on at the rate of 8| inches 

 per second, disappeared in about 13 seconds." 



Nevertheless I maintain that the ripples of the various 

 degrees of fineness seen in the diflerentf parts of the 



* Memoirs of the French Institute, 1829. 



t The dynamical theory shows that the length from crest to crest depends 

 on the corresponding component of the soUd's velocity. For very fine 

 ripples it is approximately proportional to the reciprocal of the square of this 

 component velocity, and therefore to the square of the secant of the angle 

 between the line of the solid's motion and the horizontal line perpendicular 

 to the ridge of the ripple. 



fringe are all properly " free " waves, because it follows 

 from dynamical theory that the motion of every portion 

 of fluid in a wave, and, therefore, of course, tlie velocity 

 of propagation, is approximately the same as if it were 

 part of an infinite series of straight-ridged parallel waves, 

 provided that in the actual wave the radius of curvature 

 of the ridge is a large multiple of the wave-length, and 

 that there are several approximately equal waves preceding 

 it and following it. 



No indication of the dynamical theory contained in my 

 communication to the Pliilosophical Mas;azine, and de- 

 scribed in the preceding letter to IVIr. Froude, appears 

 either in the quotation from Poncelet and Lesbros, or in 

 any other part of Mr. Scott Russell's report ; but I find 

 with pleasure my observation of a minimum velocity be- 

 low which a body moving through water gives no ripples, 

 anticipated and confirmed by Poncelet and Lesbros, and 

 rny experimental determination of the velocity of the 

 oblique straight-ridged undulations limiting the series of 

 ripples, anticipated and confirmed by Russell. W. T. 



ALLBUTT O.V THE OPHTHALMOSCOPE 

 On the Use of the Ophthalmoscope in Diseases of the 

 Nervous System and of the Kidneys; also in certain 

 other General Disorders. By Thomas Clifford AUbutt, 

 M.A., M.D., Cantab. &c. (London and New York : 

 MacmiDan and Co., 1871.) 

 '""T'HE advances that have been made in the knowledge 

 -L of the diseases of the eye since the introduction of 

 the ophthalmoscope are now very widely known, not alone 

 in the medical profession but to the general public. This 

 little instrument, essentially consisting of a mirror with 

 a hole in the centre by which a ray of light can be thrown 

 into the interior of the eye, lighting up its recesses, and 

 enabling, with the aid of a common hand lens, almost 

 every portion of it to be explored, may be said to have 

 revolutionised the surgery of the eye. Many separate and 

 distinct types of disease have been distinguished in condi- 

 tions that were formerly grouped together under the 

 general term of amaurosis, and the ophthalmic surgeon, 

 no longer administering, as was too often formerly the 

 case, his remedies in rash ignorance, is now able either 

 to infuse well-grounded hope of recovery, or to spare his 

 patient the annoyance of protracted treatment when treat- 

 ment would be hopeless. For nearly twenty years the use 

 of the ophthalmoscope has been, as was natural, almost 

 entirely restricted to those who devoted themselves to the 

 study of ophthalmic diseases. Like other mechanical aids 

 to diagnosis, as the stethoscope and laryngoscope, its 

 employment requires practice, the opportunities for ac- 

 quiring a mastery over it were till recently rare, and its 

 value in the .practice of medicine was by no means gene- 

 rally recognised. Within the last few year.-, however, 

 several excellent surgeons and physicians, amongst whom 

 Mr. Hutchinson, Dr. Hughlings Jackson, Dr. John Ogle, 

 and the author of the treatise before us may be especially 

 mentioned, have gradually begun to recognise that the 

 ophthalmoscope may be made available not only to deter- 

 mine the nature of any defect of vision of which the patient 

 may complain, but as a means of reading within certain 

 limits changes in the conditions of the system at large, 

 and of the nervous system in particular. 



