268 



NATURE 



[July 21, 1892 



morphological speculations as simple mistakes. To com- 

 pare an insect-embryo and its membranes with a Lamelli- 

 branch or an Ascidian in the extempore manner assumed 

 so lightly by Mr. Lowne (p. 244) is not creditable. He 

 tells us that he has no facts to guide him except the 

 similarity of the form and disposition of the parts. Any 

 reader who is not able to judge for himself should be very 

 much on his guard when our author mentions Vertebrates 

 or Ascidians, or indeed any other animals outside the 

 class of Insects. 



It is painful to speak with any disrespect of an author 

 so laborious and so independent as Mr. Lowne. But 

 these good qualities do not suffice to make a really good 

 book. Advice will probably be thrown away, but we will 

 offer one hint in the most friendly way. If Mr. Lowne 

 before going to press would get his sheets revised by any 

 cautious and well-informed zoologist, he would be saved 

 from making statements which seriously impair his work. 



L. C. M. 



A Mendip Valley: its Inhabitants and Surroundings. 

 By Theodore Compton. With Original Illustrations 

 by Edward Theodore Compton. (London : Edward 

 Stanford, 1891.) 



This is an enlarged and revised edition of the well- 

 known " Winscombe Sketches," and will be cordially 

 welcomed by readers who can appreciate the presenta- 

 tion of natural facts in a poetic spirit. The author has 

 spent the greater part of " thirty-three years of rural 

 life" in the valley about which he writes, and every 

 aspect of it he knows and loves. He tells much that is 

 interesting, not only about the valley itself, but about 

 the people who inhabit it, and about its archaeological 

 remains, its wild beasts, past and present, its birds, fish, 

 reptiles, butterflies, and flowers. The style is simple and 

 clear, and a certain charm is added to the writer's de- 

 scriptions by the quaint reflections with which many of 

 them are associated. An excellent chapter on the geo- 

 logical history of the Mendips is contributed by Prof. 

 Lloyd Morgan. The illustrations are daintily conceived 

 and executed, and harmonize well with the general tone 

 of the text. 



Key to Elementary Dynamics. By S. L. Loney, M.A. 



(Cambridge University Press, 1892.) 

 Those who are using the author's Elementary Treatise, 

 whether they be teachers or students, will find this key 

 very useful. The solutions to the examples are here 

 worked out in full, so that even one who is going through 

 the subject by himself will learn much in the nature of 

 attacking problems by direct methods. The author's 

 treatise is now so widely used that this key will come as 

 a great boon to many. 



LETTERS TO THE EDITOR. 



[ The Editor does not hold himself 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 ilATV^v.. 

 No notice is taken of anonymous communications. ] 



The Lightning Spectrum. 

 During the brilliant display of lightning on the evening of 

 June 28, I took the opportunity of making some observations of 

 the spectrum. The way in which the spectrum varied was very 

 remarkable, some of the flashes giving apparently perfectly con- 

 tinuous spectra, while others gave a spectrum of bright lines, as 

 already recorded by Kundt and others. The continuous spec- 

 trum appeared to be associated with the flashes of longest 

 duration, which were accompanied by very little thunder, and 

 the bright line spectrum with the more instantaneous flashes. 

 Using a Liveing direct-vision spectroscope with a very accurate 

 scale, I succeeded in measuring the positions of six lines in the 



green, all of which no doubt have been observed before, but in 

 two cases at least the positions have not besn previously 

 measured. The wavelengths of the lines observed were as 

 follows — those determined by Vogel, Schuster, and Colonel 

 John Herschel, being added for comparison : — 



Other lines were seen both in the red and blue, but time did 

 not permit any accurate determinations of their pjsitions. 



The lines (i) and (6) are undoubtedly the two brightest double 

 linesof the air spectrum which occur in this region, but in the 

 case of the other lines the coincidences are not so definite. The 

 proximity of the line 5168 to the brightest carbon fluting 

 (^ 5165) would suggest that it has its origin in the carbonic acid 

 gas, which is always present in the atmosphere. The remiining 

 lines do not appear to coincide with air lines, and their origins 

 for the present are undetermined. A. Fowler. 



Royal College of Science, South Kensington. 



On the Line Spectra of the Elements. 

 Prof. Runge has not improved the position he has taken up 

 by the new instance of a motion which he brings forward in last 

 week's Nature. The instance he gave in his preceding letter 

 is a motion which, as I pointed out, could not take place within 

 molecules. The motion he now gives is one which cannot even 

 exist anywhere in nature. It would require a supply of power 

 (energy per unit of time) increasing ad infinitum. The first 

 instance he gave belongs to inapplicable kinematics, his new one 

 to impossible dynamics. Neither has anything to do with the 

 subject of my memoir. 



He quotes the enunciation of a theorem from chapter iv. 

 of my paper, but does not quote the sentence introducing that 

 theorem, which would have made it plain that the motions spoken 

 of in it are ^notions which can take place within molecules and 

 which can produce an undulation in the ether, not the motions 

 of a mere mathematical exercise irrespective of whether they are 

 real or imaginary. The introductory sentence (p. 588) is in the 

 following words :— " The motions of the electrons, the electric 

 charges in the moleculJs, which are what excite the ethereal 

 undulation, may be motions that are not confined to one plane. 

 Accordingly to study them we must investigate what theorem 

 corresponds to Fourier's theorem when the motion takes place 

 along a line of double curvature." And then follows the 

 demonstration and the enunciation quoted by Prof. Runge. In 

 the foregoing words, in the introductory paragraphs of chapter 

 iv. of my memoir, and in other passages scattered up and down 

 through that chapter, I made it abundantly clear, as I thought, 

 that I was dealing throughout with a redl physical problem of 

 nature, not engaging in mere mathematical exercises that travel 

 into the infinite and impossible. I now see that I ought to have 

 made more explicit statements upon this point for readers who 

 would judge of each sentence apart from its context. 



In order that a motion, x—f{t), may be susceptible of treat- 

 ment by Fourier's theorem, the following are conditions that 

 must be fulfilled : — 



1°. The motion must be recurrent, or capable of being ap- 

 proximated to by recurrent motions. 



2°. The quantity represented by x must not become infinite, 



3°. The quantity represented by t must not retreat. 



I have been familiar with these limitations since I was a 

 student, more than forty years ago. They are known to all stu- 

 dents. I therefore thought it superfluous, and still think it 

 ought to have been superfluous, to state them in my memoir. I 

 thought it also irrelevant, since none of the limitations could 

 occur in the motions I was investigating ; and I wished to shorten 

 my memoir by excluding all irrelevant matter. Prof Runge, 

 however, objects that I have not treated of violations of the first 



NO. II 86, VOL. 46] 



