320 



NA TURE 



[February 2, 1899 



unattained limiting value is not new-fangled, it appears worth 

 while to quote a few words of the paper of Gauss, above referred 

 to, which is of date 1799- 



" Ex supposilione, X oblinere posse valorem S neque vero 

 valorem n, nondum .se(|uitur, inter S et n necessario valorem T 

 jacere, quern X atlingere sed non superare possit. Superest 

 adhuc alius casus : scilicet fieri posset, ut inter S et n limes situs | 

 sit, ad quern accedere quidem quam prope velis possil X, ipsum 

 vero nihilominus nunquam attingere." 



It is a curious enough fact of history that it is Weierstrass's 

 use of this principle which has destroyed the Dirichlet proof of 

 a fundamental theorem of the theory of potential (Thomson 

 and Tait's "Natural Philosophy," 1879, vol. i., first line of 

 p. 171). H. F. Baker. 



Cambridge, January 23. 



The Aurora of September g, 1898. 



I OBSERVE, from Natike, that an auroral display was 

 visible in the South of England on the evening of September 9. 

 It may interest some of your readers to know that an aurora 

 was seen here on the evening of September 10. The display 

 began at about a (juarler to eight o'clock, and lasted for an hour 

 or so. The whole southern heavens at first became suffused 

 with a bright orange light low down upon the horizon, from 

 which a few streamers issued from time to time, rising (judging 

 by the eye) to a height of, say, 45 degrees above the horizon. 

 When both glow and streamers had faded away, I noticed three 

 luminous clouds, one at the zenith. The largest of these clouds 

 increased in size, and shot forth a few streamers of light, both 

 upwards and downwards, and all then disappeared. I have 

 witnessed several auroral displays at Ashburton, but none like 

 that of September 10, the distinguishing features of which were 

 the orange glow and the luminous clouds. 



On the following day, my telephone, which had never failed 

 me before, worked irregularly, and some of the other telephones 

 in the town were similarly aiTected. Chas. W. Pur.nell. 



Ashburton, Canterbury, N.Z., December 21, 1898. 



THE APPLICATION OF PHOTOGRAPHY TO 

 THE STUDY OF THE MANOMETRIC 

 FLAME. 



THERE are {e.\s more beautiful phenomena m e.xperi- 

 mental physics than those presented by the image 

 of the manometric flame as one sees it in the revolving 

 mirror. Especially is this true when the flame is excited 

 by means of the comple.\ tones of the human voice or by 

 some musical instrument such as the violin, which 

 possesses pronounced and varying tone colour. 



Little use, nevertheless, has been made of the flame as 

 an implement in research. Indeed the whole of the early 

 literature pertaining to the manometric flame may be 

 said to consist of the three papers ' in which, at intervals 

 often years, Rudolph Koenig described the apparatus 

 which he first made public at the London Exhibition of 

 1862, together with the various experiments to which it 

 was adapted. The writers of text-books, it is true, have 

 made free use of Koenig's beautiful method, but in- 

 vestigators have been slow to avail themselves of it. The 

 use of sensitive flames in the stroboscopic study of 

 vibrations by Toepler {Pof^irendorffs Anna/en, vol. cxxviii. 

 p. 108, 1866 1, which method has since been employed by 

 Brockmann l\'utiiiiian)i's Aiinu/cn, vol. xxxi. p. 78, 

 1887) in his analysis of the movement of the air in organ- 

 pipes, and also the observations of singing and of sensi- 

 tive flames by Kundt [Poi;i^i>i</i>rff\i Annalen, vol. cxxviii. 

 p. 337 and p. 614, 1866); by Barrett {.Pliilosophkal 

 Magazine, 1867;; and by Tyndall ("On Sound," 

 Lecture vi., 1867), belong to this period. These re- 

 searches, however, form a class by themselves, and are 

 to be traced back to the earlier work of Higgins (1777), 

 Chladin (1802), De la Rive (1802), Faraday (1818), 

 Wheatstone (1832), Schaflfgotsch (1857), and Le Conte 



' KcH-nig: I'flj^geH'lorff's AntiaUti, vol. cxxii. jj. -^42 ; vol. c.vlvi. p. 161 ; 

 *' *,>uclqin:s £x(M^ricnces d■Acou.^ti^|ue, " Chapter vii. 



NO. I 527, VOL. 59] 



(1858). In them the use of the manometric capsule does 

 not occur, and they appear, from first to last, to be entirely 

 independent of the work of Koenig. 



The difficulty of securing a trustworthy record of the 

 forms taken on by the flame-image has doubtless had 

 much to do with this hesitancy. The drawings published 

 by Koenig to accompany the description of his experi- 

 ments are of great beauty, and the more intimately one 

 is acquainted with the appearance of the flame-image 

 itself, the more one is impressed with the extraordinary 

 fidelity of these representations of it. The secret of their 

 accuracy is to be found in the methoti by which they 

 were obtained, which is described by Koenig in the 

 article of 1872, to which reference has already been made. 

 In the preparation of the well-known plate of the drawings 

 of flame-images corresponding to the five principal vowel 

 sounds, which was exhibited at the annual meeting of 

 German Men of Science lyNaliir/orscherfcrsainmlung, 

 Dresden, 1868) each vowel was simg at a carefully 

 ascertained pitch, and duplicate drawings were made by 

 Koenig himself and by a draughtsman employed for that 

 purpose. When these two drawings were found to be 

 alike they were assumed to be correct, but wherever a 

 variation occurred the expermient was repeated until the 

 two were brought into agreement. Each vowel was 

 sounded with a pitch corresponding to each note of the 

 scale between «/, and w/a, so that seventy-five of these 

 drawings, perfected by many repetitions, appear in this 

 one plate. 



The most complicated of the pictures of the mano- 

 metric flame drawn by Koenig is that shown in Fig. i. 



in which an attempt is made to record the motions of the 

 flame when the tongue is going through the vibrations 

 necessary to produce the rolling sound of the German r, 

 but without permitting the vowel-producing qualities of 

 the voice to accompany it. Doubtless the difficulty of 

 securing records by the method of free-hand sketching, 

 which had been employed by Koenig, to say nothing of 

 the difficulty of interpreting the more complicated forms 

 assumed by the flame-image, has prevented the general 

 introduction of what in other respects is a very attractive 

 method of research. 



In 1886 the question, which must have occurred to 

 many observers of the manometric flame, whether these 

 fleeting flame-images could be photographed, was 

 answered affirmatively by Doumer yConiftles rcndus. vol. 

 ciii. p. 340; vol. cv. p. 1247), who used such photo- 

 graphs in the determination of pitch and of the phase 

 relations of sound waves. Doumer, however, published 

 none of his photographs ; so that we do not know w hat 

 degree of success he attained. In 1.S93 Merritt, who was 

 at that time unacquainted with Doumer's experiments, 

 undertook the photography of the manometric flame in 

 the hope of thus developing a method which would be of 

 use in connection with certain studies in phonetics. His 

 paper, entitled ".■\ Method of Photographing the Mano- 

 metric Flame, with Applications to the Study of the 

 Vowel .\" {Physical Rn'iew, vol. i. p. 166), contains the 

 first published photographs of the Koenig flame-images. 

 Merritt found it barely possible to photograph, upon a 

 rapidly moving plate, the flame produ. id by the ordinary 

 Koenig apparatus. The actinic weakness of the flame 



