298 



NA TURE 



[January 29, 1003 



Another claim made for the P. of L. A. is that it leads to 

 Lagrange's equations of motion. That is not remarkable, see- 

 ing that both are founded upon Newtonian ideas. I suppose 

 Lagrange's equations can be made to lead to the P. of L. A. 

 But the practical way of proving Lagrange's form is to derive 

 it immediately from Newton's Principle of Activity. Thus, 

 when there are n independent coordinates v, with velocities v, 

 the kinetic energy T is a homogeneousquadratic function of the 

 t''s, with coefficients which are functions of the v's. This 

 makes 



therefore 



t <*T , dT , 



(iz'i a::, 



-f, d dT . dT. , 



2T = - z>, + t\ + 



at a v. dv. 



(8) 



(9) 



But also by the structure of T 

 f 



(10) 



,17 , dT. , 



v l + — v l + . . . . 



So, by subtraction of (10) from (9) 



\dt (/,"', dxj / 

 and therefore, by Newton, the force on .i\ is the coefficient of 

 z'u and similatly for the rest. 



Some people who had worshipped the idol did not altogether 

 see that the above contained the really essential part of the 

 establishment of Lagrange's form, and that the use of the 

 activity principle to establish the equation of motion is proper, 

 instead of vice versd. To all such the advice can be given, Go 

 back to Newton. There is nothing in the ?. of L. A., or the 

 P. of L. Curvature either, to compare with Newlon for com- 

 prehensive intelligibility and straight correspondence with 

 dynamics as seen in Nature. It must, however, be said that 

 Newton's third law is sometimes astonishingly misconceived 

 and misapplied, perhaps because it is badly taught. 



Oliver Heaviside. 



Leonids of 1902, and Quadrantids of 1903. 

 Clouds and full moonlight seem to have impeded observ- 

 ations of the Leonids to a considerable extent in November, 

 1902. The night of November 14 was fine here, but as there 

 seemed little probability of a display on that date — as is fully con- 

 firmed by the negative results of other observers — no extended 

 watch was maintained. The night of November 15 turned 

 out very unfavourable. It seemed unusually bright here about 

 6h. 30m. on the morning of November 16. No observations 

 were possible in the circumstances. Even if the sky had been 

 clear, very probibly nothing unusual in the way of a meteor 

 display would have been visible, owing to the presence of the 

 full moon, then shining with almost maximum brilliancy. 

 M. D. Eginitis, with three assistants, observing at Athens during 

 the night of November 15, did not see more meteors — in fact, 

 they counted one less — than on that of November 14, 1901, on 

 which night the American maximum took place. Both those 

 nights were clear, but possibly the observations may not have 

 been equUly extensive. The maximum of 1902 probably took 

 place in America, but in the absence of reports of clear observ- 

 ations at a few stations on the other side of the Atlantic, it is 

 difficult to gauge with certainty the character of the display. 



The Quadrantid meteors, on the other hand, were well seen 

 here, considering the broken character of the weather. Antici- 

 pating Ihit the display of 1903 would occur early on the night of 

 January 3 —the maximum had been determined as due at Sh. 55m. 

 — 1 watch was begun at 8h. 45m , and during the next hour or 

 so some very fine meteors were observed. The following are the 

 times of their appearance, and their approximate flights : — 



d. h. 111. 



Jan. 3 S 53, from 2' west of Gemini to Orion, = 1st magni- 

 tude. 



.> 3 856, „ i° east of the " Guirds" to Pole Star, = 

 1-2 magnitude. 



,,39 20, ,, between Caslor and Pollux to Odon, = 

 1st magnitude. 



» 3 9 47> >> between the " Guards" half-way to Pole 

 Star, = 2nd magnitude. 



"39 59e> >> 2 °° west ol "Guards" to lo° higher up, 

 = rich streak. 



,, 3 10 o, ,, 20 west of "Guards" to Cassiopeia, = 

 Capella. 



"2. 1735, VOL. 67] 



Shortly after 10 o'clock, clouds came up from the horizon and 

 by ioh. 15m. the whole north-eastern sky up to Gemini was 

 covered. At ioh. 35m , that part of the sky had again cleared, 

 and, between ioh. 40m. and ioh. 55m., eight meteors, varying 

 from about 1st to 2nd magnitudes, were observed. They were 

 all long-pa'hed, but generally not so much so as the earlv part 

 of the display, nor did they seem 1 1 m ive in herten tracks as 

 it were, like the first meteors. The direction of their flight 

 resembled, on the whole, that of the former, but one of them 

 ( = Sirius) shot downwards for about 30° in a direction parallel 

 to the tail stars of Ursa Major. It started fr >m a point about 

 20 east of that constellation. The latter part of ihe display 

 between ioh. 40m. and ioh. 55m. was the richest I have ever 

 observed. I observed no meteors, except one or two between 

 9 and 10 o'clock, that could not be traced. They began to , 

 come so rapidly at ioh. 40m. that when making a note of the 

 course of one, another would put in an appearance, and so pre- 

 vent the completion of the first observation, their paths not 

 being near any well-known stars. An interval of quiescence 

 for a few minutes would then follow, when the phenomenon 

 would be again repeated as before. At 11 o'clock, the sky 

 became again clouded and a heavy shower of rain terminated 

 open-air observation. Between I2h. and I2h. 20m., two more 

 were seen through a window, of about the 3rd magnitude, one 

 on either side of the tail stars of Ursa Major ; then clouds once 

 more intervened. John R. Henry. 



Dublin. 



AMERICAN ASSOCIATION FOR THE 

 ADVANCEMENT OF SCIENCE. 



"THE fifty-second annual meeting of the American 

 * Association was held at Washington, December 29 

 to January 3, and was in many respects the most suc- 

 cessful meeting ever held in the fifty odd years of the 

 existence of the Association. As pointed out in the 

 article in NATURE of July 24, 1902, in the account of 

 the Pittsburg meeting of last June, this is practically the 

 first time in which the Association has met during the 

 winter since the close of the Civil War, and in this meet- 

 ing culm inated the prolonged efforts of a special com- 

 mittee of the Association, of which Dr. Charles Sedgwick 

 Minot was chairman, to bring about an agreement among 

 the scientific and other learned societies and the leading 

 universities and other institutions of learning in the 

 United States to set apart the week in which the first 

 of January falls as a " Convocation Week,'' and in ihis 

 week to bring together at one place as many as possible 

 of the scientific societies. This culmination of the 

 efforts of Dr. Minot's committee was eminently satis- 

 factory. The meeting was a great success, and the 

 institution of Convocation Week has apparently been 

 established under the most favourable auspices. 



Dr. Ira Remsen, president of Johns Hopkins University, 

 presided over the Washington meeting, and the retiring 

 president, the noted astronomer, Prof. Asaph Hall, 

 U.S.N., delivered his address on the opening night of 

 the session. His subject was "The Science of 

 Astronomy," and it was published in full in our last week's 

 issue. 



The local arrangements for the meeting were complete, 

 and the President of the United States acted as honorary 

 president of the local committee, the active chairman 

 being Dr. C. D. Walcott, Director U.S. Geological Survev, 

 and the local secretary Dr. Marcus Benjamin, U.S. 

 National Museum. 



The addresses of the vice-presidents of the different 

 sections were given in the afternoon of Monday, 

 December 29, as follows : — 



Prof. G. W. Hough before the Section of Mathe- 

 matics and Astronomy, on " The Physical Constitution 

 of the Planet Jupiter." Prof. Franklin before the 

 Section of Physics, on " Limitations of Quantitative 

 Physics." Prof. Weber before the Section of Chemistry, 

 on " Incomplete Observations." Prof. Culin before the 



