386 



NATURE 



[August i8, 1892 



faces of revolution, described in ' ' Popular Lectures and Ad- 

 dresses," vol. i., 2nd edition, pp. 31-42, suggests a correspond- 

 ing method for the solution of dynamical problems. 



Reduction of every problem of Two Freedoms in Conservative 

 Dynamics, to the draiving of Geodetic Lines on a Surface of given 

 Specific Curvature, by Lord Kelvin. 



1. Any conservative case of two-freedom motion is proved to 

 be reducible to a corresponding case of the motion of a material 

 point in a plane. 



2. In plane conservative dynamics, with any given value for 

 the energy-constant, E, the resultant velocity, q, at any point 

 {x,y) is a known function of {x,y), being given by the equation 



^■^ = 2(E-V). . . . .(I) 

 where V denotes the potential at {x, y) ; and every problem de- 

 pends on drawing lines for which / qds (the Maupertius "action ") 



is a minimum. 



3. Considering any part, S, of the infinite plane, find a sur- 

 face, S', such that any infinitesimal triangle A'B'C drawn on it 

 has its sides f^/*/,, of those of a corresponding triangle ABC in the 

 field, S, of our plane problem ; q^ denoting the value of q at any 

 particular point {xq, jfo) in the plane. By the principle of least 

 action we see instantly that the lines on S' corresponding to 

 paths on S, are geodetic. Thus the adynamic case of motion of 

 a particle on S', is found as a perfect and complete representative 

 of the motion on the plane surface S, under force with any 

 arbitrarily given function V, for its potential, and any particular 

 given value, E, for the total energy of the moving particle. 



4. It is easily proved that the 'surface S', to be found accord- 

 ing to §3, exists ; and that its specific curvature (Gauss's name 

 for the product of its two principal curvatures) at any point ; is 

 equal to 



^^ft A- log q . 



'f 



5. Examples are given of the finding of S'. As one ex- 

 ample, illustrating the practical usefulness of this method in 

 dynamics, the problem of the parabolic motion of an unresisted 

 projectile is reduced to the drawing of geodetic lines on a certain 

 figure of revolution of which the explicit equation is expressed in 

 terms of elliptic functions. 



THE PERIODIC VARIA TIONS OF ALPINE 

 GLACIERS. 



'pHIS twelfth Report, dealing with the Alpine glaciers and 

 -'■ their changes, by Dr. Forel, comes in the nick of time, 

 and will be generally welcomed, for it announces that the ques- 

 tion of glacier- changes in the Alps will in future be studied 

 systematically ; and, further, we learn in a postscript that the 

 State Council of the Canton of Le Valais have, on the propo- 

 sition of M. Maurice de la Pierre, head of the Home Department, 

 decided to take under its efficient direction the studies of obser- 

 vation and control of the variations of glaciers. These obser- 

 vations are confided to the charge of the Cantonal Adminis- 

 tration of Forests, the head of which is M. Antoine de Torrente 

 at Sion. M. Forel records this act of intelligent and prudent 

 administration with keen satisfaction and true gratitude, and 

 virould gladly see it imitated by other cantons possessing glaciers, 

 M. Forel publishes also the report, which, in compliance with 

 the wishes of M. de la Pierre, he had addressed to the Home 

 Department of Le Valais. It is equally applicable to the 

 glaciers of other cantons in Switzerland, and we therefore print 

 it in extenso. 



3!. de la Pierre, Councillor of State, head of the Home Depart- 

 ment, Sion, 



Sir, — Referring to the interview you granted me on January 

 31, and in reply to your question, I have the honour to give you 

 the following particulars : — 



Glaciers in general, and particularly those of Le Valais, are 

 subject to variations in shape, which, according to an irregular 

 periodicity, cause them sometimes to grow in length, in breadth, 

 in thickness, sometimes to decrease, often in very considerable 

 proportions. These variations, which in recent centuries have 

 attracted the attention of the populations interested and of 

 naturalists, have in this century been the subject of direct study, 

 especially during the last twenty years. 



It has been recognized that most of the great catastrophes which 



NO. I I 90, VOL. 46] 



have ravaged the region of the high Alps, have been caused by 

 these glacial variations. It is when the glacier extends, lengthens, 

 arrives at its maximum, that it not only invades the fields and de- 

 stroys Alpine chalets, but barricades the valleys, arrests the flow of 

 rivers, and creates temporary lakes, the evacuation of which 

 ravages the country ; or else, surpassing its usual dimensions, it 

 forms an avalanche, the destructive power of which is terrible. 

 Taking my examples from Le Valais, I attribute to forces of this 

 kind: the catastrophes of the Valley of Saas, 1633, 1680, 1772, 

 caused by the overflow of the lake Mattmarck, due to the stop- 

 page of the Viege by the glacier of Allalin ; the catastrophes of 

 the valley of Bagne, 1545, 1605, 1818, caused by the formation 

 of a temporary lake behind the barricades of the glacier of 

 Gietroz ; the catastrophes of Randa, 1636, 1819, caused by the 

 fall of the glacier of Bies, which had assumed extraordinary 

 dimensions ; perhaps we might also attribute to the same source 

 the inundations of St. Bartholomew, 1560, 1635, 1636, 1835, 

 which may have been due to the excessive increase and fall of 

 the terminal extremity of the glacier of Plan-neve of La Dent-du- 

 Midi. 



Since these variations of glaciers are the cause of great 

 catastrophes in mountainous regions, they are deserving of 

 attentive study ; there is scope to form theories and to recognize 

 the rhythm of their periodicity ; it is very necessary to be able 

 to foresee their development, in order to ward off" threatening 

 events. 



Now, the preparatory study which we have made within the 

 last few years has shown us that the periodicity of glacial vari- 

 ations is much longer than was formerly believed to be the case ; 

 the popular dictum that the increase in the size of glaciers recurs 

 every seven years is certainly incorrect. We cannot yet give 

 definite figures, but probably the cycle of glacial variation is as 

 much as 35 to 50 years. The latter period alone has been 

 studied attentively ; if 1850 or 1855 be fixed upon as the epoch 

 of maximum of glaciers, they have been steadily decreasing in 

 past years, so that from 1870 to 1875 we were not aware of a 

 single one on the increase. In 1875 the Glacier des Bossons du 

 Mont Blanc gave the signal for a new period by commencing to 

 lengthen out ; it was followed in 1878 and 1879 by the glaciers 

 of Trient and Zigiorenove, then successively by some thirty 

 glaciers in diff'erent valleys of Le Valais ; but the phase of in- 

 crease is not yet general in your canton ; a number of large 

 glaciers, Arolla, Otemma, Corbassiere, Le Corner, Le Rhone, 

 are still decreasing or stationary. It is only of the Mont Blanc 

 group that the increase can be said to be general ; in Le Valais 

 it is in process of development, and we are still very far from 

 the maximum stage of glaciers. If, as is probable, the maxi- 

 mum only arrives at the commencement of next century, the 

 actual period of glaciers will have lasted more than fifty years. 



Thus this is a phenomenon, whose cycle is equal or superior 

 to that of the average human life ; one generation of men 

 witnesses only one of the glacial variations. It is a phe- 

 nomenon of such majestic slowness that its study is exceptionally 

 difficult. 



A phenomenon of which a man can, in his whole life, see but 

 one manifestation, surpasses in its amplitude the powers of 

 initiative individual study. To observe the facts of so pro- 

 longed a period, organizations are required of a superior dura- 

 tion. Shall we address ourselves, therefore, to learned societies, 

 which, being continually renewed, may be supposed to have 

 sufficient continur.nce ? We fear that, even in the most power- 

 ful of these societies. Societies of Naturalists and the Alpine 

 Clubs, a sufficiently keen interest in observations, which can 

 only be utilized after the lapse of some generations will not be 

 felt for the observations to be organized and carried out with the 

 necessary perseverance. It seems to us that the State alone, by 

 virtue of the indefinite continuance it enjoys, is in a position to 

 follow out this study with a sufficiently long grasp. However 

 much we may be in favour of private individual or collective 

 initiative action in researches and scientific work, in this special 

 case we believe it advisable to have recourse to the State ad- 

 ministration, considering it the only institution of sufficient 

 duration to proceed to the study of phenomena of such extreme 

 slowness. 



We therefore take the liberty of addressing ourselves very 

 respectfully to the Government of the Canton of Le Valais, and 

 begging it to introduce the study and observation of the varia- 

 tions of glaciers, which have so great an influence on the pros- 

 perity of mountain populations. 



It seems to us that the State department best fitted for such a 



