July 27, 1882] 



NATURE 



the ether, whose density is function of the velocity of propaga- 

 tion of light and heat, as also of the wave-lengths. 



Multiplying all these masses by the square of the velocity of 

 each particle relatively to the centre of gravity of the solar 

 system, we obtain the factor \ Mz> 2 = the total kinetic energy of 

 the solar system. 



This constant kinetic energy (if the second hypothesis be 

 admitted, in which J m v- is constant) is not distributed through- 

 out the solar system in a regular and fixed manner. Sometimes 

 a planet, as Jupiter, is at the extremity of the larger axis of his 

 ellipse, and advances more slowly ; sometimes, on the contrary, 

 his velocity is accelerated and passes through a maximum to 

 another position of his orbit. 



At the same minute all the planets are revolving round the 

 sun, some with their maximum velocity, others w ith their mini- 

 mum velocity, others, agair, with intermediate velocities. We 

 may make addition of all these kinetic energies of the whole 

 solar system, and differentiate the total equation with reference 

 to time. The variations thus obtained for each hour will 

 naturally eliminate all the quantities of constant kinetic energy 

 represented by the rotati. n of the stars on their own axes ; they 

 will merely show the increase or the diminution of the whole of 

 the variable kinetic energies of the svstem. 



One may easily draw a curve of thtse variations calculated by 

 the ephemerides of the principal planets. Jupiter will play a 

 preponderating role in this calculation. 



Considering still the second hypothesis, in which the attraction 

 is merely the result of shocks, it is evident that the attraction 

 manifested by each planet for the bodies which are on its surface 

 will be the echo of the kinetic energy disposable on this planet. 

 This kinetic energy will be variable according to the day and hour 

 of observation. 



In fact, the kinetic energy of the solar system being fixed and 

 constant, if the planets, on a certain day, absorb into their own 

 mass a maximum quantity of kinetic energy, the cause of gravity 

 on the earth will be diminished by the whole of the excess which 

 is accumulated in these bodies in motion, and the acceleration g 

 will pass through a minimum. On the other hand, when, a few 

 years later, the whole of the planets give a minimum total of 

 kinetic energy for their masses in motion, the value of g, for the 

 same reasons, must pass through a maximum. 



It is easily understood that the value of the terrestrial attrac- 

 tion cannot remain con tant if the disposable kinetic energy 

 varies in function of the time and of the respective position of 

 the other planets. 



Now, n e may calculate the total mass M of the system, the 

 partial masses and their variable velocities ; we obtain for these 

 variations considerable values ; then if we register carefully the 

 values of g obtained directly during observations which must 

 continue at the least several years, and if we trace a curve of the 

 values of g so obtained, we should find the following 

 coincidence : — 



The curve of variations of the total kinetic energy of the planets 

 must be inverse to the curve of values of g referred to the :ame 

 time. 



The differences between the maxima and the minima of the 

 two curves, taken on the same ordinate, will give the measure of 

 the velocity of propagation of the kinetic energy in the ether of 

 the solar system. 



These conclusions are rigorous in the case of the hypothesis, 

 J mv- = constant, 

 being in accordance with nature. 



In the case, on the other hand, of attraction being .an essential 

 property of matter, and of our having — 



J mv 2 + the potential = constant, 

 we should find {01 g a cons/ant, since g is the sole manifestation 

 of a constant potential, supposing the mass of the earth is 

 constant during the course of the observations of g. 



It "ill lie necessary, then, to take account of perturbations of 

 the moon for the measurements of g, as also of those of the sun, 

 then to verify whether, these corrections having been made, g is 

 constant. 



I believe that this experimental method is the only means we 

 possess of diagnosticating with certainty on the essential proper- 

 ties of matter, and of deciding between those two great theories 

 which are both maintained by men of incontestable merit. 



As to the measurement of g, there are several operative pro- 

 cesses, and it will be indispensable, before commencing observa* 

 tions, to discuss analytically the advantages of each of them, 

 and the modes of inscription of the values obtained. 



The optical means of registration, the mechanical actions 

 connected with the motion of pendulums, and the kind cf pen- 

 dulums, will be so many important subjects of discussion, in the 

 case of taking these researches in hand, which I consider as very 

 useful for the definitive settlement of physical theories. 



This is a rather long letter, you see, dear Teacher ; but I 

 thought to explain to you the object which I pursue, in its 

 general traits, happy indeed if the experiments may be under- 

 taken under your benevolent auspices. 



Accent, dear Teacher, I pray you, the expression of my 

 gratitude and entire devotion. Raoul PlCTET 



A GEOMETRICAL CONSTRUCTION GIVING 



THE RELATION BETWEEN THE WASTE 



AND USEFUL WORK IN A SHUNT 



DYNAMO 



'"THE ratio between the portion of electrical energy utilisable 



in the external circuit of a shunt dynamo and the portion 



wasted in heating the wire of the armature and field magnet is 



easily calculated as soon as one knows the resistances of the 



armature and magnet wires, and the resistance equivalent to the 



external circuit ; and I do not know that there is any great 



advantage in putting it into a geometrical form. Still there are 



people « ho prefer a construction to a formula, and the following 



construction is easily made, especially with the use of squared 



paper. 



In the figure annexed, let O A represent the resistance of the 

 armature between the points where the branching occurs ; O B 



the resistance of the field magnet wire ; and O C the resistance 

 of the external circuit, or its equivalent. 



Erect lines to represent the useful work (E.M.F. x current), 

 on any convenient scale, at c and at B ; viz. c E and B D. 



Join o D, producing E c to meet it at F. 



Lay off c G equal to E F ; draw E G and a horizontal through F. 



Then from their meeting point K draw a vertical, meeting c A 

 in H. 



The length H K so determined represents the waste portion of 

 the total electrical energy, on the same scale as B D or E c repre- 

 sents the useful. 



In this figure the effect of the armature resistance in tilting up 

 the line C A and so increasing the waste is very manifest ; the 

 increase of waste by decreasing the resistance o B is somewhat 

 less striking, but quite distinct ; the effect of a change in o c is, 

 as it should be, not so obvious. It may be noted that the most 

 economical value for oc is very nearly indeed a geometric 

 mean between O A and o B-o A ; which is an easy rule to apply 

 in practice. 



Liverpool, July 19 Oliver J. Lodge 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE 

 The following is the list of candidates successful in the com- 

 peti'ion for the Whitworth scholarships, 1882, in connection 

 with the Science and Art Department :— Charles Webster, 

 apprentice ; John H. Tomlinson, apprentice ; James M. Beaman, 

 fitter ; Thomas Turner, engineer ; D. Codrington Selman, 

 engineer; Charles B. Outon, draughtsman; George H. 

 Banister, draughtsman ; Frederick Lane, fitter ; William D. 

 Laird, engine fitter; Joseph Parry, engine fitter; Albert F. 

 Kaven-hear, apprentice ; Charles W. Carter, brass-finisher ; 

 Alfred Barrow, fitter ; Henry C. King, fitter ; Malcolm Douglas, 

 apprentice; Thomas H. Gardner, engineer; Ernest E. Haine, 

 engineer ; George Halliday, engineer ; George W. Buckwell, 

 dia ghtsman ; Louis H. Cochrane, engineer; William Duncan- 

 son, engine fitter ; Henry Brown, engineer ; William T. Hatch, 



