January 12, 1899] 



NA TURE 



259 



Cal. This gives a preponderance of weight to the determination 

 of the coordinate V (X pissing through Greenwich), but a 

 station in Portugal, which may possibly be secured later, would 

 essentially increase the accuracy of X. Tschardjui, in Russia, 

 and Ukiah, in California, ate nearly opposite, and Mizusawa, in 

 Japan, is in the only remaining unoccupied quadrant. The 

 scheme proposed is, therefore, a favourable one for the study of 

 the motion of the pole. No one knows as yet how long it will 

 be desirable to continue the observations. The period now pro- 

 vided for is five years, but it is proposed to buy the land upon 

 which the observatories will be located, or lease it for one 

 hundred years. It is evident that at least twenty-one years 

 would be desirable, because during the seven years of observ- 

 ations already made the pole has returned nearly to its mean 

 position, and three of these cycles should be completed before 

 any definite idea can be had as to its mean path. The cost of the 

 entire work will be about 2000/. annually. The visual method 

 is to be followed regularly without, however, excluding the pos- 

 sibility of employing later the photographic one, which has 

 already given excellent results. Twelve groups of stars, each 

 comprising eight pairs, will be selected. Six pairs in each 

 group are destined for the latitude determinations proper, while 

 the two remaining pairs, having great zenith distances (about 

 60°), will, it is hoped, throw light on the question of refraction. 

 The observing period for each night is four hours, and will vary 

 from 7 p.m. to 3 a.m., depending on the situation of the group. 

 The instrumental outfit will consist of a zenith telescope and 

 astronomical clock for each station, except that of Japan. Here 

 a chronometer will be substituted for the clock, on account of 

 the frequency of earthquakes. 



Although the object of the general conference was scientific 

 discu.ssion, a faithful historian cannot ignore the social, and 

 humanitarian side of the function. From our entrance into the 

 beautiful capital of Wurtemberg until the time of our departure 

 we were the recipients of the most cordial hospitality. 



Before closing the present paper, attention should be called to 

 a few points of interest noted during the trip to Stuttgart and 

 return. A flying visit was made to the Royal Observatory at 

 Berlin, the Reichsanstalt at Charlottenburg, and the Geodetic 

 Institute at Potsdam. At Paris the offices of the geographic 

 service and the International Bureau of Weights and Measures 

 were examined, and part of one day was devoted to the English 

 Ordnance Survey at Southampton. 



An interesting object at the Berlin Observatory is the instru- 

 ment with which Kiistner discovered the variation of latitude ; 

 not alone because of the splendid result achieved, but on account 

 of the conditions under which the work was done. It is mounted 

 on a pier more than twenty feet above ground, on a subsoil of 

 sand, in the middle of a city, with bad atmospheric conditions 

 and about one hundred feet from the public thoroughfares. In 

 spite of these adverse circumstances a new fact was added to 

 science, which had baffled the efforts of larger telescopes under 

 immeasurably better conditions. There is much encouragement 

 in this to investigators with scanty means at their disposal. 



At the Aichungs-Kommission a balance was shown which 

 ea.sily determines the weight of a kilogram with an error of 

 1/200 of a milligram, being 1/200,000,000 part of the quantity 

 sought. They have also a complete series of weights in quartz 

 from 1/2 gram to one kilogram, and thermometers giving the 

 temperature by estimation to i/iooo of a degree Centigrade. 



At Charlottenburg the most striking feature was the extension 

 and perfection of the organisation. Nine buildings in all, of 

 which the two larger are devoted, one to theory and'the other to 

 practice, have cost, together with the running expenses since 

 1887, 3,000,000 marks. The annual outlay is at present about 

 18,000/. 



The Geodetic Institute at Potsdam has been much less ex- 

 pensive, and presents many admirable points of arrangement and 

 administration. Among the details may be cited : the clock 

 room, always maintained at a temperature between 20° and 21' 

 Centigrade ; the pendulum room, artificially heated on all sides, 

 including the floor ; a pillar over fifty feet high, and correspond- 

 ingly thick, with meridian marks several miles away, to study 

 changes in azimuth and the movement of the earth's crust ; and 

 finally a small photographic instrument, by means of which the 

 occupation of a station only requires eight minutes, and gives a 

 determination of the geographical position in latitude within two 

 seconds of arc. The subsoil, as at Berlin, is nothing but sand. 



At Sevres, near Paris, several interesting instruments w-ere 

 seen, among which may be especially mentioned that designed 



NO. 1524, VOL. 59] 



for the comparison of the metre with the wave-length of light 

 following Michelson's method, and the apparatus for the de- 

 termination of coefficients of expansion according to the method 

 of Fizeau. Some recent experiments have been made on a com- 

 position containing 36 per cent, nickel and 64 per cent, steel. 

 It appears that the expansion from heat is thus reduced to about 

 1/50 of what we should expect from the individual components. 

 This discovery will simplify enormously the solution of problems 

 where the temperature question has thus far been the great 

 difficulty. It will, for example, be a comparatively easy matter 

 to make pendulum clocks run with a daily correction of about 

 i/io of a second per day under varying temperature conditions. 



MIRAGE} 

 \X7HEN a ray of light passes from point to point oi a medium 

 '' which is everywhere similarly constituted, its path is a 

 straight line ; when it passes from one medium to another 

 medium of different density, then the ray of light is refracted or 

 bent at the surface which separates the two media. When the 

 ray passes from one medium to another which is denser, the 

 refraction or bending is always towards the normal to the surface 

 separating the two media at the point of incidence ; when, on 

 the other hand, the ray passes from a medium of a certain 

 density to one of less density, then the bending is always from 

 the normal to the common surface at the point of incidence. 

 The earth is surrounded with a spherical envelope of air, and if 

 that air were always of the same density everywhere its refractive 

 index would be the same, and there would be no terrestrial 

 refraction. But the spherical envelope which surrounds the 

 earth is not all of the same density, and the refractive index of 

 the air varies with the density. There are two causes, in the 

 main, which militate against the uniform density of the atmo- 

 sphere ; one is barometric pressure, and the other is temperature. 

 Taking no account of temperature for the moment, taking 

 merely as the cause barometric pressure, the density of the air 

 diminishes gradually upwards from the surface of the earth, so 

 that the refractive index of the air diminishes upwards. The 

 diminishing of the refractive index is not absolutely propor- 

 tional to the decrease of density, but it is found by experiment 

 to be sensibly proportional to the excess of the density over 

 unity. The circumstance of normal refraction in the British 

 Isles, as regards temperature, is that there is a gradual diminu- 

 tion of temperature upwards at the rate of about 1/300° F. for 

 every foot of ascent. As the air gets cooler the density in- 

 creases, so the tendency is to some extent to counteract the 

 effect of barometric pressure, but it does not altogether do so. 

 The result in the normal refraction of the British Isles is that 

 there is a gradual diminution of density upwards. 



We may consider the air to be stratified in horizontal layers ; 

 as a matter of fact, it is stratified in spherical layers, but it will 

 simplify matters to consider it stratified in horizontal layers, the 

 more so as the sphericity of the earth, though it is a slight cause 

 of terrestrial refraction, is not by any means the chief cause ; 

 terrestrial refraction would still exist if the earth had no 

 sphericity, and if its surface were perfectly plane. I show you 

 here a diagram representing the normal state of the atmosphere, 

 and showing the curvilinear path taken by a ray of light when it 

 pa.sses from one point of such an atmosphere to another point 

 horizontally distant from it. The reason a curved path is taken 

 is this : supposing the ray to have a general direction upwards, 

 and supposing it to have been inclined at incidence at a certain 

 angle with the normal, as it is going from a medium — air — to 

 air which is less dense, it bends away from the normal, and 

 therefore there would be a successive bending away from the 

 normal at each layer until finally the ray would arrive at the 

 highest point in the diagram. Then, if it were to pass down- 

 wards, it would be passing from a medium of a certain density 

 to one of a greater density, and it would approach the normal at 

 each surface of separation of the media, and therefore its path 

 would be a curved path presenting concavity downwards. A 

 r.ay of light will actually take some such path, because by 

 curving upwards it takes the path which it can pass over in the 

 least time. Generally, a ray of light takes the minimum path 

 as regards time, and it is found to curve up into the Layers of air 

 which are of less density, because it can traverse them with 

 greater velocity. It is important to notice that a ray of light 



1 A lecture, delivered al Ihe Camer.T Cluli, by ll.aior P. \. MacMahon, 

 F.R.S. 



