252 



NA TURE 



[April 29, 1909 



is already most appreciated in practice is tiie use 

 of tlie instrument to control tlie annealing processes 

 in connection with copper and its alloys. The whole 

 history of the constitution and structure of the more 

 important alloys of copper with one added element 

 at a time has been worked out and embodied in what 

 appear at first sight to be highly theoretical 

 " equilibrium diagrams." These diagrams, however, 

 enable us to understand the precise effect produced 

 upon the constitution and structure of any of these 

 alloys by thermal treatment. The structures resulting 

 from exposure to certain temperatures, followed by 

 either slow or rapid cooling, have been determined, 

 as well as the particular properties of the alloys 

 which correspond to these structures. An under- 

 standing of these diagrams therefore enables the 

 manufacturer or user to treat his alloys at the proper 

 temperatures, and to control the results with ease and 

 certainty by examining a few specimens of the metal 

 under the microscope and noting the type and the 

 size or scale of the structure. 



At the present moment the control of these pro- 

 cesses is only satisfactorily available for those groups 

 of alloys the constitution of which has beei) fully 

 investigated, but this is so far the case only for 

 binary alloys — i.e. those consisting of two metals 

 only. The majority of industrial alloys are much 

 more comple.K, and for these the theoretical guidance 

 is not yet available, principally because the complete 

 study of these complex systems is a matter of much 

 greater difficulty than that of the simpler binary 

 series. The fullest benefit of the microscope will 

 therefore only become available for workers who deal 

 with these complex alloys when the purely scientific 

 investigations have covered this difficult ground; but 

 meanwhile it is quite possible in practice to obtain 

 empirical data as regards the best micro-structure 

 and the treatment required to obtain it. Such data, 

 although not of equal value with the more complete 

 knowledge, form a useful temporary substitute. 



These few indications of the present practical utility 

 of the microscope in connection with engineering 

 materials, while very far from covering the whole 

 range of the subject, may perhaps be enough to show 

 that, even with existing knowledge, the instrument 

 is capable of rendering — and is, in fact, rendering — 

 the greatest service to engineering and metallurgical 

 practice. These fruits are already derived from little 

 more than twenty years of metallographic investiga- 

 tion. For the future of this young science, therefore, 

 the highest hopes appear to be well founded. 



W.^iLTER ROSENHAIN. 



THE YIELDING OF THE EARTH TO 

 DISTURBING FORCES.' 

 'T' HE problem of determining how much the earth 

 ■'- as a whole actually yields to the tidal disturbing 

 forces of the sun and moon was definitely brought 

 before scientific men by Lord Kelvin. He pointed 

 out that, from observations of the tides of long period, 

 it ought to be possible to obtain some definite 

 information, and he urged the establishment of 

 gravitational observatories fitted with instruments for 

 detecting the lunar disturbance of gravity. However 

 rigid the body of the earth may be, it necessarily 

 yields a little to the deforming action of the sun 

 and moon. This action produces two kinds of effect. 

 In the first place, it alters the shape of the earth. 

 If the earth were a perfect sphere, it would be drawn 



-' Based on a paper by Prof. A. E. H. Love, F.R.S., read before the Royal 

 Society on J; 



NO. 2061, VOL. 80] 



out by the attraction of the moon, for instance, into 

 a prolate ellipsoid of revolution. The actual earth, 

 of a shape that is nearly spherical but presents certain 

 inequalities, acquires under the action of the moon 

 a slight additional inequality of figure, of the same 

 type as that which answers to elongation in the 

 direction of the long axis of the ellipsoid and flatten- 

 ing round the parts remote from that axis. As the 

 moon moves relatively to the earth, the long axis 

 of the ellipsoid moves about in the earth, so that 

 a corporeal tide is raised in the earth. Besides raising 

 a corporeal tide, the action of the moon alters the 

 attraction of the earth. If the change of external 

 shape only is taken into account, the alteration of the 

 attraction consists of the added attraction, due to 

 the protuberances at the ends of the long axis of the 

 ellipsoid, coupled with the loss of attraction, due 

 to the flattening round the parts remote from 

 these ends. But, since the material of which the 

 earth is made up is not homogeneous, a similar 

 effect is produced by the elongation and flattening 

 of the surfaces of equal density, and, since the 

 material is not absolutely incompressible, the density 

 must be in some parts increased and in others 

 diminished, owing to the attraction of the moon being 

 different in different parts. The alteration of the 

 earth's attraction by the action of the moon is there- 

 fore of a somewhat complex character. The effects 

 produced by the action of the sun are similar to those 

 produced by the action of the moon. 



Many attempts have been made to measure the 

 changes of level that are due to the tidal disturbing 

 forces of the sun and moon. In the majority of such 

 attempts, instruments of the horizontal pendulum 

 type have been used. The displacement of a horizontal 

 pendulum that would be produced by the attraction 

 of the moon, or the sun, if the earth were absolutely 

 rigid, is known, for the attractions of the moon and 

 sun are known. In the actual case, owing to the 

 yielding of the earth, all we can hope to determine 

 by observations of the tides or of the displacement 

 of horizontal pendulums is a relative change of level, 

 and to measure this is far from easy. The effect to 

 be measured is extremely minute, and it is liable to 

 be obscured, or even disguised altogether, by the 

 effects of air currents and of changes of temperature. 

 Recently Dr. O. Hecker, of Potsdam, has succeeded 

 in overcoming the experimental difficulties. By 

 setting up two horizontal pendulums in an under- 

 ground chamber, and observing their behaviour 

 during a protracted period, he was able to show that 

 the effect of the moon, in particular, is perfectly 

 definite, that in phase it follows very closely the motion 

 of the moon, and that in amount it is almost exactly 

 two-thirds of what it would be if the earth were 

 absolutely rigid. 



Hecker 's result confirms decisively the results which 

 had been found with much less perfect experimental 

 means by previous observers. It leaves no shadow of 

 doubt of the actuality of a corporeal tide produced 

 by the moon. It accords also with those results, 

 deduced from observations of fortnightly tides, which 

 were used by Lord Kelvin in his famous estimate of 

 the rigidity of the earth. This estimate was obtained 

 by working out mathematically the change of shape 

 that would be produced by the attraction of an 

 external body, such as the moon, in a solid elastic 

 globe, of the same size and mass as the earth, if 

 the material of which it is made were homogeneous 

 and absolutely incompressible. When these simplify- 

 ing assumptions are made, the change of attraction 

 is calculable in terms of the change of shape, and 

 the measurement of the relative change of level leads 

 easily to the determination of the absolute change of 



