February 17, 192 1] 



NATURE 



789 



Mercury's apsidal motion. For the expression 



/velocity of planet V , • , • , 

 3l 1 -1' <■ 1- L^ /.which IS the angular motion 

 \ velocity of light / ' ° 



of the apse (in fractions of a circumference) 

 per revolution of the planet, involves no empirical 

 or arbitrary constant. We can express the reason 

 for the advance in simple terms thus : At infinity 

 the relative velocity is zero, and the law is the 

 Newtonian one, but the nearer we approach the 

 central orb the higher becomes the velocity, and 

 the greater the extra force. Hence we have 

 another case of the force falling off more rapidly 

 than the inverse square, which we have seen to 

 lead to apsidal advance. 



It is interesting to note that the advance per re- 

 volution varies as (velocity)- or as i la. Hence the 



advance per century varies as a"?, or it falls off 

 much more rapidly with increase of o than the 

 Hall law, which gives a"J. In the course of 

 centuries this would discriminate between them, 

 independently of the lunar test ; but the orbits of 

 Venus and the earth are so nearly circular that 

 the time for that test has not yet arrived. 



In the case of Mars we may note that F. E. 

 Ross's rediscussion of the observations of that 

 planet and of the mass of Venus takes off some 

 2" from Newcomb's value of its excess of apsidal 

 motion in a century. When we further remove 

 the Einstein term 1-3", we are left with some 

 2-7" ; as the actually observed quantity is the 

 product of 27" by the eccentricity (i/ii), it falls 

 well within the limits of observational error. 



The Displacement of Solar Lines. 

 By Dr. Charles E. St. John, Mount Wilson Solar Observatory, Pasadena, California. 



THE agreement of the observed advance of 

 Mercury 's jjerihelion and of the eclipse results 

 of the British expeditions of 191 9 with the deduc- 

 tions from the Einstein law of gravitation gives 

 an increased importance to observations on the 

 displacement of absorption lines in the solar spec- 

 trum relative to terrestrial sources, as the evidence 

 on this deduction from the Einstein theory is at 

 present contradictory. Particular interest, more- 

 over, attaches to such observations, inasmuch as 

 ihe mathematical physicists are not in agreement 

 as to the validity of this deduction, and solar 

 observations must eventually furnish the 

 iriterion. 



Prof. Eddington's view, if I understand it, is 

 that the theory cannot claim support from the 

 present evidence, nor can observed displacements 

 not agreeing with the theory be on that account 

 regarded as in the slightest degree adverse to it, 

 the only possible conclusion in his view being that 

 there are certain causes of displacement of the 

 lines acting in the solar atmosphere and not yet 

 identified ("Space, Time, and Gravitation," 

 p. 130). 



The great majority of metallic lines observed 

 for differences between their wave-lengths in the 

 sun and terrestrial sources do show displacements. 

 These differ in most cases from those deduced 

 from the Einstein law of gravitation in ways as 

 yet unexplained. If reasonable solar causes can 

 be adduced to account for the wide discrepancies 

 between theory and observation, the position of 

 the generalised theory of relativity would be 

 greatly strengthened. 



.According to the theory, the displacements arc 

 to the red, and are projxjrtional to wave-length, 

 being independent of the intensity of the lines and 

 of the element to which they belong. Observa- 

 tional results differ from those deduced from the 

 theory in at least four important ways. The 

 observed displacements are not proportional to 

 the wave-length ; they differ from element to 

 element in the same spectral region ; for the same 



NO. 2677, VOL. 106] 



element and spectral region they vary with line- 

 intensity ; the displacements show both large posi- 

 tive and negative divergences from the calculated 

 values. Interesting examples are found in 

 Jewell's early work [Asirophysical Journal, vol. iii., 

 p. 89, i8g6). The relative values here are of high 

 weight, and the data are important in that the 

 range of elements is wider than occurs in more 

 recent investigations. Divergences in the four 

 directions from the calculated displacements are 

 shown in the following extract from his observa- 

 tions on the differences in wave-length between 

 1 1 5 solar and arc lines : — 



For statistical discussion the quantity of data 

 available is as yet quite inadequate even in the 

 case of iron, the most widely studied clement. Not 

 only should the terrestrial and solar wave-lengths 

 be known to high precision over the widest pos- 

 sible range of spectrum, but also the pressure shift 

 per atmosphere. L'nfortunately, there are no pub- 

 lished data on the wave-lengths and pressure dis- 

 placements of the iron lines, in which, over a long 

 spectral range, the errors due to pole-effect in 

 the arc are reduced to the magnitude of the calcu- 

 lated Einstein displacement. I-"or other metallic 

 elements the data are even more deficient. With 

 a sufliciently large and varied accumulation of 

 material there is hope that the complex solar con- 

 ditions may he analysed, and the contributions to 

 the observed effects arising from the various 

 causes determined with some certainty. The 

 pressing need is for data of the requisite accuracy 

 and variety. This need adds interest to deter- 

 minations of wave-lengths and of pressure dis- 



