32 



KNOWLEDGE. 



[February, 1903. 



not always possible, the wave-lengths of the lines cannot 

 be detennined unless some of them are recognisable by 

 their peculiar f^roupiugs, or otherwise. In this case the 

 previous method may sometimes be used by superjwsiug a 

 solar spectrum jihotographed with the same instrument, 

 or the wave-lengths may be determined by measurement 

 of the photograph, basing the results on the lines which 

 can be idonf ified at sight. One mode of reduction may be 

 illustnitfd by (he use of Figs. 2 and 3. Suppose a finely- 

 dividcil scale, say a rule divided to hundredths of an inch, 

 to be laid on the bright-line spectrum in Fig. 2, the 

 triplet of iron lines having already been identified in Fig. 3. 

 Now read the positions of the.se three lines on the scale, 

 and those of any other bright lines for which wave-lengths 

 may be sought. Call the first three readings f j, jo, s^, and 

 the corresponding wave-lengths Aj, A^,, X.,, and solve the 



equation C 



' X = A„ -I 



S - So 

 so as to determine X„. C, and j„, by first forming three 

 (iquations in which X and 9 have corresponding values. 

 Then, by using these constants, the wave-length corre- 

 sponding to any other value of s may be readily calculated. 

 This formula for the calculation of wave-lengths from 

 prismatic spectra was first suggested by the late Prof. 

 Cornu, but has lately become more widely known and 

 adopted through its re-introduction by D.r. Hartmann. It 

 is the equation to a rectangular hyperbola with respect to 

 axes parallel to the asymptotes, A„ and Sg being the co- 

 ordinates of the intersection of the asymptotes, and is 

 based on the supposition that this curve is at least very 

 nearly identical with the curve of dispersion of a prism. 

 The measurements of the photograph must, of course, be 

 made with the greatest possible accuracy, for which 

 purpose a stage micrometer is usually employed. 



It is by methods such as these that the tables of wave- 

 lengths of lines in terrestrial sjsectra, which are indispen- 

 sable in attempts to identify the chemical constituents of 

 the heavenly bodies, have been prepared. A very great 

 service has been rendered to all engaged in spectroscopic 

 work by Ur. Marshall Watts, who has brought together 

 all the tables of wave-lengths which are scattered through 

 the numerous scientific publications.* 



In making use of such tables for the purpose of identi- 

 fying lines met with in astrophysical investigations, special 

 attention has to be given to the fact that in numerous 

 cases the spectrum of a terrestrial substance varies very 

 considerably with the conditions of experiment. The 

 spectra of metals, for example, may be studied by vola- 

 tilising them either in the oxyhydrogen flame, the electric 

 arc or electric spark, and very often great diiierences in 

 the spectra are noted. Magnesium furnishes an interesting 

 example. As will be seen from Fig. 4, the arc spectrum 



Fig. 4. — (1) Arc, (2) Spark, Spectra of Magnesium. 



shows several strong lines, most of which also appear iu 

 the spark spectrum, but the latter shows, in addition, a 



* " Index of Spectra," and Appendices. Published by Abel 

 Haywood. 



strong line at wave-length 4481'3, a line belonging to the 

 class called " enhanced lines " by Sir Norman Lockyer, 

 since its intensity is increased in passing from the arc to 

 the spark spectrum. On investigating the evidence as to 

 magnesium in the solar spectrum, it is found that while 

 the arc lines are there represented, the enhanced line is 

 conspicuously absent. But if a similar comparison be 

 made with the spectrum of Sirius, the line at 44sr3 is 

 seen to be one of the strongest in the spectrum, while only 

 the stronger of the arc lines are at all represented. It is 

 quite clear then, that comparisons must not, be limited to 

 spectra produced under one set of experimental conditions. 

 At times it is evtm necessary to go beyond our experi- 

 mental resources to identify the lines met with in some of 

 the stars, and by supposing continuity of change tr}' to 

 define what the spectrum of a substance would be when 

 subjected to temperatures greater than any at the 

 command of the laboratory worker. Thus, in the sijectra 

 of such stars as Kigel, there is a line which appears to 

 agree perfectly in position with the above-mentioned 

 spark line of magnesium, but as no other lines of 

 magnesium are certainly present, it is necessary to 

 suppose that the change, partially effected when the spark 

 is substituted for the arc, is completed by the higher 

 temjjerature of the star. 



THE PATH OF THE MOON.-I. 



By A. C. D. Crommelin. 



The subject of the Moon's motion is a frequent source of 

 perplexity to students of astronomy ; they meet with 

 statements in text-books which at first sight seem incom- 

 patible with one another, and are unable to reconcile 

 them. The key to the solution of these difficulties lies in 

 a perception of the fact that all our ideas of motion are 

 essentially relative. If we picture to ourselves one solitary 

 orb in boundless space, the statements that it is at rest or 

 in motion are alike meaningless to us. We must have 

 some point of reference to enable us to estimate any 

 change in its position, and this at once introduces the 

 conception of relative motion. Thus in discussing the 

 motion of the Sun and its attendant planets through 

 space we make the assumption that the group of stars 

 around us has on the whole no tendency to move in one 

 direction rather than another. We thus take the centre 

 of mean position of the group of stars as a fixed point, and 

 deduce the Sun's motion relatively to it. Hence different 

 groups of stars may (and do) give different results for 

 the solar motion, which simply implies that the one group 

 is not at rest relatively to the other group. So in the 

 case of the Moon our ideas of its path depend entirely on 

 the point that we select as our point of reference ; there 

 are two points that naturally suggest themselves, viz., (1) 

 the Earth, (2) the Sun. The apparent contradictions that 

 were alluded to above arise from the fact that some of the 

 statements refer to her geocentric, others to her helio- 

 centric path. 



Consider the case of a man walking round and round 

 the mast of a ship, always keeping at the same distance 

 from the mast. Then it is a perfectly legitimate statement 

 that his path on the deck is a circle described with uniform 

 speed. The words m italics are sufiicient to qualify the 

 statement and to indicate the origin from which the 

 motion is reckoned. 



On the other hand it is an equally legitimate statement 

 that his path on. the sea is an undulating or wave-like 

 curve, described with variable speed, greatest when he is 

 walking towards the bow, least when towards the stern. 



We can get a good representation of the Moon's path 



