402 



NATURE 



[August 22, 1S95 



character. For on reducing them 1 find that beside furnishing, 

 from their great number, relatively accurate %-alues of the 

 ev)uatorial and polar diameters and of the polar flattening, they 

 yield a by-product as unex|)ected as it is important. Their dis- 

 cussion reveals, in short, what appears to !« unmistakable 

 evidence of a twilight upon the planet, sufticicntly pronounced 

 to be \Tsible from the earth, and actually to have been measured 

 unconsciously by Mr. Douglass. That Mars jxjssessed an at- 

 mosphere, we had vihat amounted to ])roof positive before : but 

 that the fact should .-igain be brought to light in this literal 

 manner, as a silver lining to a cloud of figures, is a [xiint of some 

 curiosity. The measures had no such end in view ; indeed, to 

 detect the presence of an atmosphere by measures of the 

 diameters had not suggested itself to any of the most adventurous 

 of observers. Yet, as will l)e seen, the quantities u|xin which the 

 evidence rests are so large as to be quite without the (xile of 

 accidental error, lieing ten times as great as the probable errors 

 of observation, and twice as large as those that disclose the polar 

 flattening. That they have hitherto escaped detection is due to 

 their having been masked by another factor affecting the size of 

 the polar diameter, as will appear in the course of this paper. To 

 the unsuspected presence of these two causes, at times nearly 

 offsetting each other, so far as relative values go, is attributable 

 in all probability much of the discrepancy in the determinations 

 of the polar flattening hitherto m.ade. 



The first measures were m.ade on July 6, and the last on 

 November 21, 1894. Krom October 12 they were taken nearly 

 every night. Those here given were all made by Mr. Dotiglass. 

 Later in the iiajwr I shall introduce others by Prof. \V. II. Picker- 

 ing, which confirm the result. But here at the outset it may be 

 well to point out that whether the results of many observers are 

 to \yt preferred to those of one is, omitting discourteous per- 

 sonalities, a question entirely of what is to be determined. If 

 the determination l>e one of absolute quantity, the more 

 otjservers the Ix'tter, provided they l>e good ; but if, on the other 

 hand, the determination be of relative magnitudes, one observer 

 is lietter than many, a.s his personal equation obligingly eliminates 

 itself, whereas two such e<|uations can by no possibility, short of 

 chance, eliminate each other. Now, in the present case, while 

 the determination of the planet's size, and even to some extent 

 of its jxilar flattening, are matters of absolute quantity, the 

 evidence of a twilight upon it is one which rests upon relative 

 results. The former, therefore, are subject to any systematic 

 errors there may be ; the latter, essentially free of them. In con- 

 sequence, the by-product in this case is actually more trust- 

 worthythan the main results themselves. 



Much care was taken in the matter of the Martian measures. 

 In the ones I shall first discuss, those made from October 12 and 

 November 21, Mr. I)ougla.ss adjusted the longituclinal thread of 

 the micrometer, jxirallel or perix*nclicular. as the case might be, 

 to the planet's polar axis, according to Marlh's ephemeris, and 

 then placed himself, so that the line joining his eyes was kejrt 

 parallel to tbjs thread or to the fixed transverse thread 

 at right angles to it, during any one set of ol)serva- 

 tions, the position being then recorded. As' measures were 

 taken in Ixjth ]x)sitions for each diameter at various times, 

 v»e have here a commrison of some eventual value. In 

 eye-estimates such orientation in the position of the ob- 

 server is al>solutely essential in order to correct his pos.sible 

 astigmatism. Into measures, however, astigmatism enters only 

 to cancel out. For if we consider the matter, it is at once 

 evident that the v^hole field is distorlccl in the same proportion, 

 the sface lx:twcen one turn of the micrometer and the next 

 Ijcing reduced cir exiKinded in the same ratio as the part of the 

 image mea.surcd. The astigmati.sm thus eliminates itself 



From Octoljer 12 to Novemlier 21, Mr. I)ougla.ss made in all 

 275 measures ; 140 of the equatori.il, and 135 of the |x>lar dia- 

 meter. In the reduction of the mca.siircs, account has 

 Ijccn taken of the place upon the micrometer .screw at 

 which the mca.surcs were made, an<l its appropriate value in- 

 trcKluced. For by the forethought of Mr. Douglass in sus|x;cting 

 the possibility of variation, we measured the value of a micro- 

 meter turn at different points of the .scale to confirm his 

 conjecture. 



Preliminary to the discussion of the results, it will be well to 

 explain ihi' rnrrcctions determined anrl applied. The first cor- 

 rei arising from refr.aclion. "Tnis is the correction 



dii- ' rcnli.-\l effect of refraction ii|x»n the planet's op- 



Fo- ..i the extremities of the (nrticular diameter niea.surcd, 

 I depend* Iwth upon the altitude of the planet at the lime of 



observation, and upon the inclination at that moment, of the 

 particular diameter to the vertical. In many cases it was so 

 small as not to make itself perceptible in the column. 



The correction for aberration, similarly a differential elTect, 

 was so utterly insignificant throughout as not to apjiear at all. 



The next correction is thai due to irradiation. Toward its 

 determination two different tests were made, in each case ujxm 

 both Prof. W. n. Kckering and myself; in the one the etiecl 

 should have been less than in the case of Mars, in the other 

 greater. .\s in both cases the observers substantially agreed, 

 the results may be accejited as having some impersonal value. 



The first test was made upon a railroad switch-head, a white 

 circular disc with a smaller black circle painted upon it. The 

 size of these circles was unknown to the observers. 



Their estimates were : 



(W. II. P.) ... (white rim) ... i ; (diameter black circle) .. i"3 



(P. I'-) „ „ ■•■ I : „ „ ,. i"'265 



The discs and their distance were then measured and gave : 



For diameter bl.ack circle ... ... 202 mm. 



For radius white rim ... ... 126 mm. 



For ratio ... ... ... ... ii',i 



For distance from eye 57 yds. 



Therefore I mm. equalled 3"'9. 



For the amount of the irmdialion in seconds of arc, .i, assume 

 the amount of the irradiation of the while rim .against the 

 general background of earth of a brown colour to have been 

 two-thirds that of the rim against the lilack circle. We have 

 then, for the first observer, the following equation to deter- 

 mine X. 



252 mm. 10/ 3 .<■ _ 2"o 

 212 mm. 6/3 .V I '3 ' 

 for the second observer : 



from which .v = 9-2 mm. or 36" 



40 



The second lest was on the moon (November 22), when the 

 old moon was seen in the new moon's arms. In this case the 

 irradiation proved for both observers 10 be one-seventh of the 

 radius of the old moon, or about 157". 



In the ca.se of Mars, the value for the irradiation probaljly lies 

 between these two limits. For the contrast between the 

 Martian limb and the sky is pretty certainly greater than that of 

 the white rim and the black circle of ihe switch-head, and less 

 than that of the moon's bright limb and the sky, to which the 

 contrast between the limbs of the old and of the new moon 

 closely approximates. 



It is to be noted th.at with a given illumination and a given 

 eye, the irradiation correction is a personal constant, not 

 depending upon the size of the disc measured and diminishing 

 inversely as the magnification. In all the measures sulisequent 

 to and including October 15, the power used was 860 ; in those 

 of October 12, it w,as6l7. The correction, therefore, for all 

 except those of October 12 was o"'lo; for those of October 

 12, o"-l4. 



Such, then, is the correction for irradiation upon the planeni 

 limb. The double of it, therefore, would need to be subtracted 

 from the measures of a disc .similarly placed to that of Mars 

 when fully illuminated. But the disc of Mars was not fully 

 illuminated even at the moment of opposition, ami grew less .so 

 as time went on. Now il will l)e evident on consideralii>n llint 

 the irradiation from the terminator nuist be very dilTeient from 

 that uiHUi the limb, inasmuch as the light fades away to nothing 

 at the one, while it has its full value at the other. 



To determine the amount f>f the correction needed at the 

 terminator it is to be observed that if 



7 = the areocentric angle between the sun and the earth ; 



a = the angle between the terminator and tile poiiu of the il- 

 luminated .surface of which the irradiation is sought ; ami | 



III = the ratio of the irradiation at Ihe liml) to the radius of 

 the disc, we have ft>r the extent of the irradiation nl 

 the terminator 



,„( '''"° — '\!,-/'cos7 - cos(7+o)) 

 \sin(7-fo)y \ / 



where 11 denotes the ratio of the irradiation to llie illumination, 

 and is equal to alxiut 2"; thai is, it lakes 2" liiiies the illumiiw- 

 lion to produce twice the irradiation effect. This value is g"l 

 from intcr-comparison of the above tests as limiting values, the 1 



NO. 1347. VOL 52] 



