132 
errors should have less effect in proportion as the con- 
ditions for securing accuracy in the solution of the 
problem increase. “For instance, if we are going to 
measure a distance of two, four, or six hundred miles, a 
base of a mile or less in length will give us a very ill- 
conditioned triangle ; but as we increase the length of the 
base, we should expect greater consistency in the results. 
Unfortunately this expectation is not realised. As an 
illustration, we select, out of the mass of measures that 
Prof. Cleveland Abbe has collected, three series of 
observations. The earliest of these sets was made in 
1839, by MM. Bravais and Lottin in Norway, in latitude 
about +70°. The stations selected provided a base line 
about ten miles in length. Even at this moderate dis- 
tance, the two expert observers could not recognise the 
same features in the auroral arch, or be certain that the 
angles measured with their theodolites referred to the 
same point. But Bravais, greatly daring, boldly applied 
trigonometrical methods, and deduced a parallax with 
mathematical rigour. Out of seven measures, as shown 
below, three parallaxes are negative and four positive, 
the total range being more than eleven degrees. 
Parallax Parallax 
hima’ 5 A bh. m Oe 
1839 January 12, 5 37-342 | 1839 January 21, 6 2-1 34 
” ”? 12, 6 2+2 13 ” ” 21, vA Sitat 4 
” 23 {2, 9 30+9 52 ? 2” 21, 7 33 +0 45 
nn 3 12, 1036-0 8 
Bravais concluded from all his observations that the 
mean altitude of the auroral arch is between 1ooand 150 
kilometres, but suggested that in order to determine “the 
parallax of the aurora more precisely than we have been 
able to do, it would be necessary to employ a longer base 
than ours, say about 100 kilometres in length, and 
directed as nearly as possible parallel to the vertical 
plane through the culmination of the arch.” Fifty years 
later, Bravais’ suggestion was carried out. Tromholt of 
Rostock, in Norway, occupied one of the stations near 
the scene of Bravais’ earlier investigations, but extended 
the base line to a length of 66 miles. From one end 
of this base line, Tromholt made no less than 634 
measurements, while 367 were made from the companion 
site. On comparing the results, however, only sixty 
corresponded as to time and referred, or were supposed 
to refer, to identical objects. These sixty were again 
reduced to forty-two, for reasons which do not appear ; 
but it would be scarcely uncharitable to suggest that the 
remainder gave negative or impossible parallaxes. This 
modest remainder reminds one of Falstaff’s “ half-penny- 
worth of bread to his intolerable deal of sack.” The 
final result, however, taken for what it is worth, assigns 
altitudes to the auroree varying from 19 to 217 kilometres. 
Variations so great in amount cannot inspire confidence. 
It might, however, be objected that in the Tromholt 
series, since the observers were separated some too km., 
that only the upper features of the aurora could be 
visible simultaneously from both stations, and that if the 
true or localised aurora was confined to the lower strata 
of the atmosphere, more or less illusory results might be 
expected. But we have a third series, made in about 
the same latitude, in which the observers were sta- 
tioned only about a third of a mile apart, where they 
were in constant telephonic communication with each 
other, and where, therefore, the conditions were favour- 
able to the removal of some of the difficulties that beset 
the parallactic method. Without quoting in detail the 
results obtained, it will be sufficient to say that, on dis- 
cussion, the number of positive and negative parallaxes, 
even after judicious rejections, was found to be seven- 
teen and twenty-three respectively, and that consequently 
no trustworthy value of the height could be deduced. 
Prof. Cleveland Abbe shows in this particular case how 
NO. 1545, VOL. 60| 
NATURE 
[JuNE 8, 1899 
the calculus of probabilities has been forced in order to 
derive a plausible altitude from these observations. 
There is, however, no necessity to labour the point. 
We are simply concerned to show that the method tried 
under various conditions fails to give consistent results. 
Those who believe that the aurora is confined to the 
upper regions of the atmosphere reject the largest paral- 
laxes, while those who are fighting for a low aurora will 
only accept the large values. The one fact which seems 
to stand out clearly after much patient examination is 
that the parallax does not increase with the increase of 
the length of the base line, or, in other words, it cannot 
be a true parallax. There is no dearth of reasons to 
explain these discrepant results. The inevitable error of 
observation arising from the feebleness of the light, the 
want of clear definition at the boundary of the arch, the 
possible movement of the object itself, and the want of 
absolute synchronism in the measurements at the stations, 
would be more than sufficient to make the method un- 
trustworthy. 
In presence of these difficulties, other methods depend- 
ing on quite different principles have, as before inti- 
mated, been suggested and applied. The general prin- 
ciple involved is to derive the height from “observations 
made at a single station, thus eliminating the second 
observer and the errors he introduces, putting in his 
place some more or less plausible suggestion as to the 
origin of the aurora itself. Galle, for instance, assumed 
that an auroral streamer is parallel to a free magnetical 
needle on the earth’s surface, vertically below the beam. 
By observing the zenith distance of the auroral corona in 
his magnetic meridian, he obtained the angle made by 
his vertical with the parallel lines of light that compose 
the aurora, or the dip of the needle suspended in the 
region whence the lightemanates. The magnetic charts 
show at what point on the earth’s surface the needle 
would have the same dip. This gives a right-angled 
triangle whose base is known, and whose vertical side is 
the desired height. The weak point in the method is the 
assumption that the dip of the needle in the place where 
the corona is presumed to be coincides with that at the 
earth’s surface immediately beneath it. Another method 
that has been applied is due to Bravais. It assumes that 
the auroral arch throughout its whole extent exists at a 
uniform distance above the earth’s surface. If this as- 
sumption were Justified, the determination of the azimuth 
and altitude of the two ends, and of the summit of the 
arch, would lead toa knowledge of its height. The method 
has been repeatedly tried with some modifications con- 
cerning the curvature of the arch, and of the position of 
the centre of the circle; but the very number of the 
variations that have been made condemns the accuracy 
and the applicability of the method. The observed 
apparent velocity of the motion of the arch, as seen from 
two stations in a magnetic meridian, has also been tried ; 
and indeed, without further enumeration of the plans 
that have been suggested, one may say that the ingenuity 
and industry brought to bear upon this problem have 
been such, that if the definite beams and arches possessed 
a real existence and a definite locus, its solution would 
have been assured. That the parallax has remained so 
long indeterminate is probably due to the fact that the 
question has not been broached along appropriate lines. 
In his careful review, Prof. Cleveland Abbe makes some 
practical suggestions which, if applied, would go a great 
way to show how far optical illusion and perspective 
displacement affect this luminous phenomenon, which 
for so long has supplied poets with a simile for in- 
stability, and which under scientific examination gives 
additional point to the well-known lines of Burns :— 
“* Like the Borealis race 
That flit ere you can point the place.” 
