344 
is followed more closely than in previous editions, 
and the inorganic portion of the volume rather 
than the organic has been developed in accord- 
ance with the increased attention which, the 
editors say, has been directed to inorganic 
chemistry’ of late years. Precise details from 
original memoirs, outside the scope of the 
ordinary text-book, have been included and will 
increase the value of the work for more advanced 
students. 
LETTERS TO THE EDITOR. 
[The Editor does not hold himself responsible for 
opinions expressed by his correspondents. Neither 
can he undertake to return, or to correspond with 
the writers of, rejected manuscripts intended for 
this or any oiher part of Nature. No notice is 
taken of anonymous communications. | 
Distance of the Visible Horizon. 
Tue subject of terrestrial refraction and its effect 
on the distance of the visible horizon, about which Mr. 
Backhouse inquires in NaTurE of September 25, is 
very fully discussed in the second volume of Jordan’s 
- “Handbuch der Vermessungskunde.” The formula 
there proved is s 
MS 
a= Ns h 
1—# 
where a=distance of visible horizon. 
r=earth’s radius. 
k=coefficient of refraction (mean value o-13). 
h=height of observer. 
This formula reduces to 
Distance in statute miles=1-312/”height in feet. 
The subject is also discussed in Gillespie’s ‘‘ Higher 
Surveying,” where, using a slightly different co- 
efficient of refraction, the formula arrived at is very 
nearly the same, viz. :— 
Distance in statute miles=1-317/height in feet. 
It is easy to construct a table from either of these 
formula which will give the distance of the visible 
horizon at any height under average atmospheric con- 
ditions. 
The method of reducing trigonometric heights de- 
scribed by Capt. Tizard, where the refraction-angle is 
taken at 5” for each nautical mile of distance, is 
equivalent to using a refraction-coefficient of 0-18 in 
place of Jordan’s 0-13. My own experience in the 
Red Sea and Gulf of Suez is that Jordan’s value is 
tolerably correct near midday in winter and spring; 
this would imply that 4" per nautical mile of distance 
is a nearer value than Capt. Tizard’s 5” under those 
conditions, and as a matter of fact the substitution of 
the lesser value leads to a rather better agreement for 
the height of Jebel Hooswah than that shown in 
Capt. Tizard’s table. : 
Abnormalities of refraction, such as Capt. Tizard 
notes, are tolerably frequent over tropical seas, and 
one naturally avoids making measurements of altitude 
when the conditions are palpably abnormal. The 
variation of 18° in the altitude of the horizon in the 
Arctic regions, quoted by Capt. Tizard, is doubtless 
a misprint for 18’ or 18"; but in any case such a figure 
is meaningless unless the height of the observation- 
point is given. 
It is not temperature per se which affects refraction, 
so much as the vertical temperature-gradient in the 
air; this varies very rapidly in the early morning 
hours, but becomes more steady about noon. I have 
found that at fair altitudes the refraction is in general 
NO. 2299, VOL. 92] 
NATURE 
_I was previously unacquainted. 
[NovEMBER 20, 1913 | 
a orn 
wonderfully constant in the middle of the day, sa 
between 11.30 a.m. and 3 p.m.; and by restrictin 
observations for level to this time of the day I have 
obtained very much more concordant results than tho: 
quoted by Capt. Tizard. If the object is only visible 
in the early morning or late evening, an evening — 
observation is much to be preferred to a morning one. — 
The table given by Capt. Tizard is liable to give ar 
exaggerated impression of the range of refraction 
The differences of height found for the same point — 
by his various observations probably depend not so” 
much on variations in refraction, as on the roughness — 
of the angular observations; in all cases except two, — 
his depression-angles are only given to minutes, and 
a minute of arc at a distance of fifty-eight nautical 
miles subtends more than 100 ft. It is easy nowadays — 
to measure the vertical angles well within 5” of the 
truth, using only a 6-in. micrometer-theodolite; but 
perhaps in 1871 the instruments available were of a 
less accurate nature, and one must not be too critical 
of the results obtained. I would, however, venture 
to point out that it is incorrect to take the arithmetic — 
mean of the heights from a number of observations — 
at different distances when the least certain factor in_ 
the height (the correction to the height due to refrac- 
tion) varies as the square of the distance; and it is 
scarcely scientific to correct for refraction to single — 
seconds when the observations themselves are only 
taken to the nearest minute, or to calculate heights 
to four significant figures from distances given only 
to three. Joun Batt. 
Survey Department, Cairo, October 2. pity 
Wit reference to the remarks of Dr. John Ball, 1 
am much obliged to him for directing my attention 
to Jordan’s ‘‘ Handbuch der Vermessungskunde”™ and — 
Gillespie’s ‘‘ Higher Surveying,” two works with whic 
The coefficient for refraction given by Jordan is the 
mean of a number of results by different observers in 
different countries, the originals varying from o-105 to 
0-167. ; . 
These results show that the refraction is a very — 
vagiable quantity, and that the results inland are — 
different from those near the sea. In Gillespie’s work 
he shows how the refraction varies at different hours — 
in the day on the coast of California (a) from a height 
of 57 metres, and (b) from a height of 1173 metres, 
being least near noon, and greatest in the morning 
and evening. From the height of 57 metres the 
coefficient varied from 0-14 to oto, whilst from the 
height of 1173 metres it varied from 0-09 to 0-06. 
Gillespie publishes curves showing the results ob- 
tained. But he points out that the refraction is a very 
variable quantity, and it is doubtful whether the same 
curves would be obtained at all seasons at the same 
place. These are the very observations that are re 
quired. ; 
It is quite true, as Dr. Ball points out, that if a 
Jebel Hooswah a refraction of 4 seconds instead of 5 
per mile was used the results would be in close 
accordance, but he does not appear to have seen that 
if a refraction of 6 seconds instead of 5 per mile wa 
used for the Jebel Serbal observations they would be - 
still more in accordance with each other. Therefore 
on different days and from different heights the results 
in the one case would be closer if the coefficient fo 
refraction was decreased, and in the other if it was 
increased. Abnormal refractions are more common if 
high than in low latitudes; the greatest I have seen” 
personally was in the Baltic Sea. 7 
With reference to Dr. Ball’s observations on the 
table given by me I reply as follows :— 
