244 
NATORD 
[ Fan. 11, 1883 
gradient with the height above the earth’s surface, due to 
the general temperature gradient between the equator 
and the poles, in conjunction with the earth’s rotation. 
This fact has been thoroughly investigated by Mr. Ferrel 
of the U.S. Coast Survey, and the results given in his 
“ Meteorological Researches,’”’ vol. i. In this work he 
has given on p. 45 the mean west-easterly component of 
the velocity at the surface due to the causes just men- 
tioned, and the term by which this increases with the 
height (in metres) for every fifth degree of latitude on the 
mean of all longitudes, for the months of January and 
July, and for mean annual temperatures, calculated from 
the observed barometric pressures and temperatures in 
every part of the world. 
For latitude 50° the eastward velocities at the surface 
and increment terms for the elevation are as follows in 
two different measures. 
Mean temperatures. January. July. 
Miles per hour 3°35+8°6% ... 3°97+12°IA ... 2°73+5°1% 
Feet per second 4°91 + ‘0024... 5°82+'0033% ... 4700+ 0014h 
where / represents the height in miles and feet respec- 
tively.t 
Owing to ¢hzs cause alone therefore the eastward (and 
therefore in our latitudes the prevailing) motion of the 
atmosphere will be increased on the mean of the year by 
83 miles per hour at a height of 5280 feet, or by 2} miles 
per hour at a height of about 1300 feet. 
The increase in the horizontal velocity which results 
from the joint action of these two factors, is thus probably 
very different from that which would arise from a mere 
diminution of friction alone, since at great heights this 
would theoretically become almost insensible. 
For a thoroughly satisfactory solution of the matter, 
nothing will avail except anemometrical observations 
made at every possible elevation (preferably, as I lately 
suggested in a paper read before the Meteorological 
Society, with instruments attached to kite-strings), but in 
the absence of these at present, it may be worth while to 
use some excellent observations on the velocity of differ- 
ent cloud-layers recently communicated to the Austrian 
Zeitschrift fiir Meteorologie, by Dr. Vettin,? for the pur- 
pose of showing the complete breakdown of Mr. Steven- 
son’s formula when applied to “great heights above sea- 
level.” 
The following table, which is taken from Dr. Vettin’s 
paper, gives the mean velocity of the clouds from all 
directions, at five altitudes to which they respectively 
belong, and which, together with their velocities, have 
been measured by methods described in detail in the | 
paper from which it is extracted :— 
TABLE I. 
Name of Barometric Height Numbes To eee 
SENS Preaek: feet. observations. second 
In. 
Upper cirrus . 11°968 ... 23,000 879 59°5 
Under cirrus el 7kOS Steel, SOO) eens 1047 51°8 
G@loudlets4 .. |... 22°441.... (7200 —... 1588 350 
Cloud nee 25 7 38n et SROO! na LOT 30°4 
Under cloud ... 287127 ... 1600 ... 1292 374 
Wind (sea-level) ... 29°922 ... oO ... 4168 19°8 
It will be seen from this table that while there is a 
rapid increase in the velocity of the wind through the first 
1600 feet, an abrupt diminution occurs between this 
height and 3800 feet, after which the motion again 
increases at a more moderate rate. 
Now Mr. Stevenson’s formula for heights above 50 feet 
H where V7, v, H, /, are the velocities and heights 
x It must be noted that the surface velocities given in this table are some- 
what in excess of the truth, owing to the neglect of surface friction, but this 
does not affect the increment terms to any large extent. 
2 Zeitschrift fiir Meteorologie, Band xvil., July and September Heft ; 
«Die Luftstrémungen tiber Berlin.”’ 
> Reduced from the original figures in millimetres, 4 Wolkchen. 
at the upper and lower stations respectively. If we apply 
this formula to the preceding table and calculate the 
heights at the higher levels from those at the lower ones, 
we get for the most favourable cases the following 
values :— 
_ Observed — Calculated 
Velocity. Height. Velocity. Height. 
37°4 1,600 =; a 259'2 12,800 
518 12,800 113°I 23,000 
which are so absurdly in excess of those observed at the 
same levels, and so far beyond what we might reasonably 
expect as to render it doubtful whether this formula is 
true for any height above the first 100 feet. Even the 
formula which is supposed by Mr. Stevenson to fail above 
ae feet gives better results than this one at the higher 
evels. 
ff +72 
h +72 
observed values as those used above gives the following 
calculated values :— 
This formula is— = , and from the same 
uv 
Height. Velocity. 
12,800 103°7 
23,000 69°3 
but even these are far in excess of those observed. Both 
formulze moreover fail lamentably up to 1600 feet, for 
even if we assume that 19°8 represents the velocity, not at 
sea-level, but at an elevation of 100 feet above it (an ex- 
ceedingly favourable assumption since the velocity at this 
height would considerably exceed that at sea-level), the 
first formula would make the velocity at 1600 feet four 
times, and the second more than ¢hvee times that actually 
observed by Dr. Vettin. 
It is plain, therefore, that both formulze must fail con- 
siderably below 1600 feet, and until further evidence is 
furnished it would seem probable that neither of them 
give correct results much above 100 feet or so. 
For practical engineering purposes no doubt they would 
succeed only too well, since they would probably give a 
maximum velocity far in excess of the truth, and this, 
judging from examples such as the Tay Bridge, would be 
no disadvantage when the force of the wind enters into 
engineering calculations. 
It would surely be better, however, if we could arrive 
at a somewhat closer approximation to the truth, and 
better still if we could arrive at the truth itself. This, as 
I have already pointed out, will be only accomplished for 
the lower strata by further experiment in the same direc- 
tion as that already followed by Mr. Stevenson, modified 
by attaching anemometers to kite strings, and for the 
upper strata, which chiefly concern the meteorologist by 
observations of the clouds similar to those made by Dr. 
Vettin. 
Meanwhile, however, I have found a formula which 
gives very much more satisfactory values at the higher 
levels than those furnished by Mr. Stevenson. ‘This 
formula is— 
4 
ex 
u h 
And although I do not expect it will be found to hold 
very near the surface, it certainly accords, omitting the 
anomalous case at 3800 feet, from 1600 feet to 23,000 feet, 
or through a range of 21,400 feet, very closely with the 
values observed by Vettin. 
The figures observed and those calculated from this 
formula are as follows :— 
TABLE II. 
Height of lower Height of upper Velocity 
Sania” Seni Observed. Calculated. 
3,800 7,200 35 356 
1,600 F rel 
7,200 12,800 518 515 
12,500 23,000 59°9 59°5 
23,000 41,000 672 68°7 
1 The mean of the two. ? Calculated by Vettin. 
