920 REPORT—1885. 
determined by the author as the value of the exponent in the formula v= i J 
v ’ 
which best accords with the results of Dr. Vettin’s cloud observations over Berlin 
extending from 1,600 to 25,000 feet above sea-level (‘ Nature,’ vol. xxv. p. 506), 
and the result shows not only that the observations of the author agree generally 
with those of Dr. Vettin, but also that beyond a certain height the exponent 
becomes nearly constant. The author finds, apart from height, that the values of 
the exponent, or in other words the ratio of the increase of the velocity with the 
height, is affected principally by four factors: (1) the mean velocity of the two 
heights; (2) the hour of the day ; (3) the direction of the wind ; and (4) the time 
of year. 
“On comparing the exponents for each group with each of these factors in turn 
variations appear of a periodic character, which in some cases are difficult to 
exhibit independently, owing to chance arrangements of the other factors affecting 
the results co-directionally. In the first two cases, however, the results can be 
shown to be independent of the other factors, and lead to the enunciation of the 
following laws :— 
1. Above the first 160 feet from the ground, the exponent generally decreases 
with an increase of velocity, and vice versdé. Below the first 160 feet this law is 
apparently reversed, owing probably to undue sheltering of the lower instrument 
by surrounding objects. 
2. When the exponents are arranged for different hours of the day, for heights 
above 160 feet and up to 1,500 feet above the ground, the exponents in all the four 
upper groups show a uniform increase from a minimum value about 2 or 3 P.M. to 
a maximum about 7 or8 p.m. Below 160 feet the first two groups show some 
signs of a contrary variation, which may admit of an explanation similar to that 
for the preceding law. 
This second law is in complete agreement with Dr. Képvpen’s theory of the 
diurnal period in the velocity of wind and other casual observations of the author, 
but requires more morning observations to confirm it. 
The other laws of which indications have been observed are a maximum value 
of the exponent for winds from a westerly quarter and a minimum for those from 
an easterly quarter. Also a maximum value of x in October falling to a minimum 
in the winter and rising again to a maximum in spring and early summer, but 
these are more involved by the co-existence of the other factors. 
The last law, if found to be confirmed, might be due in part to the changes in 
terrestrial friction due to the falling of the leaf in winter. 
13. On the Measurement of the Movements of the Ground, with reference 
to proposed Harthquake Observations on Ben Nevis. By Professor J. A. 
EwinG, B.Se., F.R.S.E. 
Measurements of earth movements are of two distinct types. In one type the 
thing measured is the displacement, or one er more components of the displace- 
ment, of a point on the earth’s surface. For this purpose the mechanical problem 
is to obtain a steady point to be used as an origin of reference, and this is effected 
by making use of the resistance which a mass opposes to any change of motion. 
This may be called the inertia method of observing earth movements. It is appli- 
cable to ordinary earthquakes, and also to the more minute earth tremors, which 
would pass unnoticed if instrumental means of detecting their presence were not 
employed. The steady point is to be obtained by suspending a heavy mass (with 
one, two, or three degrees of freedom) in such a manner that its equilibrium is 
very nearly neutral. Any moderately sudden displacement of the ground in the 
direction in which the mass has freedom to move leaves the mass almost undis- 
turbed, and the displacement of the ground is therefore easily measured or recorded 
by a suitable autographic arrangement, which must be so designed as to introduce 
exceedingly little friction. 
The second type of measurements is that in which the thing measured is any 
