The strict decimal relation of the proposition is shown by the following table.  It has been tested by Clairaut’s theorem, and by other existing expressions, and has been found to agree, far within the probable limits of errors in observation, with the most approved values of the constant.  In fact, it is contained in the existing expressions; but the decimal relation does not appear unless we state the unit of linear measure as a decimal of the earth’s semi-polar axis, and, at the same time, divide the circle, both for time and for general purposes, geometrically, i.e., by strict decimalization upon the hour-angle.  A mathematical reason underlies the proposition.

Time in       Acquired    Squares   Total      Ratio of       Descent in
Thousandths   Velocity,   of the    Descent,   Spaces, Each   Successive
of an Hour.    Cubits.      Time.      Cubits.     Interval of    Intervals,
Time.           Cubits.

1           200          1         100          1             100
2           400          4         400          3             300
3           600          9         900          5             500
4           800         16       1,600          7             700
5         1,000         25       2,500          9             900
6         1,200         36       3,600         11           1,100
7         1,400         49       4,900         13           1,300
8         1,600         64       6,400         15           1,500
9         1,800         81       8,100         17           1,700
10         2,000        100      10,000         19           1,900

So that—­
          
                                          Cubits.  Acre Sides. 
In 1/10,000 of an hour, the total
descent = 1 = 1/100

In 1/1000 of an hour, the total descent = 100 = 1

In 1/100 of an hour, the total descent = 10,000 = 100

And so on, in strict decimal relation with the earth’s semi-polar axis.

A two-fold reason why the constant for latitude 45 deg. is vastly better than any other, is in its having this simple relation with the semi-axis, and at the same time a less complex way of applying the correction for latitude.

JACOB M. CLARK.

New York, February, 1885.

* * * * *

ORIGIN OF THUNDERSTORMS.

At the recent congress of German medical men and physicists, Dr. S. Hoppe, of Hamburg, read a paper in which he sought to show that the electricity of thunderstorms is generated by the friction of vapor particles generated by the evaporation of water.  This opinion was strengthened by several experiments in which compressed cold air was allowed to rush into a copper vessel containing warm moist air, thus generating a large amount of electricity.  He concludes that the rise of a column of warm moist air into the colder atmosphere above will be followed by a thunderstorm if it acquires sufficient velocity to prevent neutralization of the electricity generated by the friction of the air.  Hence, in his opinion, open districts denuded of forests are more liable to thunderstorms than wooded regions, where the trees forbid the rise of humid air currents.