('*.) 
3. the amplitude of a vertical pendulum under the influence of 
a celestial body can be represented by the expression 
Hp qsin 2 Si 
S = distance of zenith, 
H = general coefficient or greatest amplitude which the celestial 
body could effect on a place situated under the equator with a 
declination zero: 
3 206265" A „ A1 _ 0 _ 
Expressed in arc seconds H is for the moon = - X 2fk*~ ~~ 017d7, 
H' for the sun = 0.4604 H, 
if we put: 
/= 81.4 = quotient of mass of earth by mass of moon. 
k = 60.26 = mean distance from moon to earth, in earthradii. 
p = geographical or local coefficient, dependent on the geogr. latitude 
of the place of observation and the azimuth of the horizontal 
pendulum; for the rest different for diurnal and semidiurnal 
q = astronomical coefficient dependent on the inclination of the 
orbit and its eccentricity. 
If the general expression is developed in a series of terms, behaving 
itself purely periodically, we find for the components in the direction 
of the meridian, N (north positive), and in a direction normal to it, 
W (west positive), as far as the terms are concerned, in the direction 
of sidereal time, inclusive of P, for the moon: 
N=Hq m cos2<psinyx j nj 
W=-Hq m sin<pcos yr j 
y = geogr. latitude 
Y = 15° + ij = 15° .04107 an hour 
?« = sin I cos I (i = inclination of orbit of moon) 
and for the sun*. 
N — H'cosZtp [g s sin y t — q' sin (y — 2 tj) r] j 
W = H'sin<p[— q 6 cos yt -\-q'cos (y — 2 r] j 
The deviation of a horizontal pendulum set up in an azimuth 
180° + « is: 
If we put*. 
— (N sin a W cos a) 
then for Potsdam: 
sin q> cos a p sin % 
cos 2 <p sin a — p cos %, 
<p = 52° 23', a = 42° 
p = 0.6129, x = 286°.15, q' z=z 0.4127. 
