148 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
lum is a heavy mass whose center of gravity is vertically above the point of support; 
some additional forces must be applied in order to keep it in stable equilibrium in this 
position; these forces are usually supplied by springs connecting the upper part of the 
mass and the support. 
REGISTRATION. 
There are two principal methods of magnifying and registering the relative move- 
ments, the photographic and the mechanical. It is to be noticed that these relative 
movements are all of the nature of rotations of the pendulum about a point or a line of 
the support. The photographic method of registering may be divided into two kinds, 
the optical and the direct. In the optical method a beam of light from a stationary point 
is reflected from a mirror on the pendulum and concentrated on a moving sheet of photo- 
graphic paper which is afterwards developed. Time marks are made by periodically 
eclipsing the light. The magnifying power depends on the distance of the recording 
paper from the mirror. In the direct method the light is reflected through a longitudinal 
slit in a diaphragm on the end of the pendulum’s beam and a transverse slit in the top of 
a box, to the moving photographic paper below. As long as the pendulum is still, a 
straight line is recorded on the paper, but when the pendulum swings, the line is shifted 
from side to side. The magnifying power depends on the ratio of the length of the beam 
to the distance of the center of oscillation from the axis of rotation. In the mechanical 
method of registering the record is made by a pen on white paper or by a stylus on smoked 
paper. The marking point may be fastened directly to the pendulum or may be con- 
nected with it thru one or more multiplying levers.’ 
THE MATHEMATICAL THEORY. 
The mathematical theory of seismographs has been written by Dr. W. Schliiter,? 
E. Wiechert,* Prince B. Galitzin,s Gen. H. Pomerantzeff,® Professor O. Backlund,° 
Dr. M. Contarini,’? and Dr. M. P. Rudski,* but up to the present the general. theory has 
not been written in English. Messrs. Perry and Ayrton, however, published an important 
paper in 1879,° in which they developed the mathematical theory of a heavy mass sus- 
pended by springs in a box supposed to move with the earth. They emphasized the 
fact that the actual motion of the mass is made up of that of the earth and of its proper 
vibration; they showed the influence of damping and the relation between the relative 
movement and the motion of the earth. This paper seems to have been overlooked 
and is not referred to by later writers on the theory. 

1 Tt is not desirable here to give details of construction. They will be found in Milne’s Earthquakes 
and Seismology; in Dutton’s Earthquakes, in Sieberg’s Erdbebenkunde, and in the original descriptions 
in memoirs of scientific societies. Dr. R. Ehlert describes many forms of instruments in Gerland’s 
Beitrage zur Geophysik, 1896-1898, vol. III, pp. 350-475. 
* Schwingungsart und Weg der Erdbebenwellen. Gerland’s Beitrige zur Geophysik, 1903, vol. V, 
pp. 314-360, 401-466. 
8’ Theorie der automatischen Seismographen. Abhand. K6n. Gesells. Wissen. Géttingen, Math. 
Phys. Kl. 1902-1903, Bd. II, pp. 1-128. 
* Ueber Seismometrische Beobachtungen. Acad. Imp. Sciences. St. Petersburg, 1902. Comptes 
Rendus Commission Sismique Permanente. Liv. 1, pp. 101-183. Zur Methodik der Seismometrischen 
Beobachtungen. Same, 1903. T. I. Liv. 3, pp. 1-112. Uber die Methode zur Beobachtungen von 
Neigungswellen. Same, 1905, T. II. Liv. 2, pp. 1-144. Die Electromagnetische Registrirmethode, 
Same, 1907, T. III. Liv. 1, pp. 1-106. 
5 In Russian, Same, pp. 185-208. 
6 Formeln fiir das Horizontalpendel. Same, pp. 210-213. 
7 Rend. d. R. Accad. d. Lincei. Cl. Sci. fis. math. e. nat., 1903, vol. XII, pp. 507-515, 609-616. 
® Ueber die Bewegung des Horizontalpendels. Gerland’s Beitriige zur Geophysik, 1904, vol. VI, 
pp. 138-155. 
® On a Neglected Principle that may be employed in Earthquake Measurements. Phil. Mag., 1879, 
vol. VIII, pp. 30-50. 
