THEORY OF THE SEISMOGRAPH. 185 
SEISMOGRAPHS FOR VERTICAL MOVEMENTS. 
The older Italian form of instrument for showing vertical movements was simply a 
weight hung by a spiral spring, which would be set in motion by any vertical movement 
of the earth. Palmieri arranged it so that a 
very small displacement was sufficient to close 
an electric circuit and thus record a disturbance. 
Cavalleri added a magnifying lever, which meas- 
ured the movement of the weight. However, the 
period of such an instrument would be short 
unless the spring were inordinately long, and a 
second form has been devised to obtain a larger 
period in a smaller compass. This consists of a 
horizontal bar, pivoted at one end and carrying © 
a weight at the other; it is supported by a spring 
attached to an intermediate point of the bar. ibys 
This form of instrument was devised by Thomas Gray.’ Professor Ewing’ suggested that 
the point of support of the spring be below the bar, thus increasing the period for a 
given strength of spring. 
Let EH be the force of the spring when the pendulum is at rest; and let p be the varia- 
tion of this force for a unit stretch of the spring; then for equilibrium (see figure 59), 

El,— Mgl=90 or El,cosa— Mgl=0 (125) 
and when the pti is displaced thru an angle 6 the additional moment will be 

tx S (Ely cos a) =I, a “ @— Ely sin «- 0 = (ple — Eh) 6 (126) 
and the free ine of vibration will be 
Ty =2aV[T\/(ple — Eh =2 2 V [I] le/(pls — Mgih) (127) 
We can therefore make the period as long as we choose by selecting suitable values of 
p, l,, M, l, and h. 
The next modification for increasing the period of the pendulum is described by Prof. 
John Milne.2 The supporting spring is a curved flat steel band; and the compensation 
is obtained by a special spring fastened 
immediately above the pivot to an arm 
connected rigidly with the bar of the 
pendulum. As long as the pendulum 
is at rest this spring has no effect, but 
when the bar is raised or lowered, the 
spring exerts a moment tending to 
increase the displacement; this is 
equivalent to reducing the force of 
restitution due to the main supporting 
aia spring, and therefore increases the 
rae period of the pendulum. The prin- 
ciple here made use of seems to have been first suggested by Professor Ewing.‘ Let 


1 On a Seismograph for Registering Vertical Motion, Trans. Seism. Soc. Japan, 1881, vol. iii, p. 137. 
A similar form is reported to have been used at Comrie, Scotland, in 1841. 
2 A Seismometer for Vertical Motion. Same, p. 140. 
’ The Gray-Milne Seismograph, etc. Same, 1888, vol. xii, pp. 33-48. 
4 Same, 1881, vol. iii, p. 147. 
