THEORY OF THE SEISMOGRAPH. 171 
Q is found from the quadratic equation 
ge WP t+ 2 xp)’, og Sxn't go N+ (2p)? 4 n*r *_8NSnir_ i _o 
jug ™ . p 7p 
where N is written for n?— p’. The other letters have the same meanings as heretofore. 

Tv 
VEG | 2 
mp? — n 2xkmp 
~P cos yy, = f 
sin yy, = 
¥ V (mip? — n*)? + (2 emp)? V (mp? — n?)? + (2 «mp)? 




The presence of both sine and cosine terms in (84) shows that the movement of the 
pointer is not symmetrical about a vertical line. The solution is too complicated to be 
of any general use and is another example of the disadvantage of solid friction in our 
seismographs. 
If the disturbance is small, it may not be strong enough to overcome the solid friction; 
referring again to equation (67), we see that no record will be made in the case of linear 
displacements unless 
@E/d?>p'/V, or >nr/V, or >4’*r/VT?, or > pml,/M1; 
if é= X cos pt 
we must have the maximum acceleration, p’?X >n’r/V; that is, X >(P/T,)’r/V, or 
>(P/27)dml,/Ml. If the disturbance is a small tilt, #, must be greater than p'/Vq; 
if w,=©. cos qt, in order that a record be made we must have 0 >47’r/VgT,?, or 
>¢ml,/Mlg. In studying the action of solid friction it has been supposed to be due 
both to friction at the pivots and to friction of the marking point; where the latter 
exists at all it is apt to be much greater than the former. If we are dealing with small 
disturbances of periods not very short, the friction at the marking point is no longer a 
constant, but has the characteristic of viscous damping. So that in determining the 
smallest disturbance that will produce a record, under these conditions, we must sup- 
pose p’- to refer to the pivots only and not to the marking point. 
Professor Marvin has shown how ¢, and consequently p’ and r, can be practically 
reduced. He attaches a small electric vibrator to the frame carrying the lever, and the 
successive slight jars produced by it diminish the effective solid friction to a large 
extent.’ 
The solutions we have found, showing the relations between the disturbance and the 
record when solid friction is present, refer to the final steady condition and do not apply 
to the beginning of the disturbance. The character of the record at the beginning of 
a simple harmonic disturbance can not be shown in a continuous form, as we can not 
represent p’ as a series unless it is periodic and we know the times when it changes sign. 
In the beginning of a disturbance these conditions will, in general, not hold. The same 
remark applies to the case where the disturbance consists of two or more simple har- 
monic motions of different periods. But if p’ can be neglected, these difficulties disap- 
pear and the solution of equation (67) becomes simple. If we suppose the disturbance 
to be made up of a number of simple harmonic linear displacements and tilts, we must 
write in the equation: 
Vé = C\cos (pyt — x1) + Cy cos (pot — x2) + + + + 
' =a 
whence ves = -2 cos (p,t — x1) — = COS (Pot — x2) +°°- (85) 
and we must write Vg, =D, cos (qt — ¢) + Dz cos (got — do) ++ + + (86) 


1 Improvements in Seismographs with Mechanical Registration. Monthly Weather Review, 1906, 
vol. xxxiv, pp. 212-217 
