398 TRANSACTIONS OF SECTION A. 
10. Notes on the Construction of Seismometers. 
By Rev. W. O'Leary, S.J. 
Tremor Storms.—The minute and long-continued disturbance of the seismo- 
meter called the ‘tremor storm’ is a troublesome and to some extent a per- 
plexing phenomenon. Tremors due to high wind have an irregular period that 
is unmistakable. The causes of tremor storms of uniform period are not quite 
understood. At Limerick such movement often develops during high wind, 
frequently attaining its maximum when the wind has fallen, and continuing for 
several days after. The period of the vibration varies from about 5°5 seconds 
towards the end of winter to 15 or 20 seconds in summer. There is little doubt 
that at Limerick many of these ‘tremor storms’ are due to high seas on our 
west coasts. It would be interesting if the same cause could be recognised at 
other stations. 
Convection air currents are probably accountable for a good deal of trouble 
in other cases. A simple experiment shows how easily such currents may be 
produced. Very light rods of straw or wood are suspended in corked bottles 
from silk fibre. If a group of such bottles be placed in a room of even very 
uniform temperature, e.g., a cellar, the rods are soon observed to all point in 
the same direction. Lighting a jet of gas 10 or 12 feet away will gradually 
turn them all towards the gas jet. The effect is evidently due to heat convection 
currents. By using large flat dishes instead of the bottles we can choke down 
convection effects, and under these conditions the rods show no definite set. 
A delicately balanced seismometer should readily respond to such currents if its 
mass is small. Hence it would seem advisable to raise the mass of light photo- 
graphic recorders. 
Photographic registration, though frictionless, is unsatisfactory. High 
magnification of the preliminary tremors is essential to analyse the shock and 
determine its epicentre. The maximum phase is then generally lost, owing to 
the rapid movement of the light spot. On the other hand, a large increase of 
mass renders the friction factor in mechanical registration very small; it is 
easily calculated, and the record is complete. 
Ink Registration.—The ordinary method of mechanical registration by smoked 
paper is very sensitive, but has serious defects. The writer uses ink registra- 
tion. The mass required is greater, but the perfection of the record out- 
balances the objection. Large masses, too, are perhaps easier to work with than 
small masses. 
The vertical component instrument is essential to a first-class station, but 
many have found it mechanically unsatisfactory. Slight temperature changes 
alter the elasticity of the balancing spring. To avoid ‘pen wandering’ a tem- 
perature compensator on the gridiron principle is generally employed. The 
writer suggests prevention rather than cure. The spring, instead of being 
placed above the lever arm in the air, might be placed below it in an oil tank 
sunk deep in the concrete pier. If, in addition, a layer of non-conducting 
substance surrounds the tank, the spring should remain at a practically constant 
temperature. 
DEPARTMENT oF MATHEMATICS. 
1. Direct Derivation of the Complementary Theorem. 
By Professor J. C. Freups, F.R.S. 
2. Symmetric Linear Substitutions. By Professor H. Himton. 
3. On the Divisibility of (2?—2) by p?. 
By Ineut.-Colonel ALLAN CunnincHam, R.E. 
Up to the present time it has been supposed that 2?—2=0 (mod p*) is impossible. 
And it has been affirmed impossible by some writers (notably by M. Pratt). This 
had been tested up to p } 1000 by the present writer, and has been confirmed by 
