76 Proceedings of the Royal Society of Edinburgh. [Sess. 
turns upon changes of rate of the order of 0 S, 01 per day, sometimes more 
but sometimes much less ; that is, we may say, the accuracy attained is of 
the order 10“ 7 . It is obvious that it will not be easy to improve upon this 
standard with the help of theory. I hope, however, that the following 
studies will make it clear that many points are open to successful analysis. 
The present paper is chiefly theoretical, but the studies are conducted 
with reference to the actual clocks at the Royal Observatory, Edinburgh. 
It will therefore he necessary to describe these briefly in order to make the 
references intelligible. 
The clocks are mounted in a chamber which has been constructed 
within the great brick pillar that supports the East Equatoreal. This 
chamber is kept at a constant temperature of 63° F. by means of an electric 
radiator turned off and on automatically by a thermometer. When the 
radiator is off, a reduced current drives a fan which stirs the air and 
prevents stratification — an important point. The arrangement works well. 
Each clock is contained within an air-tight case, exhausted to a small 
degree, and the normal method of regulating rate is through the baro- 
metric effect, by exhausting or admitting air to a due amount. The three 
chief clocks rewind themselves automatically, and are never touched for 
any purpose unless it becomes necessary to alter the rate. The supports 
are bolted to the brickwork of the pillar in a very solid fashion. 
The ideal clock is a free pendulum ; but this is impracticable, because 
the motion would die out ; besides, there would be no means of marking 
its seconds. To maintain the motion and send out signals, without intro- 
ducing some noxious feature, is a task of great difficulty. It may be taken 
at once that the drum with cord and pulleys to carry a weight should be 
dispensed with, and the counting train and dial, if retained, should be made 
a mere accessory, quite free of the maintenance. Two things are, however, 
essential in one form or another. The pendulum must unlock the mainten- 
ance, losing in doing so a certain amount of energy, which may be variable. 
And, second, the maintenance for a certain portion of the arc must interfere 
with the free swing of the pendulum. To provide the maintenance in the 
simplest way, three direct methods offer, which are illustrated very distinctly 
in the three chief clocks under discussion. First, by a pressure gently 
applied to the pendulum in the neighbourhood of its vertical position only, 
the pendulum being free at the extremities of its swing : this is the method 
of the Synchronome clock. Second, by means of a small weight which the 
pendulum picks up, carries to the end of its swing, and down again to a 
low T er point than that at which it was picked up. This is illustrated by 
Mr Cottingham’s clock. And, thirdly, energy may be conveyed to the 
