456 Cambridge Philosophical Society, 



for small variations of a to be much smaller than in the dead escape- 

 ment, and in fact inappreciable. 



The author adopts the equations obtained by Mr. Airy in his paper 

 on this subject in vol. iii. of the Transactions of the Society, and 

 shows that the increase of the time of an oscillation 



\9 cc J 

 where A is the diiFerence between the time of oscillation of a free 

 pendulum and one affected by this escapement (which in clocks of 

 the best construction he shows will amount to about 1 second a day) ; 

 (p is the angular accelerating force of the escapement on the pen- 

 dulum ; d<p the variation in this force due to the variation of the 

 friction of the train and of the state of the oil on the acting part of 

 the pallets ; da the variation of the arc from the same causes, and 

 also from the state of the oil on the dead or circular part of the 

 pallets. It appears therefore that the two causes of error have a 

 tendency to correct each other ; and in practice it is found that 



is generally not far short of — , which is the reason of these 



clocks going so well. 



In a gravity escapement there is no variation of the force ; and 



rfA 

 the author shows from Mr. Airy's equations that -^sOif a=:y ^2 



in that escapement where the remontoir weight is taken up at y and 

 follows the pendulum again to — y ; and in the other kind of gravity 



</A «?A _ „ , 

 escapement -rr -3 " wnen 



a^ = 2 Va'^ -y* Va?' — /3«. 



This last construction however is barely practicable, if this con- 

 dition is to be satisfied, on account of the small difference between 

 /3 and y which is allowed by the deduction of the value necessary 

 for a — y, the angle in which the unlocking of the escapement is 

 eflFected ; although this is the construction which has been used in 

 nearly all the gravity escapements that have been tried ; and of course 

 the proper condition has been very far from satisfied, and the clocks 

 nave failed. 



In a supplement to this paper the author proposes, chiefly for 

 turret clocks, a new construction of a spring remontoir on the axis 

 of the escape-wheel. The object of such remontoirs is to remove 

 from the escapement (of any ordinary kind) the great inequalities of 

 force caused by the varying friction of the heavy train and dial- work, 

 and by the action of the wind on the hands ; and also to cause the 

 minute-hand to move only at visible intervals, such as i a minute, and 

 the striking to take place exactly at the right second. The Royal Ex- 

 change clock, made under the superintendence of the Astronomer 

 Royal, has a gravity remontoir in the train introduced for these 

 purposes ; but it is too complicated and expensive for ordinary use. 



