the author shows from Mr. Airy's equations that -r- = Oif 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 



dAdA_„ . 

 escapement -j— -j U when 



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 

 effected; 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 

 have 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 1 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, 

 and has a good deal of friction, from which the proposed remontoir 

 is free. Spring remontoirs winding up at similar intervals have been 

 tried in France, but without success, from defects in their con- 

 struction. 



December 11, 1848. 



On the Formation of the Central Spot of Newton's Rings beyond 

 the Critical Angle. By G. G. Stokes, M.A., Fellow of Pembroke 

 College, Cambridge. 



It has long been known that when Newton's rings are formed be- 

 tween the under surface of a prism and the upper surface of a lens, 

 or of a second prism, so as to allow of increasing the angle of inci- 

 dence at pleasure, the rings disappear when the critical angle is 

 passed, but the central spot remains. The existence of the spot 

 under these circumstances has even been attributed to the disturbance 

 in the second medium, which, when the angle of incidence exceeds 

 the critical angle, takes the place of that disturbance which at a 

 smaller incidence constitutes the refracted light ; but the expression 

 for the intensity has not hitherto been given, so far as the author is 

 aware. The object of the author in the present paper is to supply 

 this deficiencv. 



