77 



bridge. From a consideration of all the results derived from the 

 discussion of observations made on different occasions and at differ- 

 ent places, the following conclusions seem to be established : — 



First, that the corona of an aurora borealis is formed near the 

 point of the heavens to which the south end of the dipping-needle at 

 the place of observation is directed. 



Secondly, that the observations, while they indicate no decided 

 difference of altitude between the two points, show with great pro- 

 bability that the corona is the more westerly by about 1^° measured 

 on an arc perpendicular to the meridian. 



The paper concludes with a particular description of the aurora 

 borealis of Nov. 17 as observed at the Cambridge Observatory, and 

 with three tables of the observations of declination, horizontal force, 

 and vertical force, made at Greenwich, and used in the calculations. 

 These observations present so striking an instance of great magnetic 

 disturbances occurring simultaneously with an extraordinary display 

 of the aurora borealis, that the connexion in some way of the two 

 kinds of phasnomena must be regarded as a physical fact. 



On Clock Escapements. By E. B. Denison, Esq., of Trinity 

 College. 



The object of this paper is, first to point out the real cause of the 

 general excellence of the dead beat escapement ; and secondly, to 

 show that in a gravity, or remontoir escapement, in which the pen- 

 dulum raises an arm carrying a small weight, from an angle y up to 

 its extreme semiarc a, which follows the pendulum down again to an 

 angle /3 (either -f and less than y, or = — y), there is a certain pro- 

 portion between a, /3, and y, which will cause the errors of the clock 

 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 



\<p ~ a, )' 



where A is the difference 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 



3da . „ . .dtp 



—jj- 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 



