Cambridge Philosophical Society. 455 



the one whicli will have the greatest number. The extreme interest 

 inherent in the subject would naturally secure this result ; but in 

 the present case the interest is greatly heightened by the circum- 

 stance, that the author himself stands in the foremost rank among 

 those to whose labours we are indebted for the progress recently 

 made in this department of astronomy. The subject, indeed, may 

 be said to belong to him of hereditary right. He has devoted to 

 it a large portion of the labours of his liffi ; and after scrutinising 

 the heavens from pole to pole, he has here become the expositor of 

 the great discoveries in which he has taken so large a part, and in 

 language alike remarkable for its eloquence and perspicuity, has pre- 

 sented us with an epitome of all that is known about the fixed stars, 

 — their parallaxes, distances and distribution — their motions, relative 

 and systematic — about variable and periodic stars — double stars and 

 binary systems — clusters and groups of stars — the classification, dis- 

 tribution and resolvability of nebulae, the zodiacal light, &c. It may 

 be said without any exaggeration, that in the whole range of natural 

 philosophy there is nothing more interesting in respect of subject- 

 matter, or more admirable as regards the mode of treatment, than 

 the three chapters forming this part of the work. 



Part IV. contains a single chapter which treats of the account of 

 time, or the calendar. 



We had marked some passages for the purpose of extracting them ; 

 but on consideration this appeared to be unnecessary, as the book 

 itself will be in the hands of every one who takes an interest in the 

 science of astronomy. 



IjXIX. Proceedings of Learned Societies. 



CAMBRIDGE PHILOSOPHICAL SOCIETY. 



[Continued from p. 227.] 



Nov. 13, I^N the Elements of Plane Geometrical Trigonometry, 

 1848. v^ applicable to Trigonometrical Formulae. By the Rev. 

 F. Calvert. 



The object of this paper is to define as distinctly as possible the 

 elementary terms of trigonometry, and to explain the conventional 

 use of the negative sign in expressing such simple functions of 

 angles as the sine, cosine, tangent, &c. 



Nov. 27.— 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 tiie 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 + 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 



