Reviews, and Notices respecting New Books. 219 



<' The stability of a system of bodies in motion subject to the 

 law of mutual gravitation which obtains in nature, is a question," 

 Mr. Lubbock observes, " of great interest. It appears to me," he 

 continues, " that it may be established through considerations dif- 

 ferent from those hitherto employed, namely, by observing that 

 the quantities which have been called c and g in the Lunar The- 

 ory are rational, so that no imaginary angles or exponentials are in- 

 troduced in the expressions for the coordinates of the body in 

 motion, which are thus functions of periodic quantities. In the 

 theory of the moon I apprehend this theorem is certainly indepen- 

 dent of the direction of the moon's motion." 



2. On the Determination of the Distance of a Comet from the Earth, 



. and the Elements of its Orbit. 



This essay is intended to convey an exposition of different me- 

 thods which have been proposed for the solution of one of the 

 most important problems in physical astronomy. The author hav- 

 ing proposed, in the Memoirs of the Astronomical Society, a new 

 method, which results from a combination of the equations of 

 Legendre and Lagrange, by which the distance of the comet from 

 the sun is eliminated, and the question of the determination of the 

 distance of a comet from the earth is reduced to the solution of a 

 quadratic equation, thus superseding the necessity of having re- 

 course to repeated trials ; gives, in the present tract, details which 

 could not enter into the plan of that paper, and also a new method 

 of obtaining the perturbations of a comet, which consists in deter- 

 mining directly the perturbations of the rectangular coordinates. 



3. Account of the " Trait d sur le Flux et Reflux de la Mer," of Daniel 



Bernoidli ; and a Treatise on the Attraction of Ellipsoids. 



This tract, we believe, was the first of the series of memoirs (con- 

 tinued in the Philosophical Transactions, &c.) in which Mr. Lubbock 

 has discussed the phenomena and theory of the tides, and which 

 have had an influence so advantageous in the direction to that sub- 

 ject of the minds of British mathematicians and observers, as well as 

 in calling the attention of public bodies to the importance of insti- 

 tuting regular and comparable observations of tidal phenomena. 



The Essay of Bernoulli which forms the subject of the first 

 part was published in the Jesuits' edition of the Principia : it 

 shared the prize proposed by the Academy of Sciences at Paris 

 in 1738, and adjudged in 1740, with those of Euler, Maclaurin, 

 and Cavalleri ; but the tables contained in it, Mr. Lubbock re- 

 marks, " have solely been employed hitherto in calculating the 

 times and the heights of high water." Mr. L. observes, in the Pre- 

 face, " that the effect attributed to changes in the moon's distance in 

 the tables for finding the time of high water in Mackay's " Complete 

 Navigator," p. 58, in Riddle's " Navigation," p. 257, and in Dr. In- 

 |u'l " Nautical Tables," p. 5, is directly contrary to that which is 

 given by the table of Bernoulli, p. 165, (upon which they otherwise 

 appear to be founded,) and to observation. In order to remove this 

 error it is necessary to reverse the heading which gives the one the 

 moon's parallax, and in the others the moon's semi-diameter." 

 'I F 2 



