Notices respecting New Bookie 3 T '- 085 



the calculated volumes are 57*5, 55*5 and 55. Formic and 

 valeric acid show a similar relation in density to their respective 

 alcohols, their calculated volumes being to these as 37'3 : 39, and 

 108 : 106' 7. If to these we add butyric acid, which gives a 

 volume of 90, and the density of whose alcohol has not yet been 

 determined, the liquid volumes for the four acids C^ H^ 0"*, C'* 

 H^O^, C^H^O^ and C^'^WO^ are 37'3, 55-5, 90, and 108. 

 These numbers approximate to multiples of the liquid volume of 

 water H^O^, which is 18; or taking this as unity, are very 

 nearly as 2, 3, 5 and 6. The interval between 3 and 5 corre- 

 sponds to propionic acid C^" H^ O'^, of whose specific gravity I 

 find no recorded observation. The density of many of these 

 liquids is not accurately known, and the results of different 

 experimenters are not precisely accordant. The specific gravity 

 at their boiling-points should probably be chosen for the purpose 

 of comparison, and these approximations lead us to expect that 

 future observations will establish a simple relation between the 

 densities of liquids and their vapours. 



In a succeeding paper, it is proposed to apply the principles 

 explained in the present essay, in an examination of the equivar 

 lents of a number of minerals and other crystallized species. 



ima ■ 

 ^^"^ LXXXIII. Notices respecting New Books. 



An Elementary Treatise on the Lunar Theory, with a brief sketch of 

 the History of the Problem, up to the time of Newton. By Hugh 



? GoDFRAY, B.A., of St. John's College, Cambridge. Cambridge, 

 Macmillan and Co. : London, G, Bell, &c. 



THE author of this treatise was third wrangler a few years ago, 

 and is well-known already as one of the most successful of the 

 private tutors at Cambridge. The subject of his book is one which, 

 as our mathematical readers are aware, is perhaps the most interest- 

 ing and important of all the branches of mathematical physics ; and 

 as such has engaged the attention of nearly every great mathema- 

 tician for centuries. By slow degrees the subject has attained a 

 state approaching as near to perfection as possible, both as regards 

 our knowledge of the lunar motions, and their theoretical expla- 

 nation. But the mode of presenting the subject to the student has not 

 kept pace with the progress of the science itself, nor indeed was this 

 to be expected. Within the last twenty or thirty years, however, 

 several attempts have been made to render the subject more easy of 

 access to the student, especially in that university where it holds so 

 conspicuous and prominent a place in the course of study and exami- 

 nation. The names of Woodhouse, Airy and Pratt, will at once 

 occur to our academical readers as writers on the subject whose 

 works have had a very great and deserved influence and estimation. 

 Some of these however have only treated the lunar theory as a per- 



