300 Notices rejecting New Books. 



The advantages of this new pump, as compared with the 

 common pump of the same capacity of cyhnder, are as follows : — 



1. To effect the same exhaustion, the driving pressure moves 

 over one-half the space. 



2. From the superior construction of valves, the exhaustion is 

 carried to a much greater extent. 



3. From having a double stroke in a single cylinder, the ex- 

 pense of construction is considerably reduced. 



4. As the exhaustion proceeds, the pressure requisite for 

 moving the pistons becomes less and less. The contrary takes 

 place in the common pump. 



In the pump which I have constructed the valves are made of 

 oil-silk, and the piston-rod is moved by the direct application of 

 the pressure ; but I purpose to construct a pump on the new 

 principle, with metal valves covered with oil-cisterns, and lifted 

 up by the stroke of the piston, and also with a pump-lever (or 

 crank) attached to the head of the piston-rod. The pump thus 

 constructed will most certainly exhaust the air from the receiver 

 until its elasticity is reduced to that of the vapour of the oil. 



Hounslow, March 20, 1856. 



XXXVIII. Notices respecting Neiv Books. 



The Geometry of the Three First Books of Euclid, by Direct Proof, 

 from Definitions alone, tvith an Introduction on the Principles of the 

 Science. By Henslp;igh Wedgwood, M.A., late Fellow of Christ 

 College, Cambridge. 12mo. London: Walton and Maberly. 1856. 



MODERN mathematicians have been so much occupied in in- 

 vestigating the extent and value of the higher analysis, that 

 elementary geometry has been very much neglected. Dr. Whewell, 

 Professor De Morgan, Mr. Sylvester, Mr. Wedgwood, and a few 

 others, have occasionally done something on the subject of geome- 

 trical reasoning, but, as a general rule, with more of a speculative 

 than of a practical spirit. The work now before us has the advantage 

 of exemplifying the author's views with actual demonstrations. In 

 this respect it is far superior to anything Mr. Wedgwood has done 

 before. The main points in his system have been given from time 

 to time in our notices of the Cambridge Philosophical Society. This 

 alone prevents us from entering into any detailed account of a work 

 so well deserving of attention. 



Mr. Wedgwood traces out with much care the ultimate expres- 

 sion of the mode in which the fundamental conceptions of geometry 

 are brought into intellectual existence. He supports the views of 

 Locke and Dugald Stewart, by making the demonstrations depend 

 solely on definitions, and he shows the practical possibility of alto- 

 gether excluding reductio ad absurdum from geometrical reasoning. 

 His introduction is well worth reading. It is marked with much 

 originality, and is written in a clear and logical style. 



