Xolices respecting New Books. 61 



fused, and the higher manual arts are well paid, a compositor should 

 work at his own book ; but we do hold it to be rather a curious 

 phenomenon, that one of the earliest of such books should be an 

 attempt to associate metaphysics with mathematics, or to introduce 

 the former into the latter, to a greater extent than is usually done. 

 The following is a brief description of the character and contents of 

 the work. 



It divides mainly into two parts : the first, on the complete ex- 

 planation of the symbols of algebra ; the second, on the relation of 

 successive differential coefficients, considered as standing to each 

 other in the relation of product and power, or effect and cause. The 

 first part may be looked on as an attempt to evolve the contents of 

 Dr. Peacock's algebra (first edition) in a more a priori form, and to 

 make them the necessary consequences of a metaphysical view of 

 the fundamental operations. Those who know and profit by the 

 clearness of the principle of fluxions (unfortunately, as we think, 

 discarded with its language), will look with satisfaction at Mr. Pater- 

 son's attempt to reinstate the differential coefficients in their old 

 position of indicating something more than result of algebraic 

 operation. Every reader who can truly profess to understand the 

 subject, must, if he have thought about the progress of his own mind, 

 remember how much he was indebted to the mechanical connexion 

 of the function and its first and second differential coefficients with 

 distance, velocity, and force. Mr. Paterson has endeavoured to put 

 this connexion on a more abstract footing, and to make the laws of 

 algebraic development a consequence of his treatment of it. We 

 doubt if his success is complete ; that is, we doubt whether a mathe- 

 matical proof of Taylor's theorem fairly results : unless, indeed, the 

 author had more in his mind than he has fully made manifest ; a 

 reserve which should always be made in matters metaphysical. Be 

 this as it may, we can but express a hope that, both in Europe and 

 America, investigators will attempt to sound the channels which 

 connect the mathematics with the fundamental laws of thought. 



Mr. Paterson is evidently well-read in the writings of mental 

 philosophers. He is far too metaphysical for the general run of 

 mathematicians, and vice versd. Nevertheless, as there are always 

 a few to whom such speculations are welcome, and, even where they 

 do not convince, suggestive, and as upon these few mainly depends 

 the advance of mathematics as a discipline, we hope that he will find 

 encouragement to proceed, and that we have not seen the last of him. 



Four Introductory Lectures delivered at the Government School of Mines 

 and of Science applied to the Arts; Museum of Practical Geology. 



The struggle carried on for some years between the Gymnasia- 

 listen and Rcalisten of Germany has at length found distinct ex- 

 pression in England. Science has found her advocates in the 

 Jerinyn Street Institution, who earnestly uphold her claims, and 

 forcibly protest against our present exclusively classical system of 

 education. In lbUJ, a proposal was made by Sir Henry De la 



