372 REVIEWS — MATHEMATICAL AND PHYSICAL SCIENCE. 



the base on which our laws of symbolical reasoning are founded, and 

 thence to a total reconstruction of the whole system of abstract analysis. 

 Pushed in various directions, it has resulted in a new geometry, through 

 the quaternions of Sir William Hamilton ; in a new and effective 

 method of solving differential equations, in the hands of Professor 

 Boole ; and, still more strangely, in an application of analysis, by the 

 same gentleman, to the formal laws of thought ; while several different 

 systems, suited to attacking particular physical problems, have been 

 proposed by various analysts. So many and varied are the ways in 

 which this most fertile principle appears capable of development, that 

 at present the difficulty seems to consist in discovering which will be 

 best to choose. It is perhaps not too much to say, that here the 

 differential calculus has at length generated a successor more powerful 

 than itself, and which will ultimately absorb it. Nor should we for- 

 get our acknowledgments to the late Duncan Gregory, who was, if not 

 precisely the inventor, certainly the first to perceive the importance of 

 this method. We venture also to think that Professor Forbes has 

 done scant justice to the progress of analytical geometry ; the school, 

 of which Pliicker may be considered the founder, constitutes as great 

 an advance upon the geometry of Descartes as his was upon that of 

 "the ancients. 



That this epoch has not been distinguished "by the full maturity of 

 so many commanding minds " is compensated, and partly accounted 

 for, by the very large increase in the number of cultivators of science. 

 Contrasted with that dreary period in British science which intervened 

 between the death of Newton and the rise of that illustrious band of 

 which Sir J. Herschel may be taken as the type,* the present day 

 presents itself under a most hopeful aspect ; where we can count one 

 British name that emerges above the level for that period, we may 

 count a dozen now, and if their elevation appear less, it may be because 

 the level has risen. In great part this is due to the exertions of those 

 illustrious men above spoken of, whose claim is not only to have done 

 so much themselves, but to have produced a generation worthy to 

 r-ucceed them, and whose glories they justly share ; partly also is it 

 due to the improvement in our national seminaries, and the early intro- 

 duction in them of scientific training, and also partly to the increased 

 demand for scientific qualifications by the advance of engineering and. 

 the kindred arts ; but we would fain believe that there is also a real 

 improvement in the average mathematical faculty of the age, and that 



* Her.schel, Airy, Peacock, Whewell, Babbage, Lubbock. 



