523 Mr. R. Cannichael on the Singularities of Physical Science, 



Castle does not appear to have been as yet ascertained, nor could 

 it answer' any useful purpose to attempt the necessary inquiry : 

 the Course would probably have lost much of its value even in 

 Burrow's time, and would certainly possess no interest now, except 

 as the production of a mathematician who occupied a high posi- 

 tion in the world of science a century ago. With regard to the 

 troubles in the Macclesfield family, it may be observed that Mr. 

 Jones exerted himself very successfully in favour of reconciliation, 

 and so far arranged matters to the satisfaction of all parties, that 

 it became a common saying, as Mr. Robertson remarks, " that 

 Macclesfield was the making of Jones, and Jones the making of 

 Macclesfield." (Hutton's Dictionary, vol. i. p. 692). Dr. Brook 

 Taylor " was a profound and elegant mathematician of the old 

 school of Newton, Jones, Cotes, &c., and one of the chief writers 

 in the disputes with the BernouUis" and other continental 

 writers. His Theorem will perpetuate his name so long as the 

 Differential Calculus exists; nor will those who know anything of 

 the contents of his Methodus Increment orum, his Principles of 

 Perspective, &c., consider that his merits have been at all oyet>f 

 stated in the extracts from Burrow and Button. - -■~^-*^ 



Burnley, Lancashire, >, 



March 18, 1853. '^■■«1« 



[To be continued.] ;<-«» 



LXXXI. The Singularities of Physical Science, their Classiftca- 

 tion, and their Uses. By Robert Carmichael, A.M., Fellow 

 of Trinity College, Dublin^. 



IN the scientific study of nature, the attention is perpetually 

 awakened by the discovery of various singularities in her 

 generally regular and even course. 



In one point of view it would be unmeaning to institute any 

 comparison between such singularities and those which occur in 

 pure mathematics, since they are logically identical, the operations 

 of nature conforming to mathematical laws. In another point 

 of view, however, there is an extreme contrast. The one class 

 is the result of our own arbitrary conceptions embodied in defi- 

 nitions; the other is founded upon general laws of nature, 

 whether discovered or undiscovered : a knowledge of the one 

 serves to no practical purpose, unless we are to accept that of 

 decoration, as those singular points of an ellipsoid, the umbihcs, 

 were proposed to be employed by the celebrated geometer Monge ; 

 the great benefits which a knowledge of the other has conferred 

 upon mankind are appreciated by all who feel the slightest 

 interest in the researches of modern science. m. 



* Communicated by the Author. : «• 



