26 Observations on the Notations employed in 



time, there should be nothing cabalistic or mystifying about 

 them. The sciences are nearly universal in their application, 

 so likewise should be their notation ; and to this end, there 

 should be a sort of unity about it which would at once iden- 

 tify it ; so that when a reader opens a scientific treatise he may 

 know at a glance what calculus is adopted in its demonstra- 

 tions. He can then begin to read it, but obviously this can- 

 not be done, if he have been accustomed to one kind of nota- 

 tion and a totally different one be used in the book: he must 

 in the first place learn his letters, and if no explanation be 

 give?i, it may require much time and trouble to bring him ac- 

 quainted with an old friend disguised in a new dress : he may 

 have learned Greek and be competent to read that language; 

 but he may not be able to read the same thing in Hebrew 

 characters. Clearly, if one kind of symbolical language ex- 

 presses either of the sciences named more accurately or more 

 logically than another, that language ought to be generally 

 adopted, and no other used : such language ought to make its 

 appearance in evei*y treatise having any pretensions to ele- 

 gance, and all others be made over for the exclusive employ- 

 ment of scientific charlatans. 



Could writers on the differential and integral calculus agree 

 upon the point, as to which is the most accurate mode of ex- 

 pressing the various processes to which they are applied, and 

 use no other, and would the authors of other scientific works 

 adopt only the language thus set apart, they would very much 

 indeed simplify those important sciences, as well as their ap- 

 plications : they would save their young readers a great deal 

 of useless trouble: they would also, by giving a oneness and 

 a generality to the symbols employed, remove from those sci- 

 ences that shifting, or as some term it hocus pocus sort of 

 character, to which their appearing now in one form and then 

 in another certainly entitles them. 



Moreover, if one has learned to read a mathematical process 

 in one symbolical language, it would be difficult to prove how 

 it adds a particle to his knowledge to be able to read it in an- 

 other; and therefore the timeandthe trouble that it costs him in 

 learning to read the process in its new dress is time lost and 

 labour thrown away. It is supposed that this position will not 

 be disputed by the advocates of either notation, and if this 

 be the case, it surely behoves men of competent authority to 

 consider the subject with the view of rescuing it from such a 

 stigma ; it is hoped that they will endeavour to prevent the 

 votaries of science from having their time thus uselessly 

 wasted ; from being needlessly puzzled by different notations 

 or bewildered by a mixture: to realize this hope, by calling 



