34- Observations on the Notations employed in 



time necessary to consider integration merely as the inverse of 

 differentiation, I should prefer such a symbol as d~\ which 

 expresses the required idea better thanyj,. But what I look 

 on as a fatal objection to the suffix integral notation is, that, 

 like the corresponding one for differentials, it is not applica- 

 ble to all cases. Of this any one may satisfy himself by at- 

 tempting to use it in transforming a multiple integral from 

 one system of independent variables to another, a problem 

 which is of frequent occurrence, but which I have not seen 

 solved analytically in any work in which the suffix notation is 

 employed ; so long, therefore, as the old notation adapts itself 

 to all cases in which it is required, while that which is pro- 

 posed is not so accommodating, there appears to me no doubt 

 which is to be preferred." 



Mr. Jarrett, in the paper before referred to, recommended 

 Fourier's notation ; every one who habituates himself to its 

 use will, I think, admit that it is admirably adapted to effect 

 its purpose. 



In the commencement of these remarks I gave it as my 

 opinion that new symbolic language in a scientific treatise 

 uselessly puzzles the reader and occupies his time without in- 

 creasing his knowledge; it has been, and will be, my object to 

 make converts to this notion. Some of the writers above- 

 named adopt the suffix notation both in differentials and in- 

 tegrals, others only the suffix for integrals : must not even this 

 variety be afi incumbrance to a student, and for that reason 

 ought it not to be exploded ? 



Airy, in the commencement of his tracts, says, Ci By the no- 

 tation of fj cos n . 9 .0, f t cos n 9 . cos m 9 + D, &c, we mean 



what are usually written/ cos n 9 .©^9,/cos w9. cos m 9 -f- D d 9, 

 &c, they are the quantities whose differential coefficients with 

 respect to 9 are cos n 9 . ©, cos n 9 cos m 9 + D, &c." 



To a reader who is unaccustomed to the notation, and who 

 may perhaps here meet with it for the first time, this explana- 

 tion is exceedingly useful as a key, it sets him a-going. 



In some other books, however, in which the d x andjl nota- 

 tions are used, not one word by way of definition is said : the 

 reader has to find out the meaning of a new symbolic lan- 

 guage used in investigating intricate subjects as he best may : 

 it seems to be taken for granted, that because the writer knows 

 the meaning of the hieroglyphics, the reader must compre- 

 hend them by sheer intuition. 



At college, where lectures are constantly given, such diffi- 

 culties may be well explained viva voce. But the writers of 

 mathematical works at Cambridge should bear in mind that 



