the Differential and Integral Calculus. 37 



treatises without any explanation, and also the uselessness, as 

 I think, of adopting different notations to effect the same 

 purpose. Either the common, the suffix, or some other is 

 the best adapted for general use ; which ought to be constituted 

 and considered the standard notation, I want the opinion of 

 your readers to settle : to elicit this, I have adduced the pith 

 of what has been written in favour of and against the suffix 

 mode, so that a judgement may be formed with as little 

 trouble as possible : I have endeavoured to do my part as 

 impartially as I could. I have aimed to state the case as 

 fairly as I could in hopes to obtain an impartial judgement 

 from competent authority. Very likely I may have evinced a 

 little leaning, for I do not like the suffix notation, but I trust 

 I have said nothing distasteful to its distinguished advocates : 

 I am willing to pay homage to their splendid achievements 

 in science, but whilst I heartily respect their attainments, 

 I have some misgivings as to their orthodoxy respecting the 

 subject that has been discussed. 



It may save time and trouble if I beg to be considered as 

 the voluntary, though feeble advocate of such votaries of 

 science as the one referred to above : as far as I am personally 

 concerned, all writers may go on their own way rejoicing; what 

 they may do, or may not do, will not affect me in the least : 

 on my own account I have no favours to ask. I trust, there- 

 fore, in dealing with the subject that my mode of advocacy 

 will be entirely overlooked. 



Mr. Gregory says the d x notation is losing ground : if it 

 be not defunct, I trust it will soon become so: no suffix nota- 

 tion appears in the last Cambridge Problems : this gives some 

 hopes. I think there will be a unanimity in the opinion that 

 the fountain head of mathematical science should be kept 

 clear, that its streams should enlighten as they proceed and 

 not darken and mystify. Those who are placed at the source 

 would in my opinion do well to ponder on the influence they 

 have on the scientific world, to see how much it behoves them 

 to throw a light upon all the subjects they handle, but espe- 

 cially to refrain from making them repulsive by clothing them 

 with darkness. 



Should the preceding desultory remarks educe opinions 

 which may settle a point that now appears to be doubtful, or 

 should they have the least tendency to fix the adoption of one 

 notation, and thus to simplify the science named at the com- 

 mencement, my aims will have been fully accomplished. 



