32 Observations on the Notations employed in 



pocus operations on optical symbols without any regard to the 

 mental images they are designed to represent. In the higher 

 branches of analysis this new-fangled notation will defy the 

 presence of anything like distinct ideas: for instance, an ele- 

 mental parallelopiped d x dy dz is reduced to the confused and 

 incomprehensible form d x yd x z dx?. It is the duty of every 

 mathematician to make known his opinion concerning it." 



Mr. Woolhouse's attainments are such, that his opinion 

 upon this, or upon any other mathematical subject, is cer- 

 tainly deserving of respect. 



A writer in the Northumbrian Mirror, new series, p. 89, 

 says, " We cannot conclude without noticing the clumsy dif- 

 ferential notation which has recently captivated the publishers 

 of mathematical works at Cambridge; it offends against sim- 

 plicity, symmetry and clearness; it is a meretricious show of 

 conciseness, and an innovation that every lover of simplicity, 

 brevity and neatness, should repudiate. 



" In the differential coefficients of two or more varieties the 

 expression is, of necessity, so overloaded with those little ugly 

 off-shoots growing out of the side and stem that the body of 

 the tree is almost hidden from the view." 



I have made this quotation to show the writer's opinion, 

 I certainly do not see that a little x deserves to be called ugly 

 any more than a great one, but the phraseology is the writer's; 

 however, it will be observed that the opinions on each side 

 are made pretty strong. 



The integral calculus is the reverse of the differential ; 



integration is commonly denoted by the symbol f : thus, 



xd.v t /» xdx ,—- 



d. V a* + x* = ,-<n—* and A/T^— 'a ' = V « 2 + x* 

 Va 2 -far J va z +x l 



In the suffix notation for integrals the sign of integration is 

 f x \ in this case only the differential coefficients are employed : 

 if the d x notation be employed at the same time, then/^ is the 

 symbol of an operation precisely the reverse of d x ; thus — 



d x . V a 2 + x 2 



«s 



V a 2 + x* 



The suffix notation for integrals is found in many of the 

 mathematical works at Cambridge; for instance, Hymer's 

 Integral Calculus and Differential Equations, Murphy on 

 Electricity, Earnshaw's Works, Airy's Tracts, &c. 



The authors just mentioned are an honour to one of the 

 first universities in the world ; they are stars of the first mag- 



