252 A LOGICAL NOTATIOX FOR MATHEMATICS. 



notation the mathematicians of those days endured and to be- 

 thankful for the improvements of the century following. In the 

 present age, such changes are more difficult to introduce, and 

 there is a strong tendency to get " stereotyped " or fixed in a sort 

 of Chinese arrest. This tendency should be carefully guarded 

 against. If we consider the spelling of the English language,, 

 reform seems to be almost hopeless; although it is true that great 

 simplifications of spelling have been introduced into Spanish, Ger- 

 man, Italian, and I am glad to say the High Dutch used in 

 South Africa. We have also a successful innovator in mathe- 

 matics amongst us, I refer to Dr. Muir, who has softened our 

 path in trigonometry by the successful introduction of the useful 

 "radian. " 



D „ — (differential coefficient of) [already in. 



dl partial use.] 



The use of D instead of —j^ is, as already remarked, not 

 new, but it is rare. Should it be necessary to indicate the vari- 

 able we should write D. Thesign /might be replaced by D-i. Italic 



D might indicate partial differentiation. Some typical equations 

 compare as follows : — 



d dv du 



— (vv) = u — +2' — with DuV'^nldv-vvDu 



dt dt dt 



The linear equation 



transforms to 



/' 



udx with D-,?/ 



dv d'v 



V + X— + .1* 



dx dx* 



(i+2-D + j'^D')r 

 and thus avoids powers of the differential coefficient which seem- 

 absurd in a " Linear " equation. 



These would carry the ordinary student over the usual range 

 of his mathematics. He could be introduced to the effect of the 

 operators S and C when learning algebra (immediately after 

 Geometrical Series) ; and given exercises on 



S-.r + C-.r=i 

 and shown that he can separate the symbols of operation frorrk, 

 those of quantity, thus : — 



(S- + C).r=i 

 etc., etc. 



