68 Algebraical Notation. 



waters on the surface of the earth do not occasion any. con- 

 siderable alterations in the law of the diminution of the de- 

 grees, and in that of weight ; that the theory of any consi- 

 derable displacing of the poles at the surface of the earth is 

 inadmissible, and that every geological system founded on 

 such an hypothesis will not at all accord with the existing 

 knowledge of the causes which determine the form of the 

 earth; that the temperature of the globe has not sensibly di- 

 minished since the days of Hipparchus (above 2000 years 

 ago), and that the actual loss of heat in that period has not 

 produced a variation, in the length of the day, of the two 

 hundredth part of a centesimal second. 



TO MATHEMATICAL CORRESPONDENTS. 



To the Editors of the Philosophical Magazine and Journal. 



Since the invention of fluxions, it has generally been cus- 

 tomary among the mathematicians of this country to denote 

 the fluxion of any quantity, as a?, by the symbol x, its second 

 fluxion by x\ its third fluxion by x, &c, as was done by Sir 

 I. Newton : while those on the continent, following the example 

 of Leibnitz, have expressed the same by dx, d J x, d s x, which 

 they have called the several orders of differentials of the quan- 

 tity x. Of late years, however, some of our first mathema- 

 ticians, from a conviction of the latter notation being in many 

 respects superior to the former, have adopted it in their 

 writings; and from the circumstance of its not having been 

 long ago adopted by the mathematicians of Great Britain, 

 some of them even attribute to this cause the comparatively 

 slow progress which the mathematical sciences have made in 

 this country during the last century, to what they have made 

 in France and Germany. Now as the cause of this alleged 

 superiority has never been satisfactorily explained, so far as I 

 can learn, by any English author, except in telling us that it 

 cannot be understood by any but those who have attained a 

 great proficiency in the study of the calculus; I should, there- 

 fore, feel much obliged to any of your dx correspondents to 

 endeavour to furnish something which may throw further light 

 on this subject. Indeed, it has alwa3 T s appeared to me, that 

 if a preference could be given to either of these arbitrary sym- 

 bols, the Newtonian ought to be chosen, as being more defi- 

 nite in its signification, and less apt to produce confusion in 

 the mind of a learner, as the other is apt to convey the idea 

 of a product as well as a differential. 



I am your most obedient servant, 



