44 SIXTH REPORT — 1836. 



which might have been used, in conjunction with the initial condition 



;=i"'.{Cf^'y+(^')'-'}' <'^)' 



to determine the form (7)' of the principal function s ; and thence might 

 have been deduced, by the same new principles, the ordinary integrals 

 (3)', under the forms 



a, =: X, + a\ (a — s), 02 = x^ + a'j (« — &)• (6)' 



In so simple an instance as this, there would be no advantage in using 

 the new method ; but in a great variety of questions, including all those 

 of mathematical optics, and mathematical dynamics, (at least, as those 

 sciences have been treated by the author of this communication,) and 

 in general all the problems in which it is required to integrate those 

 systems of ordinary differential equations (whether of the second or 

 of a higher order) to which the calculus of variations conducts, the 

 method of principal relations assigns immediately a system of finite 

 expressions for the integrals of the proposed equations, an object 

 which can only very rarely be attained by any of the methods known 

 before. It seems, for example, to be impossible, by any other method, 

 to express rigorously, in finite terms, the integrals of the differential 

 equations of motion of a system of many points, attracting or repelling 

 one another ; which yet was easily accomplished by a particular appli- 

 cation of the general principles that have been here explained*. The 

 author hopes to present these principles in a still more general form 

 hereafter. 



CHEMISTRY. 



On the Chemical Nomenclature of Berzelius. By R. Hare, M.D., Pro- 

 fessor of Chemistry in the University of Pennsylvania, 



Berzelius has divided those bodies which by union with a radical 

 produce salts, and those which are capable of entering into saline com- 

 binations both as acids and bases, into two classes, designated as Halo- 

 gen and Amphigen. Dr. Hare stated his objections to this classification, 

 remarking especially on the ambiguity of the terms salts, acids, and 

 bases. He would distinguish all electro- negative compounds bj^ sub- 

 joining the termination acid, and all electro-positive compounds, formed 

 either by halogen or amphigen bodies, by subjoining the termination base, 

 and confine the use of the termination ide to those compounds of which 

 the electrical habitudes are indeterminate : lie proposed to substitute 

 the terms chlorohydric, sulphohydric, &c., for hydrochloric and other 

 analogous words ; and on this point stated that the opinion of Berzelius 

 coincides with his own. 



•See Philosophical Transaclions for 1831 and 1833; also, Report o( Edinburgh 

 Meeting of the British Association. 



