De !a Rue mid JMuller on Terephthalic Ada 'and its Derivatives. 541 



l|A|| = ||«|!x 



|-^-, 0, 0, ... 



Vn-l 



o, ^=-\ o, 



Vn-2 



0, 0, 



Vn-2 



. 

 . 



o, o, 



The following result (among many which may be deduced from 

 this transformation of a square matrix) admits of frequent ap- 

 plications : — 



" If D be the greatest common divisor of the determinants of the 

 matrix of any system of n independent linear equations ; of the D" 

 sets of values (incongruous mod. D) that may be attributed lo 

 the absolute terms of the equations, the system is resoluble for 

 D»-i , and irresoluble for D"" 1 ( D- 1)." 



As an example of the use that may be made of this result, it is 

 shown, in conclusion, that it supplies an immediate demonstration of 

 a fundamental principle in the general theory of complex integral 

 numbers, composed of the root of any irreducible equation, having 

 its first coefficient unity, and all its coefficients integral ; viz. that 

 the number of incongruous residues, for any modulus, is always 

 represented by the norm of the modulus. A demonstration of this 

 principle has, however, already been given in the ' Quarterly Journal 

 of Pure and Applied Mathematics,' in a paper signed Lanavicensis ; 

 to whom, therefore, the honour of priority in this inquiry is due. 



" Contributions to the Physiology of the Liver — Influence of Alka- 

 lies." By Frederick W. Pavy, M.D, 



Feb. 7. — The Bakerian Lecture. — On the Absorption and Radia- 

 tion of Heat by Gases and Vapours, and on the Physical Connexion 

 of Radiation, Absorption, and Conduction. By Professor Tyndall, 

 F.R.S. (This paper was printed in full in the September and October 

 Numbers of this Magazine.) 



Feb. 14. — "On Magnetic Storms and Earth- Currents." By 

 Charles V. Walker, Esq., F.R.S., F.R.A.S. 



February 21. — Major- General Sabine, R.A., Treasurer and Vice- 

 President, in the Chair. 



The following communications were read : — 



" On Terephthalic Acid and its derivatives." By Warren De la 

 Rue, Ph.D., F.R.S. &c, and Hugo Midler, Ph.D., F.C.S. 



Whilst pursuing our investigation of Burmese naphtha, an abstract 

 of which we have already communicated to the Society, we noticed, 

 among the products of the action of nitric acid on certain liquid 

 hydrocarbons contained in Rangoon tar, an acid of peculiar pro- 

 perties. A very lengthened investigation of this acid and its de- 



