560 REPORT— 1897. 



at 15°, 20°, and 25°, by his value at 15°, and do tlie same for Griffiths' values, we 

 get in each case as quotients the numbers 1, 0-998, 0'997/ 



This seems to indicate that the discrepancy between Rowland's results and those 

 obtained electrically is not one of thermometry, but an error in the measurement of 

 energy, possibly in the standards of electrical resistance, or of electromotive force. 



[A note concerning these comparisons appeared in the Johns Hopkins University 

 Circular for June 1897. The corrected values for the mechanical equivalent given 

 in it differ a little from those given above, owing to a slight error iu the method 

 used at first in reducing the comparisons.] 



15. A Comjiarison of Rowland's Mercury Tliermomeler loith a Griffiths^ 

 Platinum Thermometer. By F. Mallory and C. W. Waidner. 



SATUBDA r, A UO VST 21. 

 The Section did not meet. 



MONDAY, AUGUST 23. 

 The Section was divided into two Departments. 



The following Reports and Papers were read : — 



Department I. — Mathematics and Physics. 



1. Report on Tables of certain Mathematical Functions. 

 See Reports, p. 127. 



2. On the Solution of the C^ihic Equation. By Alexander Macfarlanb. 



In a paper recently contributed to the American Institute of Electrical 

 Engineers - the author showed that the two roots of a quadratic equation may 

 always be viewed as a pair of conjugate complex quantities, either circular or 

 hyperbolic. The real roots can be viewed as hyperbolic complex quantities. In 

 this paper it is shown how the two binomials which occur in Cardan's formula 

 may be treated as complex quantities, either circular or hyperbolic ; and a general 

 method is given for deducing all the roots of the cubic, whether the formula is 

 reducible or apparently irreducible. The trigonometrical meaning is shown of the 

 two non-real roots in the reducible case : they involve the cosine of an angle, 

 which is partly circular, partly hyperbolic. 



3. Tlie Historical Development of the Ahelian Functions. 

 By Dr. Harris Hancock. — See Reports, p. 216. 



4. On a Notation in Vector Analysis. By Professor O. Henrici, F.R.S. 



The notations in use to denote the different products of vectors are not suf- 

 ficiently expressive, and not convenient in use. The author therefore proposes 



> Griffiths, PMl. Trans., 184 A, 1893, p, 361 ; P/til. Mag., 10, pp. 437, and 447, 1895. 

 = 'Application of Hyperbolic Analysis to the Discharge of a Condenser.' 



