TBANSACTIONS OF SECTION A. 647 



point in the plane of a corresponding hyperbola which slides between rectangular 

 guides, generally inclined to the former. 



The theorem takes a curiously interesting though obvious form in the simplest 

 case, -viz., when the ellipse is a hnile straight line ; and then the apparatus also 

 takes a correspondingly simple form. 



5. A Curious Point Connected with the Parallel Axiom. 

 By Professor Chrtstal. 



6. On Conjugate Circle Oroups. By Lieut.- Colonel Allan Cunningham, 

 R.E., Fellow of King's College, London. 



"When three circles whose centres are SI, a>, Q' are coaxal, and are placed so 

 that 0) bisects the distance Q fl', the two circles 12, i2' are said to be conjugate with 

 respect to the circle w. With several conjugate pairs it is shown that — 



1. The join of the centres of two non-conjugate circles is equal and parallel to 

 the join of the centres of their conjugates. 



2. The radical axis of two non-conjugate circles is also that of their con- 

 jugates. 



3. The radical centre of any three circles is also that of their conjugates. 



A group of four conjugate pairs of circles, arranged in a certain way about a 

 triangle ABC, is styled a Bi-conjugate Quartett. Take as example the eight 

 circles which cut three given circles A, B, C, orthogonally or diametrally. 



In this case, in general, the twenty-four pairs of non-conjugate circles have 

 only nine radical axes, and the fifty -six triplets of circles have only thirteen radical 

 centres; the sides and vertices of the triangle ABC are the most important, 

 each side being the radical axis of four pairs, and each vertex the radical centre of 

 eight triplets. 



7. A Method of Finding the Logarithms of Large Numbers. 

 By Rev. Dr. T. Smith. 



MONDAY, AUGUST 8. 



The following Reports and Papers were read : — 



1. Beport of the Committee on the Ultra-Violet Bays of the Solar Spectrum. 



See Reports, p. 74. 



2. On the Construction of the New Physical Laboratory at Groningen, Holland. 

 By Professor P. H. Schoote. 



3. Interim Beport of the Committee on Measuring Optical Constants. 



4. On a Method of Determining Thermal Conductivities. 

 By Charles H. Lees, M.Sc. 



This method has been designed to determine the conductivities of liquids when 

 only small quantities are available. It follows closely the definition of conduc- 

 tivity. A cyhnder of thin copper, about 3 cm. diameter and 4 cm. high, has a 

 copper base 3 mm. thick, and is filled with water in which is placed a coil of wire 



