620 REPORT— 1895. 



dicular to the plane A OH — result in the expression of the leno;ths of the six edges 

 of the tetrahedron in terms of two positive quantities a, k as follows : — 



AD=BC=2fl; _ 



AB = BD = DC = «%/1 + A;\ 



Hence o < A; < \/3. 



The faces B D A, B D are equal isosceles triangles. 



The faces A C B, A D are equal scalene triangles. 



The planes B C A, B C D are perpendicular to each other, and so are the planes 

 A D B, A D 0. 



The planes A G B, A C D are inclined at an angle of 60°. 



The planes ABC, ABD are inclined at the acute angle whose cosine is 

 ^ V 3 — /c", and so are the planes C D A, C D B. 



The planes B D A, BD C are inclined at the angle whose cosine is | (/c^-l), 

 which is obtuse if o<li<\, hut acute if 1<A;< -v/S. 



12. On AhsohUe and Relative Motion. By Trot J. T). 'Everett, F.H.S. 



Though there is no test hy which we can distinguish between absolute rest and 

 uniform velocity of translation, D'Alembert's principle furnishes a test by which 

 deviation from such uniformity can be detected. Every deviation produces the 

 game effects which would be produced by bodily forces opposite to the actual 

 changes of velocity. The intensity of the apparent bodily force is equal in each 

 case to the absolute acceleration. 



What is called centrifugal force is an apparent bodily force directed outwards 

 from the centre of curvature of the body's path, and having an intensity equal to 

 the distance from this centre, multiplied by the square of the absolute angular 

 velocity. Angular velocity, unlike velocity of translation, involves acceleration ; 

 and by comparing the accelerations of different points of a rigid body we can 

 measure the absolute angular velocity of the body. The slope of a conical pen- 

 dulum and the concavity of the surface of the liquid in a revolving vessel are 

 phenomena whicli depend on absolute velocity of horizontal rotation ; and another 

 measure of horizontal angular velocity is furnished by differences of pressure at 

 different points in a horizontal tube full of liquid. 



13. On the Magnetic Field due to a Current in a Solenoid. 

 By W. H. Everett, B.A. 



Tlie case of a solenoid of circular section is tlie only one hitherto investigated, 

 and this has been done by considerations derived from magnetic shells. In this 

 paper the problem is approached by a more direct method, and general solutions 

 are obtained in a form which can be readily worked out to numerical values. 

 Special application is made to the case of a rectangular (or polygonal) solenoid, the 

 component forces being expressed in finite terms. For a very long solenoid of 

 any form of section the longitudinal force in either of the end sections is shown to 

 be exactly the same at all points, and in any solenoid the longitudinal force is 

 shown to be more uniform in the end sections than in the medial section. As a 

 particular case the method gives the component forces due to a plane circuit at 

 any point in its field ; and a simple expression is found for the force, at any interior 

 point, due to a circular current. 



