18 president's address — SECTION A. 



recently that I have been able to return to them. And I find that 

 the Theory of Integral Equations removes several difficulties which 

 formerly had made my progress difficult. 



This is but a slight example of the close connexion between the 

 different branches of Pure and Applied Mathematics. And it is often 

 in the most unexpected quarters that this relation is revealed. We 

 saw, in speaking of Poincare's earlier work, that his acquaintance with 

 Non-Euclidean Geometry gave him the key to a difficult question in 

 the Theory of Functions. Curiously enough, in the Theory of Rela- 

 tivity we come upon a similar instance. Sommerfeld had shown that 

 the Composition of Velocities in the Theory of Relativity agrees with 

 the formulse of Spherical Trigonometry when the radius of the sphere 

 is imaginary. Now Lobatschewsky and Bolyai long ago established 

 the connexion between their Non-Euclidean Geometry and this Ima- 

 ginary Trigonometry. It followed that an interesting field for the 

 application of the Theory of Relativity was to be found in Non-Euclidean 

 Geometry. Varicak has proved that the formulae of that theory have a 

 ready interpretation in that Geometry. His next step was to assume 

 that the phenomena happen in a Non-Euclidean Space, and he 

 obtained the formulae of the Theory of Relativity by very simple 

 geometrical argument. He states his results as follows : — " Assuming 

 the Non-Euclidean terminology, the formulae of the Theory of Relativity 

 not only become essentially simplified, but they also admit a geometrical 

 interpretation, which is wholly analogous to the interpretation of the 

 classical theorj^ in the Euclidean Geometry. And this analogy often 

 goes so far as to leave the actual wording of the classical theory 

 unchanged. We need only replace the Euclidean image by the corre- 

 sponding image in the Lobatschewsky space, whose parameter c is 

 equal to 3 x IQi*^ cm." 



1.— HARMONIC TIDAL CONSTANTS OF NEW ZEALAND 

 PORTS (WELLINGTON AND AUCKLAND). 



By C. E. Adams, M.So., F.R.A.S., Government Astronomer of 

 New Zealand. 



ABSTRACT. 



The harmonic tidal constants given in cohmins 1 and 4 of the 

 attached Schedule were obtained from an harmonic analysis of the 

 hourly ordinates from the automatic tide gauges at Wellington and 

 Auckland. For each port the Tidal Abacus of the late Sir G. H. Darwin 

 was used, and the whole of the calculations have been carried out in 

 duplicate. For the additions the Mercedes adding machine has been 

 found to be of the greatest assistance, while the Brunsviga calculating 

 machine, with the printing attachment, and the Millionaire calculating 

 machine have been invaluable in the numerous calculations. For the 

 fine plotting of curves the Coradi co-ordinatograph has been very useful. 



