230 Professor Joseph Larmor [May 1, 



recruit his energies in summer, reacted naturally towards the im- 

 provement of nautical affairs. His dynamical instinct, and expe- 

 rience in the invention of delicate instruments, found a congenial field 

 in placing the ship's compass on a scientific basis. The heavy cum- 

 brous magnets, swinging on pivots under unsuitable conditions, were 

 replaced by the well-known systems of needles, delicately suspended 

 yet insensitive to shock, so small that the iron masses compensating for 

 the magnetism of the ship could be effectively introduced in moderate 

 size. Again, by the use of steel wire, he worked up the modern 

 method of taking reliable soundings from a ship in motion, the depth 

 being calculated from the compression of the air in a narrow glass 

 tube attached to the sinker. But the most remarkable feat in this 

 domain was the thorough practical mastery of the complicated pheno- 

 mena of the tides, achieved mainly under his direction, and culmin- 

 ating in the invention, about 1876, of simple automatic mechanism 

 for performing all the laborious calculations of tidal harmonic 

 analysis, both direct and inverse. The tides are controlled by the 

 Sun and Moon, and so repeat themselves very closely in periods of 

 nineteen years. But there is another far more fundamental and 

 instructive way of investigating them. To every periodic (simple 

 harmonic) component in the motion of either Sun or ^loon relative 

 to the Earth, there corresponds a component of the same periodic 

 time in the tide produced by them at any place, and there are no 

 other components ; yet to calculate their amounts directly with the 

 existing irregular contours and depths of the ocean would be a prob- 

 lem practically impossible. The method of harmonic analysis, as 

 first initiated in this subject on a nmch smaller scale by Laplace, 

 allows us to deduce, from a tidal record for a sufficient length of time, 

 the amplitudes and phases of these harmonic components of known 

 periods ; and when the more important ones have been thus deter- 

 mined, the prediction of future tides becomes a matter of merely 

 summing up the harmonic constituents, no matter how complex the 

 physical conditions at the place in question may be, so long as they 

 are unchanging. All this and much more can now be done by the 

 machines invented by liord Kelvin and his brother,* though, owing 

 to the preliminary imperfection of construction of the analysing 

 machine, it is at present found to be safer and not very troublesome 

 to determine the amplitudes of the components by calculation. This 

 achievement — the complete mastery of the tides by means most 

 simple but adequate — is perhaps the greatest triumph of the method 

 of Fourier, which has always been one of the advances most admired 

 by Lord Kelvin in modern physical mathematics. After this success 

 it was natural to apply the same method of harmonic analysis to 

 meteorological phenomena, including the atmospheric electricity 

 which he had investigated many years before, which also are con- 



See Thomson and Tait's Nat. Phil., ed.- 2, Appendices. 



