NA TURE 



THURSDAY, FEBRUARY, 12, 1903. 



THE SCIENTIFIC WORK OF SIR GEORGE 

 STOKES. 



STOKES ranged over the whole domain of natural 

 philosophy in his work and thought ; just one field 

 — electricity — he looked upon from outside, scarcely 

 ■entering it. Hydrodynamics, elasticity of solids and 

 fluids, wave-motion in elastic solids and fluids, were all 

 exhaustively treated by his powerful and unerring 

 mathematics. 



Even pure mathematics of a highly transcendental 

 kind has been enriched by his penetrating genius ; 

 witness his paper " On the Numerical Calculation of a 

 Class of Definite Integrals and Infinite Series,'' x called 

 forth by Airy's admirable paper on the intensity of 

 light in the neighbourhood of a caustic, practically the 

 theory of the rainbow. Prof. Miller had succeeded in 

 observing thirty out of an endless series of dark bands 

 in a series of spurious rainbows for the determination of 

 which Airy had given a transcendental equation, and 

 had calculated, of necessity most laboriously, by aid of 

 ten-figure logarithms, results giving only two of those 

 black bands. Stokes, by mathematical supersubtlety, 

 transformed Airy's integral into a form by which the 

 light at any point of any of those thirty bands, and any 

 desired greater number of them, could be calculated 

 with but little labour and with greater and greater ease 

 for the more and more distant places where Airy's direct 

 formula became more and more impracticably laborious. 

 He actually calculated fifty of the roots, giving the 

 positions of twenty black bands beyond the thirty seen 

 by Miller. 



With Stokes, mathematics was the servant and 

 assistant, not the master. His guiding star in science, 

 was natural philosophy. Sound, light, radiant heat, 

 chemistry, were his fields of labour, which he cultivated 

 by studying properties of matter, with the aid of experi- 

 mental and mathematical investigation. 



His earliest published papers [Cambridge Philosophical 

 Society, April 25, 1842, and May 29, 1843, followed 

 (November 3, 1846) by a Supplement] were on fluid 

 motion ; the second of these and its supplement contained 

 a beautiful mathematical solution of the problem of find- 

 ing the motion of an incompressible fluid in the interior of 

 a rectangular box to which is given any motion whatever, 

 starting from rest with the contained liquid at rest. This 

 solution, as shown in Thomson and Tait's " Natural Philo- 

 sophy," §§ 704 and 707, is also applicable to the very 

 practical problem of finding the torsional rigidity of a 

 rectangular bar of metal or glass. For every oblong rect- 

 angular section, the solution may be put in one or other 

 of two interestingly different forms, which are identical 

 when the cross-section is square and are always both con- 

 vergent. One of them converges much more rapidly than 

 the other when one of the diameters of cross-section is 

 1 more than two or three times the other. Regarding 

 these two solutions, Thomson and Tait (§ 707) say : — 



1 u Collected Mathematical and Physical Papers," vol. 

 From Cambridge Philosophical Society, March ir, 1850. 



PP- 3 2 9-3:7- 



NO. 1737, VOL - 67] 



"The comparison of the results gives astonishing 

 theorems of pure mathematics, such as rarely fall to the 

 lot of those mathematicians who confine themselves to 

 pure analysis or geometry, instead of allowing themselves 

 to be led into the rich and beautiful fields of mathematical 

 truth which lie in the way of physical research." 



The 1843 paper contained his theory of the viscosity of 

 fluids ; and his definite mathematical equations for its 

 influence in fluid motion, which constitute the complete 

 foundation of the hydrokinetics of the present day. In 

 the same paper, by reference to known facts, relating 

 to natural and artificial solids, glass, iron, india- 

 rubber, jelly, and results of experimental investigations, 

 he relieved the theory of elastic solids from what is 

 now known as the Navier-Poisson doctrine of a constant 

 proportion between the moduluses of resistance to com- 

 pression and of rigidity (resistance to change of shape) ; 

 and, following Green, gave us the equations of equili- 

 brium and motion of isotropic elastic solids, with their 

 two distinct moduluses, which constitute the whole theory 

 of equilibrium and motion of elastic solids as we have it 

 at this day. 



Seven years later, building on the foundation he had 

 laid, he communicated another great paper to the Cam- 

 bridge Philosophical Society,' " On the Effect of the 

 Internal Friction of Fluids on the Motion of Pendulums." 

 In this paper he solved the following very difficult 

 problems, taxing severely the mathematical power of any- 

 one trying to attack them. 



(1) The oscillations of a rigid globe in a mass of 

 viscous fluid contained in a spherical envelope having 

 for its centre the mean position of the globe. 



(2) The oscillations of an infinite circular cylinder 

 in an unlimited mass of viscous fluid. 



(3) Determination of the motion of a viscous fluid about 

 a globe moving uniformly with small velocity through it. 



(4) The effect of fluid friction in causing the rapid 

 subsidence of ripples in a puddle and the slow subsidence 

 from day to day of ocean waves when the storm which 

 produced them is followed by a calm. 



Of solution (3) he makes a most interesting applic- 

 ation to explain the suspension of clouds by determining 

 from the known viscosity of air, the terminal velocity of 

 an exceedingly minute rigid globule of water falling 

 through air. His formula for this has been used with ex- 

 cellent effect in the Cavendish Laboratory by Prof. J. J. 

 Thomson and his research corps ; first, I believe, by 

 Townsend in determining approximately the diameter 

 of the globules in a mist produced by electrolysis, by 

 observing its rate of subsidence when left to itself in a 

 glass bell. 



In the interval between the two great papers of 1843 

 and 1850, Stokes gave another magnificent hydrokinetic 

 paper,'- " Theory of Oscillatory Waves," containing a 

 thoroughly original and masterly investigation of a 

 most difficult problem, the determination of the motion 

 of steep deep-sea waves. As an illustration of his results, 

 he gives a diagram (M. and P.P., vol. ii., p. 212) showing 

 the shape of a deep-sea wave in which the difference of 

 level between crest and hollow is seven-fortieths of the 



1 December 9, 1S50, M. and P. P., vol. ii., pp. 1-144., 



2 Camb. Phil. Soc, March, 1847, M. and P. P., vol. i., pp. 197-229, 

 with supplement first published in the reprint M. and P. P.,, pp. 316-326. 



