6 
REPORT— 1847. 
On the Resistance of a Fluid to ttco Oscillating Spheres. 
By G. G. Stokes, M A. 
Th (5 object of this communication was to show the application of Professor Uk®- 
Mil's method of images to the eolutioo of certaia problem# in Hydrotlp^, 
““PP®*® there exists in an tnhnite tua## of incompressible fluid a poiot frta ' 
wbteh, or to which the fluid is flowing with a velocity alike io all directiooi. Coo* 
«ivp now two such points, of intensities raruj in mogoitude and opposite iaspi, | 
to coeatat in the fluid ; and then suppose these points to approach, and uirimiidr , 
ctwU^. their intL-nsities varying invcraely as the distaoce between them. Let tii 
rrsultjng point be called a singular point r^f ttis sfcnnd order. The motion of the 
I uiu OOTUt a Bohd. oscillatinK sphere is the same as if the solid sphere were rqiliwd 
jy ttuid, in the centre of 'whicu existed such a point. It is easy to show that tk 
mohon of n fluid due to a point of this kind, when the fluid it interrupted byarfAm 
aring Its uentre m the axis of the singular point, is the same as if the sphere's pl»R 
were occupied by fluid containing one singular point of the second orto. Bytic 
pp ica lou of this principle may be tuund the resistance experienced by a sphsrtcs* 
nm ^it**l^ ‘o prosence of a fixed sphere or plane, or within a spherical envdopt, the 
Cl a ion taking place in the line joining the centres, or perpendicular to tbepUBr- 
n a similar manner may be found the resistance to two spheres which tooth, or ire 
onntc ed by a rod, or to the solid made up of two spheres which cut, pravidEti tk 
ex crior angle «if the surfaces be a submultiplu of two right angles, the oscillatit* in 
those cases also taking place in the line joining the centres. The numerical cska- 
lation IS very simple, and may be carried to any desired degree of accuracy. 
On Electrical Images. Jig Tirt>MsoN, Professor of Natural Phikapk 
in the University of Glasgow. 
ftiZul'Ii!! of natural pbilosophy of which the elementary laws are more 
bnri,,*j. ...» winch regulate the distribution of electricity upon condurtiM 
th«>rv'reproach o'f the mathen^ 
smlA'lmv/. h-a*^*^* ■ ] varied and interesting problems which hi*** 
comideshv sujywts for investigation, on account of the apparently 
from IE satisfied; and even when results have b^ 
almost lost in f a Poisson, the physical interest has 
solution h'ls fill,! niatherriatical diiflculties, and the complexity oi the 
fied in anv Mnn? lull interpretation without which the mind cannot be atis- 
Sion nftrJth in LtumlSXVr’*'^ 
as^ entirely removed Mi forbmn 
must consLitnif. electricity, aod led to the elementary propositiofi# wbidi 
that is to bo Tn»/t,*r'' foundation of every perfect inatliematical slrtct®* 
nJ only doTov furnished in the nperimental laws by Coulomb, 
tive cxp^!noniUttexplanatU# of the beautiful 
but they BUffWHt 1.1 liavc been w interesting at all tiruca to practical electric^ 
dealing wiih^rohl^. ^ ®®l|»®matician the simplest and most powerful methodjol 
ia principle Of electrical images." wkeh 
p-eat^rietv nf propositions, as the proper way of treatiui: * 
tion of eIcctricJtJ'nn Present themselves with reference to the distriiw* 
givrn maniirr onr n conductors. The cflect of a body electrified in 
bywhal mnv bi.MH «phere is shown to be completely represented 
I’lc gcojnotrical eotipfi-ii of the electrified bodyia the sphere," and a dro- 
an flfctritied body w ntailT-*’* .l»y which this image may be described, "'i'® 
duciiiv effect Is nr...j.. ®®'?hbourhood «iftwo cninsulatcd spheres, an i** 
ce.s8ive imacos " fn winch may be represented bv an infinite series of "sat’ 
lion#, by nu’noB of ^?.v algebraic expreseion of this result leads/J »lu- 
ference to the various problems which occur with re- 
n of the induced electricity, and the attractions exerted by 
