on the Besistance of the AtDiosphere to an oscillating Sphere. 325 

 Equation (3.) therefore becomes 



"~ 7- * d t- r ' d)" r^ ' dr r^ dz 



The two parts of this expression which depend upon R 

 and upon S' are essentially distinct, and the equation there- 

 fore expresses these two things : 



dS' ( , . ., , ^ rfS' ,, f/S'\ 



= —r— ( and similarly = -, — , = ~ — I 



dz \ ■^ dx dy J 



^ ~ Tt^ dr"" r ' 'd7 '^ r' ' 

 From the first of these equations S' = C, 



dS d S dS ^e. /-I 



or X y— + y-, 1- ~ -5— + 2 S = — C r, 



dx dy dz 



the integral of which is S = -j- . 4) ( —j -^j -7 ) r~ • 



The solution of the second equation is 



_ f'{r-at) f{r-ai) , W[r^at) Y{i-^at) 



W, — -) 



r r^ r r- ' 



where k a" = 1, 



And hence the complete value of in its most general form 

 f jr-at) _ f{r-at) Y'(r-^at) Y{r-^at) 



Cr 



I / X y z\ Cv 



I will now explain these several terms. 



1st. Motion from the centre is possible without any other 



C >• 



motion if the velocity is expressed by — —— , that is, if every 



spherical layer to unlimited distance increases or diminishes 

 constantly with the time in the same geometrical proportion. 

 The meaning of this term will be fully understood if we ex- 

 amine the corresponding expression for — -^^ j which is then 



S' or C. As we cannot conceive a case in which the sur- 

 I'ounding atmosphere can have the density proper for this 

 case, we may at once dismiss it as inapplicable to any practi- 

 cal problem. 



2nd. Motion from the centre is possible without any other 



1 / X V ^ \ 

 motion if the velocity is expressed by -;^ <^ ( T' .» ~T )» 



