430 Mr. J. H. Cotterill on the Further Application 



ance of a separation of the fibres or laminae, those means should 

 be adopted which, by improving the general health, are most 

 likely to restore the aqueous humour to its usual state. Nothing 

 is more easy than to determine the condition of the crystalline 

 lens; and by the examination of a small luminous object placed 

 at a distance, and the interposition of small apertures, and 

 small opake bodies of a spherical form, we can ascertain the 

 exact point in the lens where the fibres and laminse have begun 

 to separate, and may observe from day to day whether the disease 

 is gaining ground or disappearing. 



[Since the preceding paper was read, I have seen a remark- 

 able work, entitled Etudes Cliniques sur l' evacuation de VHumeur 

 Aqueuse dans les Maladies de VCEil, par Casimir Spirino (Turin, 

 1862), pp. 500. M. Spirino had, in the course of little more 

 than a year, operated upon forty-five cases of cataract. In many 

 of these the cataract was perfectly cured, and in others the sight 

 was improved. The first case was that of a lady of eighty-one, 

 who had cataract in both eyes. After thirty-two evacuations of 

 the aqueous humour by the same aperture, and almost always 

 two or three times at the same sitting, both cataracts disap- 

 peared, the lady was able to read, without glasses, Nos. 3 and 4 

 of Jaeger's scale, at the distance of 4 or 5 inches, and even to 

 thread a small needle.] 



LX. Further Application of the Principle of Least Action. By 

 James H. Cotterill, B.A., Scholar of St. John's College, 

 Cambridge*. 



IN two former articles of this Magazine the principle that 

 the work done, in a system in equilibrium of elasticity, 

 is a minimum, has been applied to cases in which the law of varia- 

 tion of internal stress is supposed to be known, and it is required 

 to find the absolute amount of that stress. I shall now consider 

 some cases in which it is required to find the law of variation, 

 chiefly with a view to verify the statement made in a former 

 article, that the results obtained are identical with those obtained 

 by other methods. 



1. A thick hollow cylinder is exposed to fluid pressure, the 

 material being perfectly elastic ; it is required to find the law of 

 variation of the principal pressures. 



Symmetry shows that the principal pressures must be parallel 

 and perpendicular to a radius of the cylinder. Let p and q be 

 these pressures ; then if a concentric cylinder, radius r and thick- 

 ness Br, be conceived divided into equal parts by a longitudinal 



* Communicated by the Author. 



