S 12 Royal Society. 



tween the acidity of the urine and the amount of uric acid in it. 

 The urine that was most acid contained least uric acid; that which 

 contained most uric acid was not most acid. All food causes an in- 

 crease in the amount of uric acid in the urine ; and there is no de- 

 cided difference between vegetable and animal food, either as to the 

 increase or diminution of the amount of uric acid in the urine. 



Part III. Variations oj the Sulphates in the Urine in the healthy 

 state, and on the influence of Sulphuric Acid, Sulphur and the Sul- 

 phates, on the Sulphates in the Urine. 



The result of these experiments is, that the sulphates in the urine 

 are much increased by food, whether it be vegetable or animal. Ex- 

 ercise does not produce a marked increase in the sulphates. Sul- 

 phuric acid, when taken in large quantity, increases the sulphates in 

 the urine. In small quantity, even when long-continued, no effect 

 on the amount of sulphates is manifest. 



Sulphur taken as a medicine increases the sulphates in the urine. 

 Sulphate of soda and sulphate of magnesia produce the most marked 

 increase in the sulphates in the urine. 



Feb. 8. — "On the application of the Theory of Elliptic Functions 

 to the Rotation of a Rigid Body round a Fixed Point." By James 

 Booth, L.L.D.,F.R.S. 



In the introduction to his investigation, the author, after noticing 

 the investigations of D'Alembert and Euler, and the solution of this 

 problem by Lagrange, refers more particularly to the memoir of 

 Poinsot, in which the motion of a body round a fixed point, and free 

 from the action of accelerating forces, is i*educed to the motion of 

 a certain ellipsoid whose centre is fixed, and which rolls without 

 sliding on a plane fixed in space ; and likewise to the researches 

 of MaccuUagh, in which, by adopting an ellipsoid the reciprocal of 

 that chosen by Poinsot, he deduced those results which long before 

 had been arrived at by the more operose methods of Euler and La- 

 grange ; observing, however, that it is to Legendre that we are in- 

 debted for the happy conception of substituting, as a means of inves- 

 tigation, an ideal ellipsoid having certain relations with the actually 

 revolving body. He then states, that several years ago he was led 

 to somewhat similar views, from remarking the identity which exists 

 between the formulae for finding the position of the principal axes of 

 a body and those for determining the symmetrical diameters of an 

 ellipsoid ; and further observing that the expression for the per- 

 pendicular from the centre on a tangent plane to an ellipsoid, in 

 terms of the cosines of the angles which it makes with the axes, is 

 precisely the same in form as that which gives the value of the mo- 

 ment of inertia round a line passing through the origin. Guided by 

 this analogy, he was led to assume an ellipsoid the squares of whose 

 axes should be directly proportional to the moments of inertia round 

 the coinciding principal axes of the body. This is also the ellipsoid 

 chosen by MaccuUagh. Although it may at first sight appear of 

 little importance which of the ellipsoids — the inverse of Poinsot, or 

 the direct of MaccuUagh and the author — is chosen as the geome- 

 trical substitute for the revolving body, it is by no means a matter 



