298 Prof. Sylvester on Double Definite Integration, 



epoch of his academic career, was destined also to mark its 

 termination. M. Moll died thirty-seven days afterwards, on 

 the 17th of January 1838, in his native city, and at the house 

 of his friend M. F. A. Van Hall, where he had gone to spend 

 his winter holidays. His remains, according to his desire, 

 were carried to Amerongen, where also repose those of his 

 mother. According to his will, his instruments, and his library, 

 which was very rich, were bequeathed to that university, of 

 which he had been one of the chief supports. 



A. QUETELET. 



XL VI. A Note on Definite Double Integration, sufplementary 

 to a former paper on the Motion and Rest of Fluids. By J. 

 J. Sylvester, Professor of Natural Philosophy in Univer- 

 sity College, London.* 



IN a paper on Fluids which appeared in the December 

 Number of this Magazine, I had occasion to remark, 

 that the mass of an area having at the point {x, y) a density 



— ^ 4- — — could be expressed by the simple formula 

 dx dy 



I i u -^ V —j — >ds; I being the length, and ds an 



element of the bounding curve: this may be thought to re- 

 quire some explanation. 



Fig. 1. 



1 . Let A P B g represent 

 any oval. 



P^; L, A 5 M any two contiguous ordinates cutting the curve 

 in Pp Qq respectively, AC, BD the two extreme tangents 

 parallel to O g, and § the density at any point (.r, y). The 

 expression ffg d x dy will serve to denote the mass of the 

 oval area Ajo Bg', and the limits may be twice taken, i.e. 



1. the two values of y corresponding to any one of x; and, 



2. the two values of x corresponding to C and D. This 



• Communicated by the Author. 



