. I 



AT.'M. 



the pectrom, o that there u ft limit to the sharpness of definition of the 

 Ifrrcg Q[ a -^ jh e widening of the lines due to this cause will be in pro- 

 portion to the Telocity of agitation of the molecules. It will be greatest for 

 the molecules of smallest mass, as those of hydrogen, and it will increase with 

 the temperature. Hence the measurement of the breadth of the hydrogen lines, 

 such M C or /' in tin- sj>ectrum of the solar prominences, may furnish evidence 

 that the temperature of the sun cannot exceed a certain value. 



On the Tfteory of Vortex Atoms. 



The equations which form the foundations of the mathematical theory of 

 fluid motion were fully laid down by Lagrange and the great mathematicians 

 of the end of last century, but the number of solutions of cases of fluid 

 motion which had been actually worked out remained very small, and almost 

 all of these belonged to a particular type of fluid motion, which has been 

 since named the irrotational type. It had been shewn, indeed, by Lagrange, 

 that a perfect fluid, if its motion is at any time irrotational, will continue in 

 all time coming to move in an irrotational manner, so that, by assuming that 

 the fluid was at one time at rest, the calculation of its subsequent motion may 

 be very much simplified. 



It was reserved for Helmholtz to point out the very remarkable properties 

 of rotational motion in a homogeneous incompressible fluid devoid of all viscosity. 

 We must first define the physical properties of such a fluid. In the first place, 

 it is a material substance. Its motion is continuous in space and time, and 

 if we follow any portion of it as it moves, the mass of that portion remains 

 invariable. These properties it shares with all material substances. In the next 

 place, it is incompressible. The form of a given portion of the fluid may change, 

 but its volume remains invariable; in other words, the density of the fluid 

 remains the same during its motion. Besides this, the fluid is homogeneous, or 

 the density of all parts of the fluid is the same. It is also continuous, so 

 that the mass of the fluid contained within any closed surface is always r.r</<7/y 

 proportional to the volume contained within that surface. This is equivalent 

 to asserting that the fluid is not made up of molecules ; for, if it were, the 

 mass would vary in a discontinuous manner as the volume increases continuously. 

 because first one and then another molecule would be included within the closed 



