488 Dr. P. Lowell on Photographs of Jupiter 



other by momenta, is valid apart from any question of 

 ignored coordinates. Thus generally the force-equations 

 being 



<ap) ~dt-dkp-lb.r p ' *^'»^- dt ~B^r' 

 and x m+r being — -^ — , there is exact agreement between 



Ogm+r 



these forces and those derived from the formula 



^BTo_BTo 

 dt ^x ~d.v ' 



When the coordinates x m+r do not appear in the coefficients 



dP 

 of T , and there is no corresponding external force, -^J— =0, 



i. e. these momenta are constant. Thus what for the general 

 case is an admissible modification of the expression for energy, 

 and of the form of the force-equations, becomes in the case 

 of ignorable coordinates the reduced form of the system. In 

 this case K has the true character of a potential energy, 

 while the existence of I marks the interaction between the 

 two groups originally shown by the presence of product 

 terms of the form ic p cc m+r . 



In conclusion it may be noted that T is the minimum 

 value of T which can be obtained by giving real values 

 to d' m +i ... ir n , because the minimum problem leads to the 

 group of equations (4) with f m+r =0. 



LIU. Photographs of Jupiter taken at the Lowell Obser- 

 vatory, April 1909, by Mr. E. C. Slipher and the Director, 

 Dr. Percival Lowell. By Dr. Lowell *. 



THE photographs of Jupiter taken here this spring may 

 be considered under two distinct heads : — 1, researches 

 on what measures of them yield ; 2, study of the markings 

 represented. 



The first investigation was rendered possible by the great 

 size to which it proved the images could be enlarged without 

 loss of detail. The results are interesting, for they have 

 something to say about the planet's physical condition. 



1. We will begin w r ith the ellipticity of Jupiter's globe. 

 Measures of the equatorial and polar diameters in five 



* Communicated bv the Author. 



