1883.] «^"* [Chase. 



ratio of the circumference of a circle to its diameter {lb., xiii, 140-1, xiv, 

 609-13, et al.). (7). Time integrals, rotation- waves, harmonic vibrations, 

 polar forces, etc. [lb. xiv, 141-7). (8). Laplace's limit, and its variation as 

 the f power of the nucleal radius {lb., xiv, 612, 622, 653, etal). (9). Con- 

 stancy of pressure and constancy of volume {lb., xiv, 651). (10). Instanta- 

 neous velocity, implying spiritual influence {lb., xiv, 611 ; xvi, 302, et al.). 

 (11). Comparative variations of distance and density, in elastic media {lb., 

 xvii, 109-12, et al). 



350. Relation of laertia to Time and Force of Oscillation. 

 M. Lipschitz, in a letter to M. Hermite {Comptes Rendus, xcv, 1141), 

 discusses some points wliich have an important bearing on my funda- 

 mental equation (Note 321), and on time-integrals in general. Supposing 

 a heavy body to turn freely about a horizontal axis, he considers two kinds 

 of movement. In the first, the angular velocity becomes at ^„ ; in the 

 second, at z — Oo- The times in the two movements may be expressed by 

 elliptic integrals of the first order, with complementary moduli. The 

 corresponding integrals of the second order represent Hamilton's accumu- 

 lated vis viva, or the integral of which the element is equivalent to the 

 sum of all the living forces of the system multiplied by the element of the 

 time. The result of the discussion, which he considers remarkable, gives 

 an equation of oscillating times and accumulated vis vim, for the two kinds 

 of movement, which depends solely on the moment of inertia of the body. 



351. Motion of Sun-Spots in Latitude. 

 Spcerer, in a letter to Faye {Gomptes Rendus, xcv, 1110), reports observa- 

 tions upon the movement of Sun-spots in latitude. Arranging the observa- 

 tions of twenty years (1861-80) in 5° belts, he finds a slight excess of move- 

 ment towards the equator between the parallels of 5^ and 10° and a slight 

 excess towards the poles between the parallels of 20° and 25^. Carrington 

 and de Rico found a predominance towards the equator between 0^ and 

 15°, and towards the poles in higher latitudes, but the indications were so 

 slight that Carrington attached no importance to them. Faye regards these 

 results as fatal to the theory of Siemens, for if the Sun is fed by the subsi- 

 dence of matter towards the poles, he thinks that the equatorial centrifu- 

 gal force should produce a constant tendency of spots towards the equa- 

 tor. He also calls attention to the fact that the centripetal force at Sun's 



equatorial surface ( V -^ »'rot ) is about 48000 times as great as the cen- 

 trifugal, and he attributes the equatorial increase in apparent velocity of 

 rotation to the continual convection-currents between the photosphere and 

 the 'n'erior of the Sun. 



352. Photodynamic Centrifugal Energy. 

 At the very outset of my planetary investigations I called attention to 

 the accelerating effects of "subsidence," and Hall's discovery of the 

 moons of Mars strengthened my conviction that such acceleration was the 



PKOC. AMER. PHILOS. SOC. XX. 113. 3V. PRINTED MARCH 19, 1883. 



