1881.] o87 [Chase. 



nebular subsidence, and tlie various forms of harmonic synchronism are 

 all dependent upon the same fundamental principles and thej^ should all 

 be kept in mind by thos.e who are investigating the consequences of elastic 

 action and reaction. 



124. Fitndamentcd Pliotodynamic Nodes. 



The principle of forced vibrations, the theory of subsidence, and the 

 laws of varying density in elastic media, are illustrated by the equation, 



(l)'= (3f 



i L 

 . • . log. L : log. M : : — : — 



L =: Laplace's limit of synchronous solar rotation and revolution ; M^=. 

 modulus of light at Sun's surface ; r = Sun's semi-diameter ; i =^ locus of 

 mean incipient subsidence for the nebular centre of planetary inertia, 

 (Saturn's mean aphelion); c = central locus of greatest belt-condensation 

 (Earth's semi-axis major). 



If we adopt the values for L and iff which are given in Note 46, we find 

 4= 9.99861c. Stockwell's value is about ^V ^f one per cent, greater, 

 or 10.000059 c. 



135. A "Derivative Oscillation." 



After announcing the principle of forced vibrations, Herschel continues 

 as follows : ' ' The system may be favorably or unfavorably constituted 

 for such a transfer of periodic movements, or favorably in some of its parts 

 and unfavorably in others ; and accordingly as it is the one or the other, 

 the derivative oscillation (as it may be termed) will be imperceptible in one 

 case, of appreciable magnitude in another, and even more perceptible in 

 its visible effects than the original cause in a third ; of this kind we have 

 an instance in the Moon's acceleration." 



A harmonic illustration of this statement is furnished by the lunar dis- 

 turbance of vertical magnetic force at St. Helena. Von Littrow's esti- 

 mate of Moon's semi-axis major is 60.2778. Earth's action upon Moon and 

 Moon's reaction should therefore be nearly 3 gL 3 as great as its action at 

 its own surface. If the resulting waves or " forced vibrations " are reflected 

 to Earth and resolved, one-half into vertical force and one-half into hori- 

 zontal force, the consequent disturbance should be y^Vr- The lunar dis- 

 turbance of vertical force (Note 121) is yx^T '' ^^ barometer, 72^99. The 

 decimal values are : 



Disturbance of vertical force .0000139 



" vibrations .0000138 



" barometer .0000137 



The derivative oscillation in the horizontal force is obscured by other 

 disturbances. 



PROC. AMER. PHILOS. SOC. XIX. 109. 3v. PRINTED DEC. 31, 1881. 



