Chase. * , ' ) [Oct. I, 



The harmonic denominators for Nos. 1-8, etc., arc of the general form 

 4ji— :). The denominators for Nos. l,-6i, are of the form 4^ — 3 ; V heing 

 equal to ( .i (4r* — 3). The first term of the second series, or the 9tb term of 

 the first series, gives the orbital distance of a planet which would revolve 

 aboul the sun synchronously with a solar half-rotation, a period which 

 IS to be determined, us we have already seen, by the action of LlGHT. 



The term 'J,, or the 45th term of the first series represents the orbital dis- 

 tance of a planet which would revolve in a sidereal day, or synchronously 

 with Earth's rotation on its axis. The corresponding planet may be fitly 

 named Themis, in honor both of the daughter of Ouranos and Gaia, and of 

 her character as goddess of law and order. 



The term :},, or the 81st term of the first series, marks the orbital dis- 

 tance of a planet which would have an orbital period synchronous with 

 Jupiter's rotation on its axis. Its designation has also a double fitness ; 

 Eunomia having been the mythical daughter of Jupiter and Themis, and 

 her name signifying "good government." 



The term 4 1( or the 117th term of the first series, gives the position of a 

 planet which would have an orbital period twice as great as if it were at 

 Sun's surface. 



The term 5,, or the 153d term of the first series, represents a planet which 

 would have an orbital period determined by Herschel's "Subsidence" 

 from opposite extremities of an early solar diameter. 



The term Q v or the 189th term of the first series, represents the present 

 surface of Sun, provided the depth of the photosphere is one per cent, of 

 Sun's radius. 



The denominator of the one hundred and eighty-seventh term of the first 

 series CI -(-186X4=745), which terminates the intra -telluric series, repre- 

 sents the ratio of the aggregate planetary mass to Sun's mass. 



Herschel's modified statement of the nebular hypothesis and Gummere's 

 criterion, not only furnish ground for a satisfactory explanation of such 

 remarkable velocities as that of the inner moon of Mars,* but they also 

 seem to require that secondary orbs, when they revolve in less time 

 than is required for the rotation of their primaries, should be denser 

 than the primaries. I find, therefore, good reason for anticipating that 

 Phobos, as well as any yet unknown possible moons of Mars which have 

 an orbital term of less than a day, will be found to be more dense than the 

 planet itself. 



Thai these accordances tind a vera causa in the harmonic undulations of 

 the luminiferous aether, is made still more evident by the constant solar 

 equation, | g7i = gt = velocity of light: g, representing Sun's superficial 

 gravity al any stage of nebular condensation, past, present, or future ; h, 

 solar modulus of light ; t, time of corresponding rotary oscillation, or half- 

 rotatlon ; t, is also time of traversing \ modulus of light, or £ mean lu- 

 miniferous sethereal atmosphere, under the constant acceleration g. 



■■■■■■ Proc. s,,e. Phil. Amer., wit. 302, :il'J, etc 



