G. Hinrichs on Planetology. 
ts 
Sg 
ae 
Equating (53) and (54), and solving for /(é), we find, 
. 
| 
4 A) =e ; Uae 
or, by (54), Ayare |e. ae area 
But Kepler’s third law gives u=a.v? (this Journal, vol. 
XXXvii, p. 38, note); hence 
. (87) 
SD) ABS ee aut B 
consequently, by (49), and a being now the same again, 
Re OR em eee ee 
or (48), cos 7 being almost equal to one, the orbit being nearly 
circular, -Revvo(1s-) oe. 6. 5 (50) 
Thus we see that (36) becomes (38) if the resistance R, instead 
_ of being simply proportional to the velocity (41), is varying ac- 
_ cording to (59), which may be comprehended in (41) by taking. 
__ the factor » to decrease from »(a= x) to 0(a=«) according to 
y’—Yy ] — ‘) . . . . . . * (60) 
a 
: _ This variation of the coefficient of resistance is conformable to 
_ (87), since 4, according to (16) (then 9), increases as a decreases. 
—2y; 
‘The law. a=a+8.e =a+8.7' 
_ 48, therefore, but an amplification of 
: —2Qyt 
apes Sit 
4 
i 
‘ 
§ 
= 
equal intervals of time; or the consecutive planets were abandon 
_ equal intervals of time. 
_ There remain yet two remarkable consequences to be drawn 
from this exponential law of the planetary distances. If in (88) 
413 sufficiently great (i. e. the corresponding planet far from the 
_ Center) to make the first term insignificant as compared to the 
_ Second, we have approximatively 
:  @sp.7, 
4 hence afti= B.yt*}, 
E AM Jour, Scr—secoxp Sertes, Vor. XXXIX, No. 116.—Marcu, 1865, 
20 
