Movement in Orbit simple Resultant of Forces. 47 1 



It would continue moving in a straight line except when deflected by 

 attraction, and therefore the curve of deflection, or orbital curve, may be 

 considered as the resultant of the two forces. The orbital curve is really to be 

 treated as a case under Law 3, Cor. 1 and 2, B. i. Principia, where the law of 

 the parallelogram of forces is stated. As the orbital curve is not an ellipse, Prop, 

 xvii. prob. ix. B. i. Principia does not apply. That proposition only applies to 

 conic sections. The shape of Fig. 37 proves the orbit of the earth or moon 

 cannot be a conic section. Why the orbit of the earth was ever treated as a 

 conic section ij difficult to- understand. By calculating the gradients of the 

 orbit— that is, the curve at different points — I find the curve is much more 

 egg-shaped than elliptical. In all the drawings of the orbit of the moon, where 

 the earth is considered stationary, from the times of Kepler to Procter, I find 

 the orbit drawn as an ellipse, with the curve at B Apogee and A Perigee — the 

 same gradient, if I may use that term. I find, however, that at A Perigee on 

 the 22nd November, 1874, the gradient of the curve was 0-01185 of a foot in a 

 mile, while at B Apogee on the 9th, the gradient was only 0-01047 of a foot in a 

 mile. On the 15th, when the moon was near the mean distance for the month, 

 D the gradient was intermediate, or 0*01082 feet in a mile. In an ellipse at mean 

 distance C or D the curve would be almost imperceptible, and also would be of 

 equal gradient at B Apogee and A Perigee. The same genera] remarks apply to 

 the orbit of the earth round the sun. I have shown the point P on the 27th of 

 November, 1874, nearer the earth, Fig. 37, than on the 1st by a considerable 

 distance. After the whole lunation on the 27th November, when the moon is 

 in the same position as to angle as that which is occupied on the 1st November, 

 as regards the earth, the moon is less distant. This is indicated in Fig. 37 reduced 

 from large drawing in which I calculated the distance of the moon for each day. 

 Fig. 37 is a complicated curve, not a conic section jl I have called this the orbital 

 curve, the velocity and gradient decreasing from A to B through C and 

 increasing from D to A through C in a simple ratio* 



NOTES.. 



1 Note to page 439. — Ice acts as. a colloid in promoting the passage of vapour 

 or of water into the interstices of cells, and thus produces the cold necessary for 

 regelation, by evaporation of water. Directly the spaces are filled the contrary 

 action ensues, and that is the reason why there is no regelation when there is 

 no superfluous water to melt the ice in contact with it, or too much water. With 

 ice (if possible) frozen of the specific gravity of water in an hydraulic press, 

 regelation would not occur, as there would be no air cells or colloidal iee. As- 

 wet ice regelates and freezes to flannel, the explanation of regelation cannot be 

 that it depends on cohesion or attraction of surfaces, except so far as these 

 affect evaporation and condensation of vapour. 



3 Note to page 442. — Fact mentioned by James Giekie, Ice Age, 1875, 



Note to Fig. 9, page 447. — 



Channel AB BC CD DE ~\ Mean velocity nearly 



Discharge 0-203 °'3 Q 7 o - 6i8 1-236 ( equal in the four chan- 



Velocity 1-278- 1/259 1*325 i'34S \ nels, notwithstanding 



Slope 0-00824 0-049 o -00208 0-0015 s difference of slope. 



The observations were made by Darcy and Bazin, 1868, without any view to 

 this theory. Recherches Hydrauliques, Paris. 



Note to Fig. 10, page 448. — I calculated in 1853 (Phil. Mag. p. 264) that the solid 

 matter in suspension in Mississippi water indicated a denudation of the whole 

 surface of 1,240,000 square miles (the area drained by that river), of I foot in 

 9,000 years. By taking into consideration the siliceous matter carried beyond 



