Prof. Milne — Across Europe and Asia. 65 



jSTow taking the same figure as that illustrating Part II., and imagining a body of 

 ■weight IF, in motion at the point b, due to its fall from a, and rolling to £, that is, 

 descending through the vertical height marked JI. 



Let fx be the resistance opposed to sliding and rolling of the body down the plane. 

 If the body meets many small obstacles in its path, this will be analogous to a 

 frictional resistance. 



1st. Owing to its initial velocitj', the body will have at starting from b, an 

 energy measured by J , but V2 = 2^Xseca .•, J = JFKsec a. 



2nd. The work done by gravity upon the body through the vertical distance H, 



is measured by JVS. 

 3rd. The work done against fi'iction is /j. TF cos a B'cosec a=fji. TFS cot a. 

 Now when the body comes to rest rolling down the height S, its power of doing 

 work must have been absorbed, or is equivalent to the work done against frictional 

 resistances, 



Therefore TFKsec a+TFJi = /x WH cot a 

 Whence if =i sec a 



fj. cot a — 1 

 Taking the angles 



10'', 20'", 30", 45°, and 60°, where for the sake of example let /t = | 

 tlieuB"co -55; 2-8; oo ; oo ; co . 



That is to say, bodies on planes wdth an inclination above 30°, where the resistance to 

 rolling was only half the weight, would roll on until they reached the base of the 

 plane, whatever its length might be, getting faster as they descended ; whereas two 

 similar bodies on planes only difEering in their inclinations being respectively 20° and 

 10°, the body on the plane of 20° would roll more than/owr times as far down as the 

 one on the plane of 10°. 



Taking another case, where ix — %, and the planes remaining the same, 

 H <a -Zh, 1, 3-9, _^, ^ 



Now it is clearly seen that as /^ might be much greater than f , the action is pro- 

 bably much more intensified than it is here shown. It is also easy to see that if we 

 take into account the probable mechanical action of water in detaching stones and 

 other possible agencies, the action would also be more intensified than is indicated by 

 the above numbers. 



It is evident, however, that no meclianical theory can take into 

 account the infinite number of phenomena which really occur; 

 nevertheless these considerations will perhaps give an idea of some 

 important circumstances which affect the rates of degradation of 

 steep mountains. 



After more than a week's rest, I left Pekin on the 24th, my 

 destination being Tiensin. This occupied two days. The country 

 travelled over was an open flat loamy plain, similar to that which I 

 crossed when entering Pekin. At Tiensin I found the river still 

 closed by ice, and if I intended travelling to Shanghai by steamer, 

 I should have several weeks' delay. This being the case, I deter- 

 mined to travel overland in mule carts, a journey which I was told 

 would occupy about twenty days. It was the 5th of February 

 before everything was prepared for the journey, and at 12 o'clock 

 on that day, in company with a Russian officer. Colonel Unterberger, 

 who also wished to reach Shanghai as quickly as possible, I started 

 off on a trip of new experiences. 



For the first six days we rattled along over a continuation of the 

 Tiensin and Pekin plain. With the exception of a few canal banks, 

 mud walls of villages, and fences round fields, everything is 

 painfully flat. Every step one takes raises a cloud of dust, 



DECADE II. — VOL. T. — NO. II. 5 



