1859.] on the determination of heights of Mountains. 



311 



others, I have elsewhere given, of 'the importance of means being 

 taken to calculate the effects of this disturbing cause more com- 

 plete! y. 



~K\ 



q „ . ^ x ^/777rF777Z?n?ffiftfi7J7!$. 





4. The diagram above is an ideal vertical section of the plains 

 and mountains, intended merely to illustrate the effect of Moun- 

 tain-Attraction upon the determination of the heights. 



OS is the sea-level, (lying on that spheroidal surface, of ellipti- 

 city _£_, of which the Ocean is supposed to form a part). To this 

 level all heights are referred in the Survey : a and b are two sta- 

 tions of observation, ah the vertical at a perpendicular to the sea- 

 level : the height of b above a is determined by the Survey, and 

 this being done at each succeeding station the height of the highest 

 peak is found by adding together the successive changes in height. 

 In this diagram I have supposed all the stations of observation, 

 leading from the sea up to the highest peak, to lie in the same 

 vertical plane. This is not the case, some will lie on one side and 

 some on the other. But taking this into account would make no 

 difference in my results. 



Draw ac parallel to the sea-level and be perpendicular to it. 

 Then be is the true height of b above a. But the plumb-line will 

 not hang in the line Jia, but in another line h'a, owing to the Attrac- 

 tion of the Mountains : and therefore the spirit-level will make ac' 

 (at right angles to ah') the apparent level line at a, and not ac. 

 Hence, if be be at right angles to ac, be is the height of b above a, 

 as brought out by the Survey. This is too small by be — bc\ 



Let the angle h'ah = v, and angle bac == 6. Then 

 be — be = ab sin — ab sin ($ — v) 



= ab sin 6 — ab sin cos v + ab cos 6 sin v 

 = ab cos 6 arc v'\ because v is very small 

 = ac y; are v" 



