770 
AECHDEACOI? PEATT O^iT THE DEELECTION 
In my former Paper I brought out the Deflections 27"-853, ll''-968, 6"-909 
The correct values are now shown to be . . . . 27"-9785 12"-047, 6 •790 
Determination of the Mass of the whole Mountain-t'egion of the Enclosed Space. 
23. The calculation on this subject needs also revision. The direct wa} of detei- 
mining the volume of this mass is to And its average height and multiply it by the area 
of the Enclosed Space. First, then, I will And this area. By examining the diagi'am 
in par. 6 (fig. 1), it will be seen that by re-arranging some of the portions fuithest from 
A the area of the Enclosed Space is equivalent to the part of a lune about 132° wide and 
stretching from A to the end of the 35th compartment, the angular distance of which 
is 21° 24'. Hence, by a known trigonometrical formula,— 
Area of Enclosed Space = area of this portion of the lune 
cos 21° 24')f"=2, 559,162 square miles. 
24. We must now find the average height of the mass standing on this space. This is 
not at first sight an easy matter. We cannot obtain it by taking the average of the heights 
given in the Table of Heights in page 750, because the bases on which these heights 
stand are of such unequal extents, that an undue advantage would be given to those 
which stand upon the smaller bases. In my former Paper I overcame the difficulty by 
finding how much I must cut down the mass in order to reduce the attraction to zero , 
this quantity I considered to be the average height. It is obwous, that, as a general 
rule this would not be true. It so happens, however, that for a mass shaped as the 
mass under consideration is, it is true. This I did not show in my former Paper, 
although I made use of the property. I propose now to supply the deficiency. The 
method I shall pursue is this. I take a geometrical figui’e which sufficiently well 
represents the actual mass in general form, but one of which the attraction upon A can 
be accurately calculated. I then show, in the case of this figm-e, that the average 
height obtained in the direct way by geometry, and also by the method of attractions, 
is the same. I infer, therefore, that it is so in the case of the actual mountain mass. 
The reason of this coincidence it is not difficult to see. The highest part of the mass 
is much nearer to A than the middle of the mass is. Suppose the highest pm-ts had 
been about the centre; then in levelling these down so as to form the table-land which 
would have the average height, equal portions would have to be brought 
distances from the middle towards A and opposite to A. The latter transfer u on c ac e 
more to the attraction than the other would detract from it; and therefore the aieia^e 
volume would not be the average mass measured by the attraction. But as the hig lei 
parts of our mass are much nearer A than the centre, it is obvious that an exact com- 
pensation is possible. The calculation shows that it is real. 
25. The accompanying diagram (fig. 5) represents the geometrical figure I have alluued 
to. It is drawn upon a scale, except that the vertical heights are exaggerated sixty times. 
A is the station Kaliana, D the point north-north-east where the mass begins, and thence 
