86 
ARCHDEACON PRATT ON THE ATTRACTION OF THE 
fill Region. This I will now examine. All the results which depend upon this part 
I will multiply by a factor 1 —x. If .r=0, the results will stand as they do now. If 
j:=1, this will amount to supposing the mass standing on the whole Doubtful Re- 
gion to be non-existent, an hypothesis clearly impossible. By giving x any interme- 
diate fractional value we shall be supposing that all the heights, and therefore the 
whole mass, are reduced in that ratio. Let A, B, C represent the deflections in meri- 
dian at the three stations A, B, and C. Then from art. 42. we gather — 
A= 1 2-972 -l-(l—cr) 14-881 
= 27-853— 14-8SIX 
B= 3-219-f(l— 8-749 
= 11-968— 8-749j^ 
e= ]-336+(l— :c) 5-573 
= 6-909- 5-5/3 x; 
A — B=15-885— 6-]32.r 
A— C = 20-944— 9-308 a? 
B — C= 5-059— 3-176a?. 
These show that the extravagant hypothesis of supposing x= 1 , or that the whole 
mass on what we have called the Doubtful Region is non-existent, will not reduce 
the difference of deflections at A and B lower than 9"‘T53, which is greater than 
5"-236 in the ratio of 13 : 7- Nor will this even come down sufficiently if we reduce 
also the density of the remaining mass, that on the Known Region. 
46. A third means of reduction may be looked for in the Known Region. By 
examining the results gathered together in art. 42, it will be seen that the chief part 
of the meridian attraction of the mass on the Known Region arises from the limes II. 
III. and IV. for A, and lunes II. and III. for B. By attentively examining these 
columns in Tables I. and III, in art. 41, we see that a large portion of the attraction 
arises from the Great Plateau. The result I arrive at is, that of the deflection 12"*972 
at A, as much as 8''-772 arises from this plateau ; and of the 3"-219 at B, as much as 
2"-010 arises from the same cause, Flence if 1 — y be an arbitrary factor, 
A (Known Region) = 4-200-f- (I — 3 /) 8-772 
B (Known Region) = l-209-l-( 1 —?/) 2-010 
A — B (Known Region) = 2-99 1-1-(1— 3 /) 6 - 762 . 
It will be necessary, then, to cut down the height of the plateau as much as 6000 
feet, to make this come down to 5"-236; or, if we suppose that all the heights in the 
other part of the Known Region are twice too large, and if we therefore replace 2"-991 
by its half, l"-496, even then 3 / must equal 0-55, and the elevation of the plateau* above 
the sea be reduced from 10,000 feet to 6000 feet. And all this in addition to the 
hypothesis of the non-existence of the whole mass on the Doubtful Region ! 
* I should mention to what extent I assume that this plateau is comprised within what I have called the 
Known Region. Let four points be marked down on the map, viz. W in lat. 34° and long. 76°, Xin lat. 32° 45' 
