794 
AECHDEACON PEATT OX THE ESTLEEXCE OE 
viz. 6"-8 sec 22° 30' or 7"-36, 6"-8 being the meridian deflection at that station. Above 
this point up to Karachi I shall suppose the deflection to vary as the inverse distance, 
and below it down to Punnoe as the inverse square. This will give results rather under, 
than over the mark; for it makes the deflections at Punnoe and Karachi only 2'-65 
and 9"T5, as will be seen below. 
Let h and u be the distances from the fixed line of Damargida and of any point on 
the line between Punnoe and Karachi, of which X is the number of degrees of latitude 
above Punnoe ; 
h— arc 15° cos 22° 30', u~ arc 25° cos 22° 30'-X sec 30° sin 37° 30'. 
Hence from Punnoe to the 20° latitude, the deflection 
X5 cos 22° 30' ^ ^ 
/ ^5 cos 22° 30 
— ' y25 cos 22° 30' — X sec 30° sin 37° 30' 
2 8 60"- 6 
■ (32-86 -X)'-'’ 
At Punnoe this =2" -6 5. 
Calling Ml the force producing this deflection, 
M, tan2860"-6 0-0138666 
‘7'“(32-86-xp~(32-86-X)2' 
17. Also since du=:—dx.&ec 30° sin 37° 31'=--0-702937dX 
*,= 0-0097473{^-3^} = 0-0001706 
the limits of X being 0 and 12. This is in parts of a degree : in feet it =15-88. This, 
it will be seen, is the rise of the point between Punnoe and Karachi abo-se Punnoe in 
consequence of mountain attraction. 
18. From the point in latitude 20° up to Karachi, the deflection 
cn 15 COS 22° 30' _ 145"-1 
= ^ ’36 25T3^22®“3d'^^^X^^^3d^dh37^~32-86-x' 
At Karachi this =9"-16. The force producing the deflection being called 
Mi tan 145"- 1 0-00070298 
“y 32-86 — X 32-86— X ■ 
19. Also J-^dw=^^^^^||^log^ = 0-0001355inpartsof adegree =50-44feet. 
This is the rise of the sea-level at Karachi above the point in latitude 20°, in conse- 
quence of mountain attraction. This, as well as the similar statements in pars. 15 and 
17, I now proceed to prove. 
20. The equation to the surface of a fluid mass acted on by forces XYZ at the point 
xyz is, 
constant —^(^dx-\-Ydy-\-7jdz). 
In the case of the ocean the forces are the centrifugal force, the attraction of the general 
