1866.] 



Mr. Tarn on the Stability of Domes, 



187 



From (5) . . . 'P,a=3l6'767 ^ +191-06975; 

 „ (6). . . F .c= 164-6725 50-54; 

 „ (7) . . . Q.g'= 1308-98 t^-l- 43-63275 

 Hence the equation for equilibrium (3) is 



4915=43-63275^^1308-98^^ + 481-4395 ^-f- 140-52975, 

 which reduces to 



jfH30^'+ 11-03^-109-42=0. 

 "We can solve this by means of Horner's process, and find ^ = 1*7 ft. for 

 equilibrium. 



The equation for stability (4) becomes 



9830=43-63275^^+1308-98^2 + 481-4395^+ 140-52975, 

 which reduces to 



^3+ 30^24. 1 1-03^-222-069=0, 

 from which we obtain, by Horner's process, 



t=2'45 ft. for stability. 



Example 2 : — 



Let r=30 ft., R=33 ft., H = 80 ft., 3 and as before. 

 From (1) . . . N = 2483-84; 

 „ (2) . . . b = 90-2606 ; 



therefore 

 and 



=224192-8, 



2N6 =448385-6. 

 From (5). . . P.«= 8552-71 ^+ 15476-65 ; 

 „ (6) . . . F.c= 4446-16 ^+ 4094-17; 

 „ (7) . . . Q.q= 69-8124^3+ 6283'U6t\ 

 Adding and reducing, the equation for equilibrium becomes 

 ^' + 90^^ + 186-2^— 3048-31=0, 

 whence ^=4*83 ft. for equilibrium. 

 And the equation for stability is 



^H90j5Hl86-2jf-6159-7=0, 

 whence ;=7'07 ft. for stability. 



Example 3 : — 



I will apply the formulae to the case of the dome of Sultan Mohammed's 

 tomb at Beejapore, described in Mr. Fergusson's * Handbook of Archi- 

 tecture.' One peculiarity of this structure is that the inner face of the 

 dome is set 5 ft. 6 in. within the inner face of the wall on which it rests, 

 as shown in fig. 3. ; so that in calculating the values of «, &c., we must 

 add 5-5 ft. to the thickness t ; hence we shall get a proportionately less 

 value for t from the resulting equations. 



In this dome, r=62 ft., R = 72 ft., H=116 ft. ; and we will suppose, as 

 before, that a=125 lbs., ^, = 150 lbs. 



From(l) N = 31132; 



„ (2) . ; . . . b = 137-20524 ; 



