188 



Mr. Tarn on the Stability of Domes. 



[June 7, 



therefore 



N5 =4271473-522, 



and 



2N6 =8542947-044. 

 From(5). . . P . «=-957 (134920j (?^+ 5-5) +3-56745 (134920) 

 = 129118-44^+1191511-78; 

 „ (6) . . . F.c=-4975 (134920) (i^ + 5-5)--4975 (527854-4) 



= 67122-7^+106567-28 ; 

 „ (7) . . . Q. 5=101-22798/3+186x 101-22798^2^ 



Adding and reducing, the equation for equilihriim (3) becomes 

 186^^ + 1938-6^-29373-24=0, 

 whence ^=8-2 ft. for eq^uilihriim. 



And the equation for stability (4) becomes 



186^2+ 1938-6^—71570 = 0, 

 whence ^= 14-66 ft. for stability. 



In the construction of this particular dome, the values obtained above 

 for t will only apply to four points on the walls which carry the dome ; for 

 instead of being built on a circular " drum," this drum is made to cover a 

 square chamber by means of " pendentives," which are so arranged as to 

 throw the thrust principally on the angles of the building, where the values 

 of a and c will become very great, and it is only at the centre of each of 

 the four sides that the above equations can be employed to compare the 

 thrust of the dome with the strength of the walls. At these four points 

 the walls are about 11 ft. thick, so as to be considerably more than suf- 

 ficient to produce equilibrium ; and the coefficient of stability at these 

 points is 1-374 instead of 2. Had the dome therefore been built on a 

 circular drum of 1 1 feet thickness, in all probability the edifice would not 

 have stood for any length of time. 



Much of the thrust of a dome may be counteracted by means of an iron 

 belt placed round it at the point where the thrust is greatest. This point 

 I have shown to be at 70° from the crown, or 20° from the springing. 



June 7, 1866. 



The Annual Meeting for the election of Fellows was held this day. 



Lieut.-General SABINE, President^ in the Chair. 



The Statutes relating to the Election of Fellows having been read. Pro- 

 fessor Brayley and Mr. Toynbee were, with the consent of the Society, 

 nominated Scrutators to assist the Secretaries in examining the Lists. 



