1840.] 



THE CIVIL ENGINEER AND ARCHITECrS JOURNAL. 



S3 



other dimensions being taken from the transverse section given 

 Journal, page 433, Vol. II 



in the 



Evample 2. — Other dimensions remaining the same as in the last 

 Lample, what is the value of * when d and k' are each equal to 7 ft. 



exam 



From equation (5) 



/.■ 



= V- 



12,500— 17x (2X 17x 7 + 7=) — 33x7^ 7x33 + 7x171^ 



17 



7x33h 7x 17 

 17 



V- 



.12500-2499-1617 350 



17 

 350 



V'493-2 + 424-3 — 20-G = V/ 917 



17 17 17 ~ 



■ 20-G = 30-3 — -20-6 = 9-7 feet. 



E.i-ample 3. — Other dimensions remaining the same as those in ex- 

 ample 1, what is the value of i' when d= 7 feet and *= 9 feet ? 



From equation (6) we have k' =: V 

 IG 



12500 • 



16 X (7= + 126) 



— 9 = V- 



12,500 — 2800 



17 



V- 



,9700 



17 



17 



■16= v/ 570-6— 16 



23-9 - 16 = 7-9 feet. 



When/=/' and also i=i', we find from equation (4) by a few easy 

 reductions 



d—^' 



m c3 (6-y)AV (/ + 6) X /' 



(')• 



6 6 6 



also from the general equation of equilibrium, 2A^/+ 2k/d + h\f 



+ -2kdb + bd'- x/i-2 = OTC^ = 4A=/+ 2h/d + 2hdb + bd^, from 



bd- 



, and by quadratics, 



, . , , bd + db mc 

 which /i- + — k = 



2/ 



4/ 



'-^Tf + 47 — 



(i f)d 

 4/ 



(8). 



Example 4. — Required the width of the main dam in fig. 6, the 

 depth of water being 30 feet, and the other dimensions as follows, viz. 

 t'=*=8 feet,/=/'= 15 feet, and 6 = 34 feet. 



,12,500 , (34 

 From equation (7) a ■=z v „ + 



15)11= (34 + 15) 8 



34 



34 



1'2,500 23,104 



392 

 34 



= V367-7 + 20—1 1-5 = V387-7 



— 11-5= 19-7 — 11-5 = 8-2 feet, the width required. 



Example 5. — What is the value of i=i' when the depth of water 

 is 27 feet/= 15 feet, 6 = 30 feet, and i=6 feet? 



From equation (8) A =: V- 

 9 



M X 27' 30 — 15 X 6> 45 x ' 



,91,125 

 = ^-600" ^ 4 



60 60 



4-5 = V 15 1-9 + 2-2— 4-5 : 



60 

 VIsFl 



— 4-5 = 12-4 — 45 = 7-9. 



Example 6. — What width shall vpe adopt for the main dam, the 

 depth of the water being IS feet, when /{•= i'= 5 feet,/=/'= 12 feet, 

 and 6 = 21 feet? 



d=^-- 



r= 18^ (21— 12)X5> (21 + 12) x 5 



21 



21 



21 



,2700 



2JJ25 

 iTl 



165 

 IT 



= Vl28-6 + 4-6 — 7-9 = V 133-2— 7-9 



= 3-6 feet, the width required. If s = 80Itjs., we would find d = 

 4-3 feet ; and if s was still farther reduced to GO His., d would require 

 to be increased to 6-1 feet. 



It appears that the value of s in the foregoing formulae greatly 

 operates on the result in finding the width of the cofier-dam under its 

 different forms. Unless where otherwise mentioned it has been taken 

 at 90 lbs. in the examples given, but this value may be much reduced 

 if water presses under the dam, and the reduction will be in proportion 

 to the quantity of the, bottgin surface pressed upon, or exposed to the 



action of the water. As the construction of some forms of coffer-dams 

 are more liable to admit water underneath than others, s may proba- 

 bly in such cases have to be reduced so low as 60 lbs. 



The dimensions in the last example are nearly those of the coffer- 

 dam used by Simple for constructing the piers of Essex Bridge, in 

 Dublin, in 1753, the depth of water varying from 13 to 2l) feet along 

 the line of the coffer-dam. This coffer-dam deserves particular atten- 

 tion as being probably the first constructed in the kingdom, at that 

 time, for such a depth of water ; and from the difficulties the engineer 

 had to encounter in the execution of the work, and overcoming one of 

 the prejudices of the time then supported by the authority of a 

 Labylye. 



Figs. 7 and 8 show a plan and section of the coffer-dam taken fiom 

 Semplt's Treatise of Building in Wakr, which the author acknow- 

 ledges to have taken from Belidor'i Hydraulic Architecture. The 



Fig. 7. 



Tig. 8. 



piles are about 6 inches square, placed at 4 feet apart along the line of 

 the dam, and sheeted along the inside with, apparently, inch boarding. 

 B high-water mark, A low-water mark, D bed of river, C C occasional 

 braces, f, g, and e, auxiliary braces, and P pudling. The width be- 

 tween the sheeting from out to out is 15 feet, and the main dam is 5 

 feet wide. This construction is however far inferior to that of con- 

 tinuous sheet piling as adopted at St. Katherine's Docks, and at the 

 New Houses of Parliament ; as the resistance, offered by the depth of 

 bed penetrated by the pileing, is trifling in the former plan compared 

 with that in the latter, but on the other hand the quantity of timber 

 employed is less in the former. 



It may be necessary in conclusion, to remark that the depth of water 

 ought to be taken from the surface to the bottom of the exposed coffer- 

 dam, inside ; for though that depth may not be on the outside, yet the 

 water generally forces its way down so far ; or if not, forces the bed 

 with nearly an equivalent pressure against the coffer-dam. 



Ancient Greek Mwuiseript.— An important discovery has been made by M. 

 Didron, during his recent archaeological tour in Greece and Turkey, of a 

 Greek manuscript, about 900 years old, containing a complete code of reli- 

 gious monumental paintings. This document, found at Mount Athos, gives 

 lull instru tions concerning all the subjects and persons that ought to be 

 painted in chnrclies, with the age, costume, and attributes that each fi.gure 

 ought to have. A copy of this manuscript is making at Mount Athos \villi 

 the greatest care. Another mrinuscript, containing a similar code on religious 

 architecture, is believed by M. Didron to c.-dst at Adrianople, and he has 

 some hopes of obtaining it. — French paper. 



M 2 



