072 the different Theories of Arches, Vaults. &c. 415 



-the thrust of all kinds of domes : they were published in 

 the volumes 1774 and 1776, Acad. Scie/i. Par. His theory 

 is similar to that of De la Hire, though more extended. 



M. Coulomb in 1773 published a memoir on some pro- 

 blems in architecture, in which he treats of ' the equilibra- 

 tion of arches, with a view to practice. 



Dr. Charles Hutton, in a work entitled The Principles of 

 Bridges, published, in the year 1772, a tract on the equili- 

 bration of arches and on their thrust on their abutment 

 piers, in which he has followed the theory of Emerson. 

 His theory of abutment piers has been taken up under the 

 the same notions as that of De la Hire. The method and 

 simplicity with which Dr. Hutton has treated these sub- 

 jects cannot be too much praised, and forms a strong con- 

 trast with the writings of the French mathemaiician in this 

 respect. His formulae are short, and the calculations to 

 be made from them by no means laborious : but as the 

 theory seems rather to apply to the weight to bear upon an 

 arch, than to the arch itself; and as it is admitted that an 

 arc of a circle, ellipse or cycloid of equilibration, containing 

 more than leo degrees, cannot be constructed, much re- 

 quires to be done before this theory can be applied to 

 practice. Dr. Hutton has since promised a full elucidation 

 of the subject. Professor Robison in the article yirc/i, in 

 the Ency. Brit. Sup. gives the theory of Emerson, but, 

 before he quits the subject, leaves a strong conviction on 

 the mind of his reader, of its inutility in its present state. 

 He gives a geometrical mode of deicrminiug the cxtrados 

 of a circular arch according to this theorv, which is as fol- 

 lows. 



Draw the vertical CS [fig. 5) cutting the horizontal dis- 

 tneter in S, and ST cutting the radius OC perpendicularly 

 in T. Draw the horizontal line Tz, cutting the vertical in 

 ■c. Join zo. Make zu = Vv, and ilraw i/.v pijrallel to zo. 

 Then Cc, the height above C required, will be equal to Cx\ 



Professor Robison also investigates the theory of the 

 equilibration of domes, after the manner of Bougucr. 



Professor Robison gives a popular mode of determining 

 a curve to a given extrados, by suspending I'rom ilie links 

 of a chain, suspended, forming a curve of a given iieight 

 and span, bits of chain, whose extremities should be ad- 

 justed to the given line : hence are to be deduced the arch 

 itself, and the weight thereon. This method is more plau- 

 sible than real : so much modification is necessary in the 

 experiment, and the bits of chain arc such inadequate re- 

 presenialives of the filling up of the vault, as wlII as the 



chain 



