ROT 



2. Any number of given beams, arranged as sides of a polygon, in a 

 vertical plane, support each other, and support also given weights at 

 the ^/.s ; it is required to find the horizontal pressure at the points of 

 support. 



Let B and B be the weights of two contiguous beams, a and the an- 



gles they make with the horizon, and C the given weight at the ^, or 

 point of junction j then 



% (B + B) + C 



H rr 



tan. ot tan. 

 This horizontal pressure is the same at all the angles. 



Cor. If we suppose the weights of the beams o, H -= - 

 If we suppose no weights, except the beams, 

 H _ % (B 4. B) 

 tan a. tau ' 



3. To find the position of the beams, having given their weights 

 B, B, B &c. the weights C, C, C &c. and the position of two of them. 



1* 2 3 123 



By the last Prop, we have the following equations, , a, <* being the 



^.s which the beams make with the horizon. 



H (tan. tan. ) = ^(84. B) 4. C 



H (tan. * tan. ) = }i (B 4. B) 4. C 



&c. &c. 



If there be n beams there will be n 1 weights C, C &c, and^t- I 



1 9 



equations. The'number of unknown quantities is n 4- 1 viz. the n tan. 

 gents, tan. , tan. &c. and the pressure H. Hence if we know two of 



the /.s , . we can find the rest, 

 i a 



RO OTS of numbers. See Involution. 



ROPES, rigidity of. See Friction, 



ROTATION of bodies about a fixed or moveable axis. 



The following Proposition is of the greatest use in Mechanics, and is 

 general under the circumstances there mentioned, whether bodies move 

 in right lines or have a rotatory motion. It applies with peculiar facili- 

 ty to the investigation of the motion of revolving bodies, and by the help 

 of it the most difficult problems admit of a simple and easy eolation. 

 51 O i 



