430 A Resultant System for the [Oct 



The chain was not at first attached, but the forces necessary to pre- 

 serve equilibrium at the points of attachment of the oblique rods with 

 the platform, first attended to, as follows, each of the portions of plat- 

 form (c, c 1 , c 2 , &c.) being separate at first, and afterwards flexibly 

 connected. 



To the portion (c) with a weight (d) of 56 lbs. was attached a single 

 rod (a) passing over a pulley at point of suspension ; a weight (x), and 

 part of weight (Y) passing over a pulley in a horizontal line, were added 

 in such proportions till they produced an equilibrium, i. e. till the por- 

 tion of platform (c) was made horizontal by the joint effects of the 

 two weights x and Y. 



The subjoined table shows in its several columns what the propor- 

 tions of the weights (x, x 1 , x 2 , &c, and Y) should be, theoretically 

 calculated, to produce equilibrium at the different points as the rods 

 were successively attached ; and it also shows what the actual weights 

 were particularly applied in succession, as well as the collective results 

 on the whole series, with the differences. 



At the distance of 7 feet the oblique rod (a') was attached to a second 

 piece of platform (c 1 ), with its weight of 56 fts., which latter was also 

 connected to the piece (c) flexibly ; the weight (x 1 ) appended to the rod 

 (a 1 ) and weight (Y), increased till the equilibrium was produced, or 

 both pieces of platform (c, c 1 ) were in a horizontal line. In like man- 

 ner were all the obliques (a 2 , a 3 , a*, a 5 ,) attached to the several portions 

 (c 2 , c 3 , &c.) of platform, and the weights added and corrected : when 

 the whole series was complete, the weight Y had attained its maximum. 

 The table will show the differences between the actual weights (Y, Z, x 1 , 

 x 8 , &c.) and the numbers on the plate, which are those mathematically 

 calculated as due to the several rods and beam. 



The result shows that the whole were increased slightly beyond the 

 calculated amounts ; but this may be attributed to the friction of the 

 chains upholding the oblique rods, which passed over cast iron pulleys 

 9 /y diameter. It will be observed, however, that the increase was pro- 

 portional : thus the originally calculated weight (x 1 ) due to the oblique 

 rod (a 1 ) was 74 lbs., but, to produce equilibrium, required to be increas- 

 ed to 95, and the calculated total amount of Y was 406 ibs., afterwards 

 practically requiring 519 ; but the numbers 74 and 406, are relatively 

 proportional, to 95 and 519. 



