140 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737. 



Exper. 2. — If the same prop, of 5 inches, be placed under a point in the 

 bar at 30 inches from the centre of motion, the power or pressure will be 8 oz. 

 12 dwt. 13 gr. and the friction equal to 2 dwt. 21 gr. The foot of the prop is 

 to be distant from the centre of motion 1Q inches -/oV- 



Case II. In which the Prop is perpendicular to the Bar, exemplified by three 



experiments. 



Exper. ] . — Now let the prop, still 5 inches long, be placed so as to be per- 

 pendicular to the bar at a point 12 inches from the centre of motion. Here 

 the power expressive of the pressure should be 1 9 oz. 18 dwt. 4 gr. and the 

 friction 6 dwt. 15gr.; but on account of a correction necessary to be made to 

 this, because the bar is thick as well as heavy, and the centre of gravity above 

 the surface to which the prop is applied, the power or pressure sustained will be 

 only IQ oz. 15 dwt. 5 gr. and the friction 6 dwt. 14gr. The distance of the 

 foot of the prop in this case is 13 inches from the centre. 



Exper. 1. — ^The prop here is JO inches long, still perpendicular to the bar, 

 under a point in the bar, 24 inches from the centre. The power equal to the 

 pressure sustained, should be, if the bar was only heavy, and not thick, g oz. 

 J 9 dwt. 4 gr.; the friction 3 dwt. 1 l^gr.; but with the proper correction, ex- 

 plained hereafter, it must be only 9 oz. 17 dwt. 15 gr.; the friction 7 dwt. 7 gr. 

 Here the foot of the prop is to be 26 inches from the centre. 



Exper. 3. — If the end of the prop be placed under a point in the bar, so 

 that the horizontal distance of the foot of the prop be exactly equal to the dis- 

 tance of the centre of gravity from the said centre of motion, viz. 20.5 inches, 

 the power or pressure sustained by the prop will be precisely equal to the weight 

 of the bar, viz. 12 oz. 12 dwt. 12 gr. In this case, the prop is distant from 

 the centre of motion on the bar 1 7.9 inches, and the friction 4 dwt. 5 gr. 

 Case III. In which the angle made by the prop with the horizontal line is given, 



either acute or obtuse. 



As this case is very intricate, on account of the several powers of the sine 

 and cosine of the given angle, which are multiplied into the prop, and into the 

 weight of the beam, we will exemplify it only in one experiment; which is, 

 when the angle made by the prop, with the horizontal line contained between 

 the foot of the prop and the centre, is acute: then there is a maximum of pres- 

 sure, which it appears by experiment is the very same as the calculation gives. 

 Suppose the angle made by the prop and the horizontal line to be 60 degrees; 

 the calculation of this maximum shows, that if the prop be 10 inches long, 

 the distance measured on the bar, to which the upper end of the prop must be 

 applied, will be 10 inches -^\, the bar itself making then an angle of about 

 52° 12'; and the horizontal distance between the centre of motion and the foot 

 of the prop, is then 1 1 inches ■^^. 



