1836.] On the Position of Frames in a Sloping Gallery. 369 



sity ceases when the earth has accumulated and settled on the sheet- 

 ing. The frames however in this way now support the whole weight, 

 and the question is whether thev may not be relieved of a portion of 

 the weight by giving them an oblique position, and if so, what is the 

 position in which they will have least strain upon them. 



a dead vertical pressure. But suppose them placed as a c perpendicular 

 to the gallery : here the force of gravity is divided into the two forces, 

 one parallel, and the other perpendicular to the inclination of the gal- 

 lery ; and, supposing the sheeting to be securely supported at p } the 

 weight, actually sustained by the frame, is reduced in the proportion of 

 a b to a c ; for in the triangle a be, if the total vertical pressure be repre- 

 sented by a b, the pressure on the frame will be as a c, and that on the 

 point p as c b; and it is evident that when a c is perpendicular to cb, as in 

 this case, it is a minimum, and bears the least possible strain. For this 

 reason, and because the frame has the advantage of being shorter, and 

 has no tendency to slip at the head or foot, and as it seems undeniable 

 that some obliquity from the vertical position is necessary at first, this 

 position has been adopted on a general rule. 



In ordinary galleries no great inclination is required; it is easier and 

 more convenient to sink a shaft, and carry a level, or slightly inclined 

 gallery, to the point required, but for the sake of a general view of the 

 subject, if I am not trespassing too much on your pages, let us see how 

 this position would answer in a gallery of great slope. 



When the gallery is completed, the sheeting rests securely on the 

 solid earth at p, and if a sufficient quantity of loose earth has fallen, 

 so as to prevent any one plank from sliding over that next below, the 

 frames placed as a c will be secure, but if the gallery is to be carried on, 

 the support at p is for the moment removed by the miner, and the whole 

 mass supported, has a tendency to fall forwards : this I should think 

 a sufficient difficulty to show itself even in galleries of no very great 

 inclination, though a little management may prevent any ill effects ; but, 



In the annexed figure I 

 have endeavoured to repre- 

 sent the loose earth acting 

 J on the sheeting, and which 

 with the sheeting itself, 

 forms the mass to be sup- 

 ported. If the frames are 

 placed as a b vertically, 

 they can have no tendency 

 to fall backwards or for- 

 wards when the particles 

 have ceased to fall, because 

 they have to resist only 



