176 Geometrical Construction of the Cell of the Bee. [Mar. 17, 



teen years within the experience of the present manager. During the 

 whole of that time no blasting had ever been done in any intake air- 

 way. On the 2nd of October last, however, a party of men were 

 instructed to blast away a portion of the side of the west chain road 

 at a distance of about 550 yards from the bottom of the shaft. They 

 tired three shots in all, and the third caused the explosion. It was 

 not a blown-out shot in any sense. 



The mechanical effects were exactly the same as those produced 

 by other explosions. Timber was torn out, and falls of roof some- 

 times of great magnitude and extent were caused all through the 

 intake air-ways, as far as the flame reached. In the endless chain 

 roads the box part of each empty tub was swept away from the frame, 

 and shattered into small pieces, not one being left whole. A spare 

 pulley- wheel, 4 feet in diameter and weighing 15 cwt., which had 

 been standing on its edge leaning against the side near the end of the 

 west chain road, was carried four yards inwards towards the face, and 

 laid flat on its side. 



The flame traversed all the intake air-ways, except the new east 

 road, and died out in some nearer to, and in others further from, the 

 faces. It did not in any case pass into a return air- way. It did not 

 reach the face of the workings at any point. 



The new east road was quite undisturbed. Two men who were 

 working in it felt a concussion of the air, but saw no flame, and came 

 out unscathed. This result appears to be due entirely to the circum- 

 stance that the principal stables were ranged along the entrance to 

 this road, and the ground having been kept constantly wet with the 

 water used in the service of the horses, the flame was unable to pass 

 that point for want of coal-dust to sustain it. 



II. " Second Note on the Geometrical Construction of the Cell 

 of the Honey Bee ('Roy. Soc. Proc./ vol. 39, p. 253, and 

 vol. 41, p. 442)." By Professor H. Hennessy, F.R.S. 

 Received February 21, 1887. 



If from the intersections of the diagonals of the three lozenges 

 forming the apex of the cell, perpendiculars be erected, these will 

 meet at a point on the cell's axis, and each of them is manifestly the 

 radius of a sphere tangent to the three lozenges. A plane passing 

 through a radius and the axis passes through the short diagonal, e, of 

 the lozenge whose length is h^(S/2) ; using the notation and results 

 of the paper above cited. 



The distance intercepted on the axis by a perpendicular let fall 

 from the middle of the lozenge is equal to x = h/(2^/2), and as this 



