64 



cosa, cosj3, C0S7. Let a, h, c be the coordinates of the point 

 D. Then the direction cosines of the line DP will be 

 x — a y — h z — c 



Td"' pd"' pd' 



Therefore we have 



{x — a)cosa + {y- 6)cos/3 + {z- c)cosy 



Also we have 



^ = KG 



j/ = HG 



z = PG 

 Let ^, 1], Z, denote the coordinates of the corresponding 

 points on the derived solid, then 



^ = KG 



7, = HG 



^=LG = PDcosDPFcosy 

 Hence we obtain 



l, = x 



^=C0By[{x - a)cosa + {y - b)cosj3 + {z- cjcosyj 

 Hence the equation to the derived solid will be 

 4" (4 - a)cosa + (?7 - &)cos/3 



<«• ■", 



+ c 



cos''y cosy 



or if z be given as an explicit function of x and y 



z = (p{x, y) 

 then the derived solid will be 



^ = cosy({^ - a)cosa + (jj - 6)cos/3 - CCOSy) + cosV0(^, r}) 

 The remainder of the paper consists of a proof by means 

 of these substituted coordinates of the relation 



V, = cosVV 

 and so, of the equation 



which was given in a previous paper, and a discussion of 

 some other properties of projected solids. 



" Notes on the Meteorology and Hydrology of the Suez 

 Canal," by Dr. W. G. Black, F.KMet.S. Communicated by 

 Joseph Baxendell, F.R.A.S. 



The observations of the meteorology of the stations on 

 the line of the Suez Canal were taken by the officers of the 

 Canal and Telegraph Departments of the Canal Company 



