of Edinburgh , Session 1885-86. 
839 
By proceeding to deduce the next case from that just obtained, in 
the same way as we deduced the case of a tetrahedron from that 
of a triangle, we multiply the expression | 6 1 c 2 6? 3 e 4 | 3 ^P m by the x of 
four equations of the form ax + by + cz + du + e = 0, and thus obtain 
1 ¥2^*4 l 4 
| a 1 b 2 c 3 (i 4 1 P m 
which is denoted by (1234). In like manner we obtain the 
expressions denoted by (12345), &c., and so the general type of 
expression denoted by (123 . . . m-1); but as these expressions 
are of 4, 5, and higher dimensions, the results involving them are of 
little importance geometrically. 
PRIVATE BUSINESS. 
James Oliver, M.B., was balloted for, and declared duly elected 
a Fellow of the Society. 
Monday, 21s£ June 1886. 
Sheriff FOEBES IEVINE, Yice-President, in the Chair. 
The following Communications were read : — 
1. The Diurnal Variation in the Direction of the Summer 
Winds on Ben Nevis. By E. T. Omond, Superin- 
tendent, Ben Nevis Observatory. 
The most cursory examination of the wind records of the Ben 
Nevis Observatory shows that there is, even in fine weather, no 
strongly marked daily variation in their direction; nothing compar- 
able to the land and sea breezes observed on our own coasts in 
summer. In order to see whether there was not some regular daily 
change concealed in the extremely variable winds actually observed, 
I reduced, by means of a traverse table, to north-south and west- 
east co-ordinates each observation during the summer months (June, 
July, August) of 1884 and 1885, taking account of the velocity of 
the wind as well as of its direction, so as to get the actual mean air 
motion at each hour of the day. As the anemometers at Ben Nevis 
cannot be trusted to work continuously even in summer, but get 
