of Edinburgh, Session 1883-84. 
303 
We shall therefore suppose that the travelling points p and q 
leave A simultaneously in the same direction^ but that p moves 
thrice as fast as q ; here we see that the radius Op must make more 
than half a turn before its intersection with the tangent can over- 
take q. Proceeding by the same method of approximation, wo 
readily find the arc AP to be 233° 40', its tangent AQ being 1.359f 
in terms of the radius. Each succeeding coincidence must occur 
after an interval of rather more than half a turn, so that the 
approximations are rapid. The second coincidence is when 
= AP'PAP' reaches 428° 07', the tangent AQ' being 2.4907. 
The same method is applicable to the other cases of the general 
problem. 
Thus the consideration of this elementary problem in mechanical 
construction leads us to examine the properties of a whole class of 
functions, which, again, may serve to suggest further extensions and 
inquiries. 
3. Notes on the Madi or Mom Tribe of Central Africa. By 
Eobert WT Eelkin, E.E.S.E., E.E.G-.S., Bellow of the 
Anthropological Societies of London and Berlin, &c. 
(Plate V.) 
The following notes have been compiled from my own observa- 
tion, when in Central Africa in 1880, from inquiries I made on the 
spot, and from the information I have obtained from a native who 
has been my faithful servant during the past few years. 
They treat of a people inhabiting a large tract of country situated 
5° N. lat., 30° 20' E. long, of Greenwich, of which the chief town 
is said to be Bengu6. 
The Arab customs, which are being introduced among the races 
in Central Africa, are rapidly breaking down the boundaries which 
exist between the tribes, and superseding their primitive habits and 
customs, which in a few years will be things of the past. For this 
reason I have been induced to bring together all the information 
it has been my good fortune to collect, and whilst regretting that 
the record is not so complete as one could have wished, I yet hope 
that it may prove of some value, or at all events of interest, to those 
engaged in the study of anthropology. 
