Dec. 14, 1857.] GALTON ON THE EXPLORATION OF ARID COUNTRIES. 69 
Diagram 6. Diagram 7. 
End of 
End of 
End of 
End of 
End of 
End of 
Third 
CAMP. First 
Second 
Third 
CAMP. First 
Second 
— Stage. 
Stage. 
Stage. 
— Stage. 
Stage. 
Stage. 
EXPLORING PARTY. 
Latest detachment— £ 
3 
3k 
>o Last but one— 2 e . • 
5 
X 
X 
3 
9 
.Last but two — 4 e . 
of diagram (4), beginning at the lower end and ending at tbe npper. 
In his four trips to the end of the first stage, he would have trans- 
ported and deposited in cache exactly as much as four men could 
have done who travelled simultaneously, and so on throughout his 
whole career. He, of course, would lose in time the exact equiva- 
lent of what he gained in diminution of numbers ; and thus, since 
the above diagram represents 4 e as being occupied for two stages 
(one out and one back), 2 e during four stages, and 1 e during six, 
in carrying on the work of the supporting party, it follows that, if 
the exploring party themselves undertook this work, they would be 
engaged upon it for 4x2-f2x4+lx6 = 8 + 8 + 6 — 22 
stages.* 
The following little Table (8) shows how much delay is caused 
by employing the method of repetition for the first few stages : — 
Number of stages during which the repeating method] 
is used J 
J 1 
2 
3 
4 
&c. 
Additional number of stages that have to be travelled ) 
over by parties who adopt it \ 
J 2 
8 
22 
52 
&c. 
The first column, and to a lesser degree the second one, are avail- 
able for practical purposes. 
* It would be more convenient to the exploring party to transpose the order of 
their trips, and to adopt that shown in diagram (7) ; because, as their object is sup- 
posed to be to seek for water, if it be found near at hand, a more distant excursion 
becomes unnecessary, and the plan of (5) would enable them to push forward the 
earlier stages of their exploration with as little delay as possible. 
