On measuring the Distance travelled by Wheeled Carriages.

When no instrument for this purpose is obtainable, the best plan we know of is that adopted by the late Dr. Burchell, the eminent South African traveller, and after him by Captain Cornwallis Harris, the explorer and naturalist, in the more distant parts of the same country; and this is, to measure the large wheel carefully, to mark one of its spokes, and count its revolutions during any given time, say a minute, and then convert the result into miles or parts of a mile per hour. Thus, if a wheel be 5yds. in circumference, and it makes six revolutions in a minute, the distance in that time will be 30yds., or 1800yds., i.e., 40yds. more than a mile per hour; twelve revolutions will of course be 80yds. over two miles; and, during former journeys, when our wheel was making eighteen revolutions, we used to reckon the waggon was going, allowing for occasional unavoidable stoppages, two and a half miles per hour. With a watch having a second hand it is easy to note any fraction of time, but with one not so provided less than a minute cannot easily be estimated. After a little practice we became so accustomed to this that we seldom used a watch; but when sitting on the waggon-box would just look over the side, and estimate the rate at which the wheel was going, just as a sailor would in like manner make a very fair estimate of the speed of his ship.

It will generally be found that an African ox-waggon, not overloaded, and on tolerably fair ground, travels about two and a half miles an hour; and we have also found that with pack horses in Australia, if the same rate is assumed, the resulting measurement of the day’s work will be very nearly correct.

We tried once to make a trocheameter, but at the time had never either seen one or read a description of it, and therefore the principle cost us some thinking out. It was perfectly evident that, for motive power, an axle so weighted that it could not revolve in a revolving box would produce the same effect upon the works as an axle made to revolve, by weights or otherwise, in a fixed box would have on those of a clock. We therefore made a box of such a form as to fit between spokes of the hinder wheels of a waggon, and in it fitted an axle with a heavy plummet, so fixed to it as to prevent its turning when the box revolved; on this axle was one tooth fitting into the cogs of a sixty-toothed wheel, which therefore moved one tooth for every revolution, or once round for every sixty; the axle of this had also one tooth acting on another of sixty teeth, so the two were capable of registering sixty times sixty, or three thousand six hundred revolutions, which, supposing the wheel to be only 5yds. in circumference, would measure ten miles and a quarter, the number of revolutions being indicated by a hand fixed upon the axle of each wheel, each moving on its own dial-plate, like those of a patent log. We found that the machine answered quite well enough to convince us that we were right in principle, and to make us regret that we had not the tools and appliances at hand to fit it so perfectly as to insure smoothness and uniformity of action.

To all, however, who have the means, we would say do not fail to buy a trocheameter: it is a small, compact instrument, fitted in a copper case, capable of being strapped on any convenient part of the wheel; and one of fair quality need not cost above 2l. 10s. or 3l. The instrument is composed of two revolving toothed wheels, the upper wheel having 101 and the lower 100 teeth, suspended from and turned by an endless screw; there are two indices, that on the upper wheel pointing out every single revolution, and that on the lower every hundred. The whole circuit of the instrument is 10,100 revolutions, and the following is an example of its power:

“One complete circuit of 10,100 revolutions, with a carriage-wheel of 12ft. circumference, would indicate 23 miles, minus 80yds. Thus, 55 revolutions give 220yds., or 1 furlong; 110 give 440yds., or a quarter of a mile; 440 give 1760yds., or 1 mile; 7040 give 16 miles; 10,100 equal to 23 miles, minus 80yds.

“To set the instrument unscrew the milled nut from off the steel endless screw, and move the wheels round until both the indices coincide; screw the nut firmly in its place, shut up the instrument, and strap it securely to the off-wheel in the centre of the nave.”

In Africa we cannot literally follow out these instructions, for the nave is not brass capped, as with carriage-wheels at home, but the end of the axle comes through, and the wheel is secured to it by a washer and a linch pin; therefore, we strap the trocheameter between the spokes as near to the nave as possible, and in our journey to the Zambesi Fall we secured a pint pannikin permanently between the spokes as a protection to the trocheameter, which just fitted nicely into it during this journey. We measured a distance of between 2000 and 3000 miles, and do not remember that this instrument failed, except once from being choked with fine dry sand, and once again from equally fine sand and water.

We subjoin a table, by which it will be seen that our waggon-wheel was 5yds. 2½in. in circumference; this fraction gave some little trouble in the preliminary computation, and it looked very absurd to calculate the stages to half an inch, but if we had thrown it out a considerable error would have accumulated, and when the table was once formed the trouble was at an end.

Trocheameter Table.

First Wheel.

No.	Fur.	Yds.	Ft.	In.	No.	Fur.	Yds.	Ft.	In.
1	—	5	0	2½	52	1	43	1	10
2	—	10	0	5	53	1	48	2	0½
3	—	15	0	7½	54	1	53	2	3
4	—	20	0	10	55	1	58	2	5½
5	—	25	1	0½	56	1	63	2	8
6	—	30	1	3	57	1	68	2	10½
7	—	35	1	5½	58	1	74	0	1
8	—	40	1	8	59	1	79	0	3½
9	—	45	1	10½	60	1	84	0	6
10	—	50	2	1	61	1	89	0	8½
11	—	55	2	3½	62	1	94	0	11
12	—	60	2	6	63	1	99	1	1½
13	—	65	2	8½	64	1	104	1	4
14	—	70	2	11	65	1	109	1	6½
15	—	76	0	1½	66	1	114	1	9
16	—	81	0	4	67	1	119	1	11½
17	—	86	0	6½	68	1	124	2	2
18	—	91	0	9	69	1	129	2	4½
19	—	96	0	11½	70	1	134	2	7
20	—	101	1	2	71	1	139	2	9½
21	—	106	1	4½	72	1	145	0	0
22	—	111	1	7	73	1	150	0	2½
23	—	116	1	9½	74	1	155	0	5
24	—	121	2	0	75	1	160	0	7½
25	—	126	2	2½	76	1	165	0	10
26	—	131	2	5	77	1	170	1	0½
27	—	136	2s	7½	78	1	175	1	3
28	1	141	2	10	79	1	180	1	5½
29	1	147	0	0½	80	1	185	1	8
30	—	152	0	3	81	1	190	1	10½
31	—	157	0	5½	82	1	195	2	1
32	—	162	0	8	83	1	200	2	3½
33	—	167	0	10½	84	1	205	2	6
34	—	172	1	1	85	1	210	2	8½
35	—	177	1	3½	86	1	215	2	11
36	—	182	1	6	87	2	1	0	1½
37	—	187	1	8½	88	2	6	0	4
38	—	192	1	11	89	2	11	0	6½
39	—	197	2	1½	90	2	16	0	9
40	—	202	2	4	91	2	21	0	11½
41	—	207	2	6½	92	2	26	1	2
42	—	212	2	9	93	2	31	1	4½
43	—	217	2	11½	94	2	36	1	7
44	1	3	0	2	95	2	41	1	9½
45	1	8	0	4½	96	2	46	2	0
46	1	13	0	7	97	2	51	2	2½
47	1	18	0	9½	98	2	56	2	5
48	1	23	1	0	99	2	61	2	7½
49	1	28	1	2½	100	2	66	2	10
50	1	33	1	5	101	2	72	0	0½
51	1	38	1	7½

Second Wheel.

No.	Miles.	Fur.	Yds.	In.	No.	Miles.	Fur.	Yds.	Ft.	In.
1	—	2	72	0½	20	5	6	120	0	10
2	—	4	144	1	30	8	5	180	1	3
3	—	6	216	1½	40	11	5	20	1	8
4	1	1	68	2	50	14	4	80	2	1
5	1	3	14	2½	60	17	3	140	2	6
6	1	5	212	3	70	20	2	200	2	11
7	2	0	64	3½	80	23	2	41	0	4
8	2	2	136	4	90	26	1	101	0	9
9	2	4	208	4½	100	29	0	161	1	2
10	2	7	60	5

We give also an example of the work:—

December 27, 1861.—From Christmas Tree, south-west angle of Lake Ngami, two miles from Bolebeng—trocheameter at zero.

First halt south of the Lake:—

Trocheameter	6	37
	m.	fur.	yds.	ft.	in.
6	1	5	212	0	3
37	0	0	187	1	8½
	1	6	179	1	11½

28th.—North of the Vlei Moslenyan:—

Trocheameter	22	91
	6	37
	16	54
	m.	fur.	yds.	ft.	in.
10	2	7	60	0	5
6	1	5	212	0	3
54	0	1	53	2	3
	4	6	105	2	11

29th.—The Big Tree, or Baobab at Mamakahooie:—

Borrow		101
Trocheameter	50	73
	22	91
	27	83
	m.	fur.	yds.	ft.	in.
20	5	6	120	0	10
7	2	0	64	0	3½
83	0	1	200	2	3½
	8	0	165	0	5

29th, p.m.—A hollow, with water:—

Borrow		101
Trocheameter	76	53
	50	73
	25	81
	m.	fur.	yds.	ft.	in.
20	5	6	120	0	10
5	1	3	14	0	2½
81	0	1	190	1	10½
	7	3	104	0	11

30th.—A small Vlei:—

Borrow		101
Trocheameter	93	44
	76	53
	16	92
	m.	fur.	yds.	ft.	in.
10	2	7	60	0	5
6	1	5	212	0	3
92	0	2	26	1	2
	4	7	78	0	10

31st.—Outspan in the Bush.

Trocheameter	12	89
Add	100
	112	89
	93	44
	m.	fur.	yds.	ft.	in.
10	2	7	60	0	5
9	2	4	208	0	4½
45	0	1	8	0	4½
	5	5	56	1	2

As a means of measuring a base line for triangulation of a country the trocheameter is invaluable. Suppose the course is north, and that a mountain bears 90°, or east; let the waggon travel till the mountain bears 45° more southerly, or 135°, i.e., south-east; then stop the waggon, read the trocheameter, and the length of road travelled will be equal to the distance of the mountain from the starting place. Even if the course does not form a right angle with the bearing, the same method may be followed, involving only a little more calculation, or the trouble of laying down the angle upon paper. In places where a waggon cannot travel, it would be well to have a large wheel, on the principle of the old perambulator, and fix the trocheameter upon it; only let it be loaded, so as to bear the semblance of usefulness in the eyes of natives, or even of illiterate white men, or they will infallibly carry it over the bad places, as Captain Sturt’s men did, to save themselves trouble. The trocheameter may be fitted to any piece of machinery, as the screw or paddles of a steamer, the sails of a windmill, a waterwheel, or anything capable of turning round.

No.	Miles.	Fur.	Yds.	In.	No.	Miles.	Fur.	Yds.	Ft.	In.
1	—	2	72	0½	20	5	6	120	0	10
2	—	4	144	1	30	8	5	180	1	3
3	—	6	216	1½	40	11	5	20	1	8
4	1	1	68	2	50	14	4	80	2	1
5	1	3	14	2½	60	17	3	140	2	6
6	1	5	212	3	70	20	2	200	2	11
7	2	0	64	3½	80	23	2	41	0	4
8	2	2	136	4	90	26	1	101	0	9
9	2	4	208	4½	100	29	0	161	1	2
10	2	7	60	5

No.	Miles.	Fur.	Yds.	In.	No.	Miles.	Fur.	Yds.	Ft.	In.
1	—	2	72	0½	20	5	6	120	0	10
2	—	4	144	1	30	8	5	180	1	3
3	—	6	216	1½	40	11	5	20	1	8
4	1	1	68	2	50	14	4	80	2	1
5	1	3	14	2½	60	17	3	140	2	6
6	1	5	212	3	70	20	2	200	2	11
7	2	0	64	3½	80	23	2	41	0	4
8	2	2	136	4	90	26	1	101	0	9
9	2	4	208	4½	100	29	0	161	1	2
10	2	7	60	5

No.	Miles.	Fur.	Yds.	In.	No.	Miles.	Fur.	Yds.	Ft.	In.
1	—	2	72	0½	20	5	6	120	0	10
2	—	4	144	1	30	8	5	180	1	3
3	—	6	216	1½	40	11	5	20	1	8
4	1	1	68	2	50	14	4	80	2	1
5	1	3	14	2½	60	17	3	140	2	6
6	1	5	212	3	70	20	2	200	2	11
7	2	0	64	3½	80	23	2	41	0	4
8	2	2	136	4	90	26	1	101	0	9
9	2	4	208	4½	100	29	0	161	1	2
10	2	7	60	5