506 
by Professor O. Lodge in his address on the ‘‘ Functions of 
the Ether” (NATURE, vol. xxvii. p. 328), while this system also 
explains the kind of conservation which has been noticed in- 
dependently by Dr. G. Lippmann and Professor S. P. Thompson * 
as characterising the phenomena of electricity, and the close 
resemblance which not only exists between the processes of con- 
duction of heat and of electricity, but also, as noticed by the 
former writer, between the laws of electrical potential and the 
thermal principle of Carnot’s law. 
It seems scarcely probable that so many converging views 
can be all fallacious, and ingenuity may without doubt be 
spent with profit and advantage in further attempts to adapt and 
reconcile some comprehensive theory of the ether’s properties, of 
a mechanical description, to embrace in a common review all the 
multiplicity of remarkably analogous laws, which physics in its 
various branches at present offers to our contemplations. 
If the description which precedes of a connected outline of 
such a system of synoptic views has extended to a much greater 
length than I was originally prepared to offer as comments on 
Mr. C. Morris’ communication, it is because the logical develop- 
ments which I have repeatedly found them to admit of induced 
me to try to establish them on a satisfactory foundation. In 
many trials, moreover, of their applications, I have met with 
such frequent proofs of the validity of some such general prin- 
ciples as those here indicated, that the results to which they have 
easily conducted me in numerous directions, are in general so 
accordant with those which Mr. Morris has skilfully reviewed, 
that, save in the small divergence between us, upon which I have 
dilated, in the main principles adopted for explaining them, Mr. 
Charles Morris’s and my views of the properties and laws of 
motion, of the distribution of the ‘‘ Matter of Space,” and of 
the mec’ anical behaviours of ‘‘motor-vigour,” are for the most 
part only varie /ectiones of each other. A. S. HERSCHEL 
Newcastle-on-Tyne, February 10 
P.S.—It will perhaps serve to correct some misconceptions 
which, although they were not intended to be produced, may 
yet not impossibly have arisen from the form of defective rea- 
soning, which at some few points of this letter’s descriptions it 
has been unavoidably necessary to introduce, to notice in reca- 
pitulation that it formed at the outset no part of its main object 
to define and represent exactly the extremely complicated part 
which (at least in combinations of its periods) it is evident that 
time discharges in determining the operative efficacies and 
strengths of motor-couples, in exerting ‘‘ vigour” of undirected 
motion. With a well-grounded geometrical substructure, there 
need be no occasion to entertain a doubt that the first principles 
at least of time’s use in definitions of the actions and effects of 
wrests or motor. couples will be easily identified and laid down 
with all the precision and accuracy needed for purposes of their 
mathematical ap;lications. 
The principal object, however, here aimed at and sought to 
be attained has not been to offer such an exact description of 
time’s relations of form and economy to the different sates of 
action and repose of undirected motion (which do not actually 
admit of successful discussion without much more abstract ele- 
mentary conceptions than those ordinarily recognised of geo- 
metrical principles), but simply as a preliminary step towards 
this question’s future surer treatment, to point out clearly and 
plainly the distinctive and peculiar character of undirected 
motion’s space-relations. 
This kind of motion, it has been eudeayoured to explain, 
consists in change of magnitude of a certain ratio-index, 9, of 
tractional configuration between collocated points. In the capa- 
city of a ratio-index @ very closely simulates, in its algebraical 
and geometrical properties, all the analogous properties of 
angles. But it differs from them in this important particular, 
that it possesses no directional qualification. For a crank-arim’s 
description of angle at once a-signs the plane of the crank’s 
revolution, and this plane has direction ; but extension of a con- 
necting-rod is a ratio which affects the rod’s le gih equally 
in all positions, without giving rise in so doing to any new 
direction. 
On the other hand, neither motion in angle nor in traction- 
index can by their unaided t»-and-fro presence in a crank or 
connecting-rod give backward and forward motion to a piston or 
piston-rod, but only by virtue of certain constraints involving 
the properties in one case of trigonometrical, and in the other 
case of hyperbolic, sines and cosines. It is probably because 
changes of angle are, like the changes of the angle’s sine which 
* NaTUuRE, Vol. xxiv. p. 140; and pp. 78, 164. 
NATURE 
| 
[March 29, 1883 
result from them, directed quantities, that the relations of angle- 
variations to changes of coordinate lines by means of trigono- 
metrical ratios is a familiarly applied and well-established theory. 
But no such theory having the same scope and extent of appli- 
cation connecting changes of coordinate lines with variations of 
the ratio-index @, by means of hyperbolic sines and cosines, and 
showing what neces<ary conditions directed geometrical quanti- 
ties (including angle) must satisfy to make a fixed law of hyper- 
bolic connection with the undirected quantity @ have any pos- 
sible existence, has yet been brought into general notice and 
acceptance. 
But that the directed and undirected geometrical quantities do 
satisfy and fulfil such a condition, and that the fixed law of 
connection between them does actually exist, there is sufficient 
evidence to assure us in the consistency with which such reasonings 
as those which Mr. Morris has produced, and which I have tried 
to base on that geometrical assumption, represent correctly a very 
large array of physical phenomena. Forming therefore, as the 
undirected quantity p does, a position-scale in space, of whose 
possession Of certain distinctive and special geometrical and 
physical properties no theoretical employment has yet been 
made, and no sufficient proof of satisfactory evidence has, in 
fact, heretofore been produced, no excuse, it is opined, for 
hyperbole or figurative use of speech need be presented, for 
describing the new quantity, as it was termed in a former part of 
this letter, as a new position-scale of interspheral, ethereal, or 
aérilian motions foreign to and independent of our ordinary 
graphic field of space. 
Mr. Stevenson’s Observations on the Increase of the 
Velocity of the Wind with the Altitude 
I aM sorry if I took Mr. Stevenson too literally when I 
understood his remark, ‘‘ great heights above sea-level,” to 
mean absolutely great heights ; but I certainly think the phrase 
is extremely liable to such interpretation, and as no superior 
limit was assigned, I naturally inferred that the author deemed 
the formula“ — s 
[po TEL 
sidered in my paper. 
On his own showing, however, this formula succeeds no better 
than mine on Arthur’s Seat ; while mine possesses the unques- 
tionable advantage of approximating to the truth throughout the 
higher levels, where all Mr. Stevenson’s formule fail according 
to Vettin’s data. If the data furnished from Arthur’s Seat 
correctly represent the conditions in a free atmosphere up to the 
same level, which I very much doubt ; we must infer that the 
velocities increase in a more rapid ratio with the heights than that 
given by the formula 7 =(%)» which is preferred by Mr. Ste- 
applicable to such heights as those con- 
: 3 : Cae 
venson, but in not so rapid a one as that given by = =F and 
in fact, if we make the index 2 instead of 3, we get a formula 
which gives far better results, as far as the Arthur’s Seat observa- 
tions are concerned, than that preferred by Mr. Stevenson. The 
agreement is so close for nearly all the velocities, that I give 
below a comparison of the results aff rded by both formula :— 
Velocity Velocities computed for lower station Velocity 
recorded at recorded at 
high eleva- By Mr. Steven- By the lower station, 
tion, 775 feet son’s formula formula 550 feet 
above sea- v_{k\t gas ¢ z above sea- 
level. V-\a ) Va =) level. 
885 703! 704 Ec 720 
1,698 ... 1,430 1,351 1, 364 
2,620 eid 2,206 2,084 2,133 
3,416 ao 2,876 2,718 2,718 
4,328 .. 3,646 3443 3,465 
5,575 4,697 4,435 4,592 
6,763 5,698 5,391 5,640 
8,035 6,765 6,393 6,782 
9,368 7,893 75453 7,862 
10,820 ee 9,115 8,609 8,765 
12,410... + —*10)455 9,874 9.789 
13,700 11,542 10,900 10,639 
15,058 12,687 11,980 11,680 
Sums 79,713 76,325 76,149 
Means 6,132 5,871 5,857 
This value is wrong as given by Mr. Stevenson. It should be 745. 
