TRANSACTIONS OF THE SECTIONS. 111 
first instance, all the questionable experiments, I found it necessary to discard all 
the experiments made with accelerating velocities, and to retain only such as were 
made on uniform velocities, in the same circumstances, over a large space; most of 
my own experiments having a steady uniform velocity over from one mile to six. I 
have also selected those which were most free from the action of wind—an element 
of much importance. By thus weeding out the experiments, and taking only the 
most unquestionable, I simplified the subject very materially. Those which remain 
are given in the table. In this table the weight of each train in tons is shown, and 
the number of pounds of force required to keep each ton weight of that train in mo- 
tion at a given number of miles per hour, is shown by actual experiment. The 
analysis of those experiments I made as follows :—I take the friction of the axles and 
wheels as an ascertained quantity equal in the best-conditioned carriages to 6 lbs. per 
tonof train, This I conceive we may consider to have been proved by all experiments 
of friction, including those of Mr. Morin, the latest and best, to be a source of re- 
sistance constant at all velocities. This I call friction proper, and I consider it as the 
first element of resistance. Friction proper, the first element of resistance,—or 
Ry SO mye af Seger agin. pew 
where C = 6 lbs., and m = the mass of the train in tons weight. ~ 
The second element of resistance is the resistance of the air to the front of the train, 
This has been variously estimated, and somewhat erroneously. Some persons have 
taken for it Smeaton’s tables of the force of the wind. But such a table gives a 
quantity quite in excess ; for these tables were made from the force of the wind upon 
a thin plate, a case where the minus pressure behind is added to the plus pressure 
before the plate; whereas, in the case of the railway train, there is a solid body, 
whose third dimension extends the whole length of the train. I have therefore taken, 
not the table of the force of the wind, but a table of the resistance of air calculated 
from the height due to the velocity, which I have found to represent most accurately 
the resistance of fluids to bodies passing through them; and I have taken this as the 
second essential element in the resistance to railway trains. Resistance of the air, 
the second element :— 
Reecanput 8. ES 2 ees 
where A = the area in square feet of the front of the train, and p = weight of a 
column of air, whose basg¢ is a square foot, and whose length is the height due to the 
velocity of one mile an hour; v being the velocity of the train. 
After having deducted from the results of the experiments the sum of these two re- 
sistances, 1 have found a large amount still unaccounted for ; and I find this quantity 
to be not only large, but dependent also on the velocity. The question which I now 
submit to the Section is the determination of the nature and cause of this third ele- 
ment of resistance. The third element of resistance appears by the experiments to 
increase very nearly as the velocity, simply; that is, it amounts at 10 miles an hour 
to about 3 Ibs., at 30) miles an hour to 10 Ibs., and at 60 miles an hour to 20 lbs. per 
ton. It is therefore proportioned to the mass or weight of the train and to the ve- 
locity jointly. Other resistances due to velocity or third element :— 
R, =Bmyv, iti opibeis 2 clley! 
where 4 Ib., m the weight of the train in tons, and v its velocity in miles an hour, 
Whence the total resistance (R) to any train of any weight moving with any velocity 
is to be obtained from the formula 
R=R,4+R,+R°=Apv?+Bmv+Cm .... « [4] 
‘The results of this formula are shown in the last column of the table; and from the 
close manner in which they follow the experiments through their various and ap- 
parently anomalous results, they may be regarded as an approximation to the truth 
sufficiently close for all practical purposes. The next question discussed was the 
nature of this third element—resistance. The author attributed it mainly to the con- 
cussions, oscillations, frictions and flexures to which all the portions both of the train 
and permanent way are subject, at high velocity. 
_—_ 
Modification of Dr. Whewell’s Anemometer for measuring the velocity of the 
Wind. By the Rev. T. R. Rozrnson, D.D., MRLA. 
The author explained briefly to the Section the nature of the various anemometers 
which have hitherto been used. Most of them measure the pressure of the wind, and 
