April 26, 1883] 
of the kind known to me was very imperfect in its details ; 
it was revised for the next year, and since that time many 
lists, in one form or another, have been published. The 
figures for the animals with records of 2.25, or better, are 
reasonably accurate ; for the others there is much dis- 
crepancy. In the following table the numbers are my 
own, counting down to 1872, inclusive ; the numbers after 
that date are derived from various lists published since 
that time in the sporting and breeding periodicals. From 
the very nature of the case, the table cannot be accurate 
in the larger numbers, but the numbers do not lose their 
value for comparison with each other from such faults as 
to the details of the larger numbers, and, as such, it is 
undoubtedly the most significant series of numbers ever 
compiled to show progress in evolution, whether of a 
breed or species. The number of horses with records of 
2.40, or better, is now stated to be over five thousand. 
I leave it to mathematicians to plot the curves which 
immediately suggest themselves, and determine how fast 
horses will ultimately trot, and when this maximum will 
be reached. 
Table showing the numbers of Horses under the respective 
Records, 
sg [sel se | sy lselselse|ssleglsy 
oe Bs] ws os He | OS) ee) ws | me] as 
aa aides) all aces ies |) Rest] See pee ees aa 
Cy i a lies | 
1844 2 x | | 
1849 Te | lane 
| 
1852 1o| 3 | | | 
P8530 | x4.) 5 
1854 | 16] 6 
1855 | 19| 6 | 
1856 24 7 I | | | | 
L857 aN 205 a7 |e 2s | | 
1858 3yoy|) Gp et | | | 
BESO SZ Oli 2a ced |e or | 
ESCM eAGierx |i A) (ees | 
1861 | 48 | 14 4 | 2 I | 
1862 54] 17 Vale As | act | 
1863 59 | 19 9 A.) 1 
1864 6622) 12] 4] 
SORT Sazo rs | 5 | 2 x | 
1866 | 1o1| 32 | 17 ®| gi a 
1S67e| eae |) 2r | | 5 | 2 
1868 | 146/52 | 28| 13| 6| 2} 
1869 | 171) 63] 34| 15/10} 4 | 
1870 | 194) 72| 35 | 16|11| 5 | | 
1871 | 233} 99] 40| 7/12) 6] t | 
ii) |) eee || Se Se 
1873 | 376)—| 74.) 28)15| 5| 2) — | 
1874} 505|—]| 98| 40|16|)11|) 5] 1 | 
1875 | — | —| 134| 61 | 30] 13] 5} 2 | 
1876 | 794) — | 165 | 81 | 39| 16] 6| 2 | 
1877 | 836) — | 214 | 105 | 51| 19 | 8 | 2 
1878 | 1,025 | — | 270 | 129 | 68 | 24] 9| 4 
1879 | 1,142 | — | 325 | 164 | 88 | Se |) Lee lpagiey ar 
1880 | 1,210 | — | 366 | 192 |106 | 41 | ivi O i) 2 |) a 
1881 | 1,532 | — | 419 | 227 |126 l49|15| 7 | 2h |W 
1882 | essa — | 495 | 275 |156 | 60 | 18 | 8 | 2 | x 
| 
INSTITUTION OF MECHANICAL ENGINEERS 
WP Institution held their usual Spring meeting at 
the Institution of Civil Engineers, 25, Great George 
Street, on April 11 and 12, the president, Mr. Percy G. 
B. Wesunacott, in the chair. Three papers were read, 
and discussed at length; a fourth, by Mr. A. C. Bagot, on 
“The Application of Electricity to Coal Mines,’’ was 
postponed for want of time. 
The first paper was by Prof. A. G. Greenhill, of Wool- 
wich Arsenal, and deait with the strength of shafting 
NATURE 
611 
when exposed both to torsion and end-thrust. He has 
worked out for this case, by a complete mathematical 
investigation to be published in the Proceedings, the 
following formula :— 
ip We 4 Te 
EES IVE WUE 
where P = end-thrust, 7 = twisting moment, 7 = moment 
of inertia of cross-section, “ = modulus of elasticity, 
2 = maximum distance between bearings, which will allow 
a shaft to be stable. 
When there is no twisting moment, as in a long column, 
the second part of the right-hand expression vanishes, 
and we have the ordinary formula of Euler. If there be 
no end-thrust, as in ordinary mill shafting, the first part 
vanishes, The special case where both occur together is 
that of the screw-shaft of a steamer ; but here, it appears, 
on working the figures out with ordinary dimensions, that 
the second part is small in comparison with the first, and 
may be neglected. Hence a screw-shaft may so far be 
treated as if it were a long column only; and it follows 
at once that the numerous bearings interposed between 
the engines and propeller (say, about every 25 feet) are quite 
unnecessary so far as stiffness is concerned. If retained, 
as seems desirable, simply to support the weight of the 
shaft, they might at least be made in some way elastic, 
so as to enable the shaft to accommodate itself to the 
sagging and straining of the vessel. It was, in fact, ad- 
mitted on all hands that screw-shafts never give way 
from twist or thrust, but always by cross-breaking through 
strains induced by the unequal movements of the ship ; 
and if so, there seems every reason for taking some steps 
at least in the direction which Prof. Greenhiil indicates. 
Another point which the paper touched upon was the 
question of hollow verszs solid shafts. Now that shafts 
can be conveniently cast out of ingot steel, they are fre- 
quently made hollow, with the obvious advantage of 
increasing the stiffness as compared with the weight. 
Thus, in the case of the screw-shaft of the C7¢y of Rome, 
which is 25 inches diameter, with an internal hole of 14 
inches diameter, it appears that the moment of inertia is 
o’9 of that of an equal solid shaft, while the weight of the 
latter would be 1 45 that of the former. Again, if a solid 
shaft were used of the same weight as the hollow shaft, 
or 20°7 inches diameter, its moment of inertia, and there- 
fore its stiffness, would be barely half that of the latter. 
Even if a transverse crack, 1 inch deep, were to occur in 
the hollow shaft (which it might be urged would place it 
at a serious disadvantage) the loss of stiffness comes out 
to be 6 per cent., whereas in a solid shaft of equal dia- 
meter the corresponding loss would be 5 per cent.; so 
that even here the advantage on the side of solidity is 
only I per cent. 
These figures might seem to be conclusive, yet the solid 
shaft has its defenders. Mr. Edward Reynolds, of Messrs. 
Vickers and Co., stated roundly that the history of hollow 
screw-shafts was a mere history of disaster (which, however, 
was denied by a subsequent speaker) ; and he quoted some 
experiments of his own on shafts one-fourth the size of 
that in the Czty of Rome, where, tested under a I-ton 
weight falling from about 20 feet, the hollow shaft was 
rapidly destroyed, while the solid shaft remained un- 
injured. This occurred even when great care was 
taken to prevent the hollow shaft from getting flattened 
during the process. His explanation was that the com- 
paratively unstrained fibres towards the centre of the 
section came in to support and relieve the exterior parts, 
whenever, by cracks or otherwise, these became unduly 
loaded. Prof. Kennedy, who followed, seemed to lean to 
the same view, and quoted the increase of strenzth obser- 
vable in the metal between the holes of a drilled plate, 
as being due, in some unexplained manner, to the in- 
fluence of the unstrained metal behind the holes. A very 
satisfactory explanation of this fact was, however, given 
by Mr. Wrightson at the last meeting of the British 
