998 REPORT—1874. 
analysis of this problem, when it was considered as subjected to the two condi- 
tions which were necessary to the most economical use of a homogeneous material, 
namely,— 
(1) That the thrust along a meridian shall equal the thrust along the parallel 
er unit of area at every point. 
(2) That the normal thickness shall vary in such a manner that the area under 
compression shall be proportional to the thrust. 
The paper contains the investigation of the differential equate of the profile of 
the dome subject to these conditions, and the discussion of that equation, as well 
as of the law of variation of thickness under the same conditions. The theorems 
are also extended to the case of stratified stone, in which the thrusts in condition 
(1) are proportional instead of equal. 
The investigation is printed im extenso in the ‘ Proceedings of the London Mathe- 
matical Society’ for 1874, vol. v. pp. 113-119. 
On an Improved Tuyere for Smiths’ Forges. By W. Morean. 
This is a simple but important ras pote gla in smiths’ forges, by which the forge 
is much more fully under the control of the workman, and by which the life of the 
tuyere is greatly prolonged, the work of heating the metal more uniformly and unin- 
terruptedly carried on, and a great economy of fuel effected. A cast-iron trunk or 
box is made which is placed horizontally from the back and the front of the forge. 
The front end is closed by means of a slide or door; the back end has a hollow 
tower, which rises above to a suitable height, and upon which is fitted a cast-iron 
tuyere-block with, by preference, two long slot-holes for the blast. Within the 
trunk is a long lever working in an axle or spindle, which at its longer end has 
two punches, which rise vertically, and are from time to time projected through the 
slots to displace the slag, and keep the tuyere-openings clear. This the workman 
does by moving a lever upon the outer end of the spindle or fulcrum of the levers. 
The iron trunk or box becomes heated by the surrounding fuel, and utilizes the 
heat which would otherwise be wasted, and effects a considerable economy of fuel 
by heating the air of the blast, and the inventor employs air in a peculiar manner 
for keeping the tuyere-block cold, 
On the means adopted for the Improvement of the Outer Navigable Channel of 
Dundalk Harbour. By Joun Neviite, C.H., M.R.LA. 
The harbour of Dundalk is entered by a channel 4 miles long from and in the 
bay, beginning at the bar and terminating at Soldiers Point. This channel, called 
the “Outer Channel,” discharges the waters of the Castletown River at low water. 
In 1867 it had shifted so much that it became necessary to alter its course and fix 
it. A plan for this purpose was selected by the Harbour Commissioners, and 
approved of by the Board of Trade. This consisted of directing the ebb and flow 
currents into a more direct course, and fixing this course by means of jetties and 
side walls constructed of loose rubble boulder-stones, varying in weight from a few 
pounds to a few cwts., dropped in from punts, and raised about 2 feet over low 
water neap-tides. The stones were not quarried, but picked from off the lands on 
the mountain side near the shore, carted to the shipping-places by the farmers, and 
sent out in punts. About 60,000 tons have been deposited up to the present time ; 
about 2 miles of jetties and walls have been constructed, and about £8000 expended 
out of an estimate of £40,000. As the income of the Commissioners is limited, 
the works are carried on from time to time as the funds are available. It was at 
first thought by many that at a distance of a mile or two from the shore, the loose 
stones in these jetties and walls would be washed away. This has not been so. 
Not a single stone has been removed ; but when subsidence takes place new materials 
are supplied, and the walls raised up from time to time as before. The jetties, or 
grains, were used to force back the channel gradually, in some cases to an extent 
of about 700 feet without any interruption of the navigation. This communication 
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