1819.] of Cast-Iron Shafts in Machinery. 203 
have only to find what weight suspended to the end of this rope 
multiplied into its velocity in feet per 1’, would equal the 
momentum of the piston ; if x = this weight, then v 2 = m 
; ao t-~= ee 
which is, perhaps, as easy a method as any to find such a weight 
as would exactly balance the power of the engine. And referring 
to the abstract of the experiments, in the column entitled “Total 
Weight which broke the Shaft,” we find the number of lbs. = z ; 
and opposite to it, im the column entitled .“‘ Diameter of round 
Part of Shaft :” we have the diameter of the shaft required in 
inches ; that is, however, the diameter of a shaft which would 
break with a force not less than the whole power of the engine. 
Tt will then remam for the mill-wright, or his employer, to 
decide, upon how much stronger he would choose to have the 
_ shaft in question than the one already found in the abstract ; and 
if he fixes upon having six times that strength, it will still be 
small, compared with most of those in Glasgow and the neigh- 
bourhood ; for it would appear that most of them are unnecessa- 
rily strong, or at least unnecessarily heavy. Butit may be said, 
why not have these shafts so strong as to put all risk of their 
breaking out of the question? This is certainly right ; but havin 
them unnecessarily strong, is attended not only with additional 
expense at first, but with a constant waste of power to drive 
them ; besides, it does not follow that by increasing their diame- 
ters we increase their strength ; for although large in diameter, 
and apparently sound, they may have very little strength, on 
account of air lodging in the heart of them at the time they were 
cast; hence the propriety of having all shafts proved by 2 
wrenching apparatus, whatever may be their diameters ; and in 
contracting for shafts, it would surely be better to have them 
at so much per lineal foot, of a certain strength, and not exceed- 
ing a certain weight, than by the ewt. which is the common 
practice. 
Dec. 17, 1818, 
Artic.e VIII. 
On Captain Cook’s Account of the Tides in the Endeavour River. 
In the 60th volume of the Philosophical Transactions there is 
a paper of Capt. Cook’s on the tides, which he observed in part 
of the coast of New Holland. 
About 11 o’clock in the evening of June 10, 1770, the Endea- 
vour struck on a reef of coral rocks about six leagues from the 
land, on the east coast of that country. This happened about 
the time of high water, and the crew immediately began to 
