234 SECTION MECHANICS. 



for the internal diameter you have to allow for the thickness of the 

 planks and the curve of the cask. Supposing that you know the 

 shape of the cask, you would then have the elements for a tolerably 

 accurate measure of it. But, in the first place, casks are not always 

 in the same shape ; and no person has yet been able, so far as I can 

 discover, to make up his mind as to what the proper shape for a cask 

 ought to be. Those difficulties, however, are very small, and are not 

 very important. For fiscal purposes it has been found quite sufficient 

 to take the head diameter and the bung diameter. Where much more 

 accuracy is required that is to say, where any large casks have to 

 be specially measured, it is necessary to take a diameter intermediate 

 between the bung and the head ; the actual measurement is then done 

 on paper and also by the slide rule. Here is one of the slide rules 

 ordinarily used. It is a good long one, and that is an advantage, 

 because it is read much more easily. The scales laid down upon it 

 are the ordinary ABC and D scales of a slide rule. These serve 

 generally for ordinary calculation, which merely requires the scale to 

 a half radius on one side of the rule and a whole radius on the other. 

 Besides this there is another method for measuring casks in a rough 

 way, and that is the diagonal measure. Here is a diagonal staff. It is 

 simply thrust through the bung, and put to the edge of cask, and then, 

 on the supposition that all casks are of the same size ; the volume of the 

 cask, of course, varies with the cube of the diagonal. There is also a 

 scale on the slide rule for that purpose. The ullage of a cask is also 

 of some importance. It means the measuring a cask which is partially 

 full. At the same time, as the measurement is chiefly done for fiscal 

 purposes, it is not a matter of much consequence, in measuring a cask 

 perhaps one-third full, whether there is a pint this way or the other. 

 Therefore the measurement is very rude. What is really done is to 

 dip a stick into it, and to see how much of it is wetted, and then by 

 comparing that with the known measurements of a standard cask you 

 find the quantity in the cask. There is no attempt at an accurate 

 geometrical measurement of ullage. 



What remains for me to say is on the measurement of gases and 

 liquids, and on that I shall be very short. I shall first speak of gas 

 meters ; for although the engineers present are pretty certainly aware 

 of the construction both of dry and wet gas meters, some of my hearers 



