1G2 Pit. Clark on the Arithmetical Calculation of Solids. 



can give with strict accuracy the relation between rectilinear and circular 

 dimensions. The cylindrical, spherical, or conical dimensions, will be too 

 much, by one in 13,931 of cubical dimension, corresponding to one in 

 41,792 of linear dimension. This would be an eighth of an inch on the 

 height of St. Rollox chimney. Such minuteness must, more than ten 

 times, exceed the accuracy that is attainable in the ordinary operations 

 of measuring, in subservience to manufacture and the arts; and, therefore, 

 for all ordinary purposes, it were idle to apply for any correction. My 

 recollection leads me to doubt whether minuter accuracy has been reached 

 in the most scientific measurements, where measurement itself is a primary 

 object, instead of being, as it commonly is, a subsidiary one; for example, 

 in the comparison of standard measures of length. But it is important 

 that the correction be such as can be made without calculating the results 

 over again. Now, this is what can be done most easily. Subtract one- 

 14,000th, and you get a remainder, that is one in about 2,800,000 of 

 cubical content, still above the truth. If we choose again to subtract 

 one-200th of the former correction, we shall get a remainder that is now 

 too low by 3 of cubical dimension, corresponding to one of linear dimen- 

 sion, in 1,000 millions, or, more correctly still, 999 millions. These are 

 very simple and easy corrections. Were they less easy, the objection to 

 them, as corrections, would be of little practical weight, for the applica- 

 tion of any correction can but very seldom be needed. Subject to the 

 foregoing corrections, 1728 is the fourth part of the circumference of a 

 circle whose diameter is 2200. This remarkable numerical coincidence, 

 you will perceive, is the foundation of the table. 



Such a table as the foregoing should find a place, not only in every 

 book of mensuration, but in every book of common arithmetic. I need 

 not point out to you how much, by the aid of it, the most generally 

 required parts of mensuration might be taught in ordinary schools, as part 

 of the course of arithmetic. 



By making so useful a discovery generally known, there is the reality 

 of the diffusion of useful knowledge without the cant; there is honour to 

 the worthy dead, and such advantage to the living as he felt delight in 

 conferring. 



Under this impression, it has occurred to me that the subject will pro- 

 bably appear to you a proper one to submit to the Glasgow Philosophical 

 Society, not only as likely to be grateful to many of the members, so 

 recently after the departure of the venerable author of the discovery, but 

 in the view of making it more useful, as they will be able, and, I have no 

 doubt, they will be disposed to make it more widely known. 



In all questions relating to the simplification of weights and measures, 

 a subject much studied by Mr. Wilson, his discovery has long appeared 

 to me to have an important bearing; for he seems by this discovery to 

 have conclusively determined that the inch, as the twelfth part of the 

 foot, must ever be retained, for the sake of its convenience, in computing 

 cubical dimension, whenever the circle is an element of that dimension. 



