22 ANNUAL OF SCIENTIFIC DISCOVERY. 



ing between given limits of numbers at the end of a certain time, I 

 came, of course, upon the introduction of n, which I could only de- 

 scribe as the ratio of the circumference of a circle to its diameter. 

 " Oh, my dear friend! that must be a delusion ; what can the circle 

 have to do with the numbers alive at the end of a given time?' 1 " I 

 cannot demonstrate it to you; but it is demonstrated.' 11 '*Oh! 

 stuff! I think you can prove anything with your differential calcu- 

 lus : figment, depend upon it." I said no more ; but, a few days af- 

 terwards, I went to him and very gravely told him that I had discov- 

 ered the law of human mortality in the Carlisle Table, of which he 

 thought verv hijfhlv. I told him that the law was involved in this 



^3 ' C7 k/ 



circumstance. Take the table of expectation of life, choose any 

 age, take its expectation and make the nearest integer a new age, do 

 the same with that, and so on ; begin at what age you like, you are 

 sure to end at the place where the age past is equal, or most nearly 

 equal, to the expectation to come. "You doivt mean that this al- 

 ways happens?' 1 "Try it." He did try, again and again; and 

 found it as I said. " This is, indeed, a curious thing ; this is a dis- 

 covery." I might have sent him about trumpeting the law of life : 

 but I contented myself with informing him that the same thing would 

 happen with any table whatsoever, in which the first column goes up 

 and the second goes down ; and that if a proficient in the higher 

 mathematics chose to palm a figment upon him, he could do without 

 the circle: a corsaire, corsaire et detni, the French proverb says. 

 Prof. De Morgan, London Atlienceum. 



STRAIGHT EDGES AND FLAT SURFACES. 



At the recent meeting of the British Association, Mr. James Wil- 

 liams read a paper on the "Flexibility of Iron," from which we ex- 

 tract the following interesting passage : 



"It is a common saying, 'rigid as a bar of iron, 1 and but few 

 persons are aware how very flexible iron, as well as other metal is. 

 Many builders in introducing cast and wrought girders, or beams to 

 support enormous weights, are of opinion that such beams are strong 

 enough to what they call ' bear any weight without bending, 1 and 

 are much surprised to be told by a mechanician that these same 

 girders, however stiff they may appear, will not even bear their own 

 weight without considerable deflexion. Many good working me- 

 chanicians even are quite unaware of the extreme subtlety of the 

 metal they are operating on. It is only that class of mechanics who 

 are engaged in scraping up valve faces, slide lathes, and similar 

 tools, and, above all, attempting to make 'flat surfaces 1 and 'straight 

 edges,' that can comprehend in a fair way the trying difficulty of 

 keeping s:idi works true after they have once got them so. In the 

 engineers 1 workshop, where straight bars of metal arc used for the 

 purpose of testing the work under process of manufacture, it is neces- 

 sary to keep at least three bars of surfaces of each kind for the pur- 

 pose of testing each other, for it has often been known that a straight 

 edge, got up with all the care and accuracy possible, true to-day will 

 be bent to-morrow ; indeed, the very handling of it while in use is 

 quite sufficient to distort to such a degree that the workman frequent- 

 ly has to put it by awhile until it comes to the natural temperature of 



