1881.] Mr. A. J. Ellis. On the Potential Radix. 



377 



The method which I am advocating is open to no such objection ; 

 it is moreover rapid, allowing little time for the alteration by exposure 

 of the surface under consideration, and it is independent of the very 

 difficult determination of the contact angle of liquid and solid, which 

 enters into some other methods. 



At the same time the results are probably not so accurate as could 

 be obtained by the use of photography for recording the form of the 

 drop. 



I am in hopes of obtaining, by its means, results which may, in some 

 measure, serve to verify the fundamental assumptions of the theory on 

 which the value of the so-called surface tension is calculated. 



Of the phenomena, to which I have ventured incidentally to call 

 attention, that of the approximate constancy of the drop-depth, re- 

 quires closer investigation than I have been able to give it, as it seems 

 to offer a very satisfactory means of obtaining a first approximation 

 to the value of the surface tension. In all experiments on this sub- 

 ject the scrupulous cleanliness so absolutely necessary renders pro- 

 gress slower than many would suppose, which is my excuse for pre- 

 senting an investigation, which I trust may be found useful, though 

 obviously incomplete. 



III. " Postscript to the Chronological Summary of Methods of 

 Computing Logarithms in my Paper on the Potential 

 Radix." By Alexander J. Ellis, B.A., F.R.S., F.S.A. 

 Received May 18, 1881. 



After the publication of my " Chronological Summary of Methods of 

 Computing Logarithms," in the " Proceedings " for 3rd February, 

 1881 (vol. 31, pp. 401-407), Mr. Isaac Todhunter, F.R.S., kindly 

 pointed out to me an almost unknown pamphlet by George Atwood, 

 F.R.S., inventor of " Atwood's Machine," which he informs me is 

 not mentioned even by Dr. Thomas Young, in his account of Atwood. 

 A copy of the pamphlet is in the library of the Royal Astronomical 

 Society, and at the request of Mr. Peter Gray, F.R.A.S., was kindly 

 lent to me for inspection. The following account of this important 

 and little known work should be inserted in my summary, on p. 403, 

 between 1771, Flower, and 1802, Leonelli : — 



1786. Ahvood, George, FR.S. "An Essay on the Arithmetic of 

 Factors, applied to various computations which occur in the practice of 

 numbers." This is essentially a method, when any number A is given, 

 of finding factors, M, p, q, r, s, t, such that A X M being very nearly 

 =1, of the form *9 . . . or 1*0 . . ., and p, q, r, s, t being of the form 

 l + 'O^ (where 0« means n successive zeroes, as in the notation of my 



