1867.] On the Numerical Value of Euler^s Constant. 



429 



perty of the angle of convergence, by which the most minute differences 

 in the distances of objects and the slightest relief on their surfaces can be 

 detected, and by which also in the abnormal conversion introduced in its 

 action by the pseudoscope all our sensations are reversed. Therefore the 

 pseudoscope is the great test of the phenomena of binocular vision ; for 

 by reversing certain sensations which by constant habit we may hardly 

 notice, it renders them more conspicuous by the comparison of the abnor- 

 mal state brought out by its action, and proves the theory of binocular 

 vision in the most effective manner. 



A truth is never better established than when it can be shown that the 

 same principles are capable of producing contrary effects when they are 

 applied in a contrary way. 



Professor "Wheatstone, by adding the pseudoscope to the stereoscope, has 

 thus in the most scientific and ingenious manner completed his splendid 

 discovery, and left very little (we might almost venture to say that he has 

 left nothing) for further investigations in the physiology of binocular 

 vision. 



II. " On the Calculation of the Numerical Value of Euler's Constant, 

 which Professor Price, of Oxford, calls E." By William 

 Shanks, Esq., Houghton-le-Spring, Durham. Communicated 

 by the Rev. B. Price, F.R.S. Received March 28, 1867. 



In the year 1853 Dr. Rutherford, of the Royal Military Academy, Wool- 

 wich, sent a paper on the Computation of the value of v to the Royal 

 Society, and the paper was published in the * Proceedings' of that learned 

 body*. The value of tt is there given to 607 decimals, the first 440 being 

 the joint production of Dr. Rutherford and the author of this paper, and 

 the remaining 167 decimals having been calculated by the present writer, 

 for the accuracy of which he alone is responsible. Subsequently, the 

 Astronomer Royal, G. B. Airy, Esq., kindly presented the author's paper 

 on the Calculation of the value of the base of Napier's logarithms, to 

 upwards of 200 decimals ; the aforesaid paper also contained the Napierian 

 logarithms of 2, 3, and .5, as well as the modulus of the common system, 

 all to upwards of 200 places of decimals. This paper was not, however, 

 pubhshed, but deposited in the Archives of the Royal Society ; but an abs- 

 tract, containing the numerical results, was printed in the * Proceedings 'f. 

 In a paper sent by the author to the Astronomer Royal, and forwarded by 

 him to the Royal Society, will, the author believes, be found the reciprocal 

 of the prime number 1 7389, consisting of a circulating period of no less 

 than 1 7388 decimals, the largest on record. Some few remarks are also 

 given touching circulates generally, and the easiest modes of obtaining them. 

 The writer now desires to supplement what he then did, by giving the 



* Vol. vi. p. 273. 



t Vol. vi. p. 397. 



