290 Mr. J. Cockle on the true Amplitude of a Tessarine. 



ent hours of the day and night, at different seasons of the year, 

 and through different media. May not the velocity through 

 the ground vary with the direction of the current, — whether 

 east and west, or north and south ? 



I place great confidence in these results, as every care was 

 taken to eliminate all possible sources of error. Every mag- 

 net in use was in the observatory, and all the connexions and 

 adjustments were under my own eye. 



The adjustment of the receiving magnet was unaltered during 

 the experiment, and no change occurred for more than thirty 

 minutes after the experiments were finished. Each of the 

 pens recorded, in every instance, the armature time in the 

 distance from the primary to the vibratory dot. One-half this 

 record was shown to be the armature time, as follows : — 



The variable pen could not begin to descend until the 

 standard pen was down. Hence, considering the armature 

 time of the receiving magnet as insensible (as it was), with a 

 short circuit the interval of the two records would be equal to 

 the armature time of the standard pen. This interval, being 

 measured, was found to be exactly one-half the interval be- 

 tween the primary and vibratory dot of the standard pen. 



The length of this article forbids me to go into further de- 

 tail. In case further particulars are desired, it will give me 

 pleasure to furnish them by correspondence, or by a further 

 publication. 



Cincinnati Observatory, 

 November 16, 1849. 



XXXV. On the True Amplitude of a Tessarine; 07i the De- 

 rivation of the 'word Theodolite; and on Light under the 

 action of Magnetism. By James Cockle, Esq., M.A., of 

 Trinity College.^ Cambridge, Barrister- at-laxi^'*. 



ANY tessarine "w + i'x+fy + Jc'z, or t, may be put under the 

 formf 

 M^qcosp + i'rsmp+f{l — q) cosp + k'{l—r) s'mp}, 



* Communicated b)' the Author. Mr. Cockle takes an opportunity of 

 stating that remarks on the Tessarine Theory, as well as on the impossible 

 equations and quantities so intimately connected with it, will be found in 

 his Horce A/gebraicce, published in vols, xlvii. to 1. of the Mechanics' Ma- 

 gazine; and he also begs to refer the reader to the following papers pub- 

 lished in the same work, and in which he has adverted to the same subject; 

 viz. " On Algebraic Symbols," Mechanics' Magazine, vol. 1. pp. 292-294; 

 " On the Symbols of Algebra, and on the Theory of Tesssarines," Ibid, 

 p. 534; "On the Tessarine Algebra," Ibid. pp. 558, 559; " On certain 

 Researches of Mr. Boole, and the Symbol of Infinity," Ibid, vol.li. pp. 124, 

 125; "On Systems of Quadruple Algebra," Ibid. pp. 197-199; and see 

 some further remarks " On Quadruple Algebra," Ibid. vol. ii. pp. 557, «'58; 

 ^od " On Tessarines," Ibid. p. 610. 



t See Mechanics' Magazine, vol. li. p. 610. 



