292 Mr. J. Cockle on the Derivation of the word Theodolite. 



him in the opening of his " Abstract of a Paper on Algebraic 

 Triplets," &c. in part 1 of vol. iii. of the Proceedings of the 

 Royal Irish Academy, where he establishes similar relations 

 between the moduli and amplitudes of couplets. 



On the Derivation of the word Theodolite. 



Professor De Morgan has (see Phil. Mag. S. 3. vol. xxviii. 

 pp. 287-289) upon this subject offered some remarks which 

 attracted my attention to the point, and induced me to make 

 a conjecture as to the derivation, which I communicated to 

 the Mechanics' Magazine*. Mr. De Morgan's remarks have 

 given an interest to the topic ; and to this Journal, as the most 

 fitting place, I have ventured to transmit these comments 

 upon his remarks. 



The question whether the word theodolite is derived from 

 alidade entails upon us (not necessarily perhaps, but suffi- 

 ciently) the consideration of the point (1) whether the instru- 

 ment called alidade or alhidada is peculiar to the theodolite ; 

 and this latter point again conducts to the further question (2), 

 whether the alhidada differs from what is termed in the Panto- 

 7netria the " index with sightes." 



It will be convenient to consider the latter question first. 

 Let us turn to " The. 22. Chapter." of the " fyrst Booke " 

 (Longimetra) of the Pantometria (edition of 1571). This 

 chapter treats of " The making of an Instrument named the 

 Geometricall square." And, among other instructions, we are 

 told " . . , forget not to haue an index, not with commune 

 sightes, but thus, . . " Then follow directions for their con- 

 struction, and we are informed respecting the index that " it 

 hath place in the cetre, and there made to tarry, so that with 

 ease it may be turned from the first to any pointe." This is 

 the " index with sightes " as it is afterwards expressly called 

 in chapter 29 of the Longimetra. And, if there be any differ- 

 ence between this index with sightes and an alidade^ it must 

 consist in this, — that the index has one extremity Jixed to the 

 centre of the circle of which a quadrant is employed, while 

 the alidade, which may be regarded as a double index, has its 

 centre fixed to the centre of the circle to which it appertains. 

 In effect, if not precisely in form, the index must be a revol- 

 ving radius, and the alidade a revolving diameter ; each fur- 

 nished with " sightes." Mr. De Morgan, in his paper above 



and li Pt?-\-W=.a'^ (or a^—C^, as the case may be), we see that the point so 

 determined will be situate at a distance a from the given one, though not 

 in the axe. But, this last condition not being essential to the inquiry, the 

 virtual solution is complete. This is the theory of the Virtual Solution. 

 ♦ See pp. 159, 160 of vol. xlv. (No. 1201) of that work. 



