THE 



THE 



THELPHU'SIANS. The name given 

 by Milne Edwards to a tribe of brachyu- 

 rous crustaceans belonging to his family 

 Catometopes, and constituting a connect- 

 ing link between the Cancerians and the 

 Gecarcinians, or land-crabs. They are 

 named from the genus thelphusa, sup- 

 posed to be the Heracleotic crabs of 

 Aristotle. 



THE'NARDITE. Anhydrous sul- 

 phate of soda, found in crystalline crusts, 

 at the bottom of the briny waters at the 

 Salines d'Espartines, near Madrid. It is 

 used in the preparation of carbonate of 

 soda. 



THEO'DOLITE. An instrument for 

 measuring horizontal angles contained 

 between lines supposed to be drawn from 

 any point to two distant objects. In its 

 simplest form, the theodolite consists of 

 a divided circle, which is to be set parallel 

 with the horizon ; and a telescope which 

 has so much motion in a vertical plane as 

 to enable the observer to view any object 

 which he may require above or below the 

 horizon. The etymology of the term is 

 obscure. 



THE'OREM (^ewpujua, that which is 

 looked at). In Mathematics, a theorem 

 is a proposition in which the truth of 

 some principle is asserted; the object of 

 the demonstration being to show how the 

 truth of the proposed principle may be 

 deduced from the axioms and definitions, 

 or from other truths which have been 

 previously and independently established. 

 The theorem asks for demonstration only, 

 and thus differs from the problem, which 

 asks for discovery both of method and of 

 demonstration. See Problem. 



THEORY {Oeuypla, speculation). A 

 system of rules, intended to explain cer- 

 tain facts, with reference to some real or 

 hypothetical law. Thus, the theory of 

 the planetary motions is deduced from 

 the principle of gravitation ; that of 

 light, from the undulatory hypothesis. 

 A hypothesis differs from a theory, as 

 being an assumption conceived to afford 

 a support to the re il or supposed law : 

 thus, to refer the phenomena of gravi- 

 tation to the universal diffusion of ether, 

 is a hypothesis. The theory is, however, 

 unaffected by the hypothesis. 



THEORY OF COUPLES. The term 

 couple was applied by M. Poinsot to a 

 pair of equal and opposite forces, not 

 equilibrating each other, and not capal le 

 of being replaced by a single force, or 

 resultant, — in fact, an incomposible cou- 

 ple. The plane of the couple is the 

 336 



plane drawn through the parallel forces 

 the arm of the couple is any line drawn 

 perpendicular to the forces from the di- 

 rection of one to that of the other , the 

 axis of the couple is any straight line 

 perpendicular to its plane, if we con- 

 sider any axis, it will be evident that the 

 moment or leverage of the couple to turn 

 the system about that axis is represented 

 by the product of one of the forces and 

 the arm. For if, with reference to the 

 axis, X be the arm of one of the forces, 

 X + a is that of the other, a being the 

 arm of the couple. Hence, if P be one 

 of the forces, the united leverage is 

 P (a? ± a) — Pa; or ± Pa. This product 

 Pa is called the moment of the cou- 

 ple. Pen. Cycl. 



THEORY OF EQUATIONS. The 

 Theory of Algebraical equations is that 

 branch of analysis, which relates to the 

 discussion of equations when presented 

 in their most convenient form for solu- 

 tion ; and its great object is to develope 

 the properties and to evolve the values of 

 the real and the imaginary roots. See 

 Equation f Algebraic. 



THERMAL RAYS (6»epM»j, heat). 

 Luminous thermal rays are those rays of 

 heat which are combined with flame, as 

 those emitted from the sun, which pene- 

 trate all diathermanous substances. 

 Those rays, on the contrary, are said to 

 be opaque, which proceed from bodies 

 heated below the point of active com- 

 Imstion. Hence, bodies are either per- 

 fectly or partially diathermanous, the 

 former transmitting all the thermal 

 colours, the latter only some of 

 them. 



THERMAL SPECTRUM. When 

 Thermal rays have been transmitted 

 through a diathermanous prism, they 

 compose a thermal spectrum, in like 

 manner as the sun's rays form a solar 

 spectrum. See Spectrum. 



THERMO-ELECTRICITY {Oep^t), 

 heat). A term applied to the phenomena 

 which are exhibited by electricity as de- 

 veloped by heat. The condition of the 

 electrical equilibrium of bodies is dis- 

 turbed by heat, especially when the tem- 

 perature of a part of their mass is either 

 raised or lowered ; the effects being exhi- 

 bited by the deflexions of a magnetized 

 and balanced needle. 



THERMO-MULTIPLIER {OeptJ^n, 

 heat). A thermo-electric pile, employed 

 by Melloni for detecting changes of tem- 

 perature, and endowed with much greater 

 sensibility to the impressions of heat 



