Dehra is the headquarters of the Trigonometrical Survey and of the Forest Department, besides being a cantonment for a Gurkha force.
The point separating the integers from the decimal fractions seems to be the invention of Bartholomaeus Pitiscus, in whose trigonometrical tables (1612) it occurs and it was accepted by John Napier in his logarithmic papers (1614 and 1619).
The heights of peaks determined by exact processes of trigonometrical observation are bound to be more or less in error for three reasons: (1) the extraordinary geoidal deformation of the level surface at the observing stations in submontane regions; (2) ignorance of the laws of refraction when rays traverse rarefied air in snow-covered regions; (3) ignorance of the variations in the actual height of peaks due to the increase, or decrease, of snow.
The calculation of the logarithms not only of numbers but also of the trigonometrical functions is therefore due to Briggs and Vlacq; and the results contained in their four fundamental works - A rithmetica logarithmica (Briggs), 1624; Arithmetica logarithmica (Vlacq), 1628; Trigonometria Britannica (Briggs), 1633; Trigonometria artificialis (Vlacq), 1633 - have not been superseded by any subsequent calculations.
Among the contents of this book we simply mention a trigonometrical chapter, in which the words sinus versus arcus occur, the approximate extraction of cube roots shown more at large than in the Liber abaci, and a very curious problem, which nobody would search for in a geometrical work, viz.
A trigonometrical survey of British India was begun in 1800 and the country can now boast of a survey which in most respects is equal to those of most European states.
The French academician Bouger, who was chief of the scientific commission sent to Ecuador in 1736 to measure a degree of the meridian on the equator, made a trigonometrical measurement of Iliniza, and Wagner ascended to within 800 ft.
The treatment of an angle as generated by rotation, the investigation of the relations between trigonometrical ratios and circular measure, the application of interpolation to trigonometrical tables, and the general use of graphical methods to represent continuous variation, all imply an analytical onlook, and must therefore be deferred to this stage.
At length he would reach the corn, and selecting a suitable ear, frisk about in the same uncertain trigonometrical way to the topmost stick of my wood-pile, before my window, where he looked me in the face, and there sit for hours, supplying himself with a new ear from time to time, nibbling at first voraciously and throwing the half-naked cobs about; till at length he grew more dainty still and played with his food, tasting only the inside of the kernel, and the ear, which was held balanced over the stick by one paw, slipped from his careless grasp and fell to the ground, when he would look over at it with a ludicrous expression of uncertainty, as if suspecting that it had life, with a mind not made up whether to get it again, or a new one, or be off; now thinking of corn, then listening to hear what was in the wind.
Russian explorers and natives of India trained for geographical reconnaissance, and employed in connexion with the great trigonometrical survey of India, had done so much towards clearing away the mists which enveloped the actual course of the river, that all the primary affluents were known, although their relative value was misunderstood, but the nature of the districts which bordered the river in Afghan Turkestan was so imperfectly mapped as to give rise to considerable political complication in framing the boundary agreement between Great Britain and Russia.