IX 



4. T)ii<it.njram*. -Tliis is the name given by Smith to diagrams exhibiting 

 the magnitude and direction of the resultant of the terrestrial magnetic 

 force and the force of the ship's magnetism at the point occupied by the 

 compass. The solution of the problem of finding for a ship in all 

 azimuths on even keel the dygogram of the whole resultant force is 

 given by him in the chapter headed "Ellipse and Circle," of the 'Ad- 

 miralty Manual,'- Appendix 2 (3rd edition, 1809, page 169-171). But it is 

 only for horizontal components of force that he has put dygograms into 

 a practical form ; and for this case, which includes the whole compass 

 problem of ordinary navigation, his dygograms are admirable both for 

 their beauty and for their utility. " Dygogram Number I." is the 

 curve locus of the extremity of a line drawn from a fixed point, O, in. 

 the direction, and to a length numerically equal to the magnitude, of the 

 horizontal component of the resultant force experienced by the needle- 

 when the ship is turned through all azimuths. This curve (however 

 great the deviations of the compass) he proves to be the Limagon oi' 

 Pascal that is to say, the curve (belonging to the family of epitrochoids) 

 described by the end of an arm rotating iu a plane round a point, which 

 itself is carried with half angular velocity round the circumference of a 

 fixed circle in the same plane. The length of the first-mentioned arm is 

 equal to the maximum amount of what is called (after Airy) the 

 quadrants! deviation ; the radius of the circle last mentioned is the 

 maximum amount of what Airy called the polar magnet deviation, and 

 Smith the semicircular deviation. ( When, as the writer of this article trusts 

 before long will be universally the case*, the quadrantal deviation is 

 perfectly corrected by Airy's method of soft iron correctors, the dygogram 

 Number I, will be reduced to a circle.) Besides the form of the curve 

 in any particular case, which depends on the ratio of the first-mentioned 

 radius to the second, to complete the diagram and use it we must know 

 the position of the fixed point through which the resultant radius-vector 

 is to be drawn, and must show in the diagram the magnetic bearing of 

 the ship's head, for which any particular point of the curve gives the 

 resultant force. {Smith gave all these elements by simple and easily 

 executed constructions, in the first and second editions of the ' Admiralty 

 Manual.' In the third edition he substituted, for his first method of 

 construction of the dygogram curve, a modification of it due to Lieut. 

 Colongue of the Russian Imperial Navy and of the Imperial Compass 

 Observatory, Cronstadt, and added several elegant constructions, also 

 due to Lieut. Colongue, for the geometrical solution of various compass 

 problems, by aid of the dygogram Number I. 



* The barrier against this being done hitherto has been the perniciously great length 

 of the compass needles used at sea, the shortest being about six inches, l^or a standard 

 compass the noedles ought not to be more than half an inch long. 



