174 PROCEEDINGS OF THE [AugUSt, 1887. 



of the field of view tlie beam sent through the two apertures will be acciuately 

 sent to the distant point. 



Instruments of each of these forms have long been in use, with some addi- 

 tional modifications for greater convenience of manipulation; the former in the 

 geodetic surveys of the EngHsh service, and the latter in those of the United 

 States. 



Several forms of Heliotropes have been devised by Drummond, Struve, 

 Gauss, Steinheil, Galton and Miller, each based upon some ingenious applica- 

 tion of optical principles ; of these I can sjjeak definitely only of the first and 

 of the last two. Although I know where the original descriptions of the other in- 

 struments are to be found, the works themselves are inaccessible to me, nor have 

 I yet been able to find the desired information in those works that are accessible. 

 Under article Heliotrope in the ninth edition of the Encyclopedia Britcinnica, 

 are described the plant and the mineral bearing that name, but no allusion is 

 made to the instrument. Under Heliography. instruments are described simi- 

 lar to the first of the above mentioned, including modifications apphed to those 

 in use in the English surveys. No mention is made of the writers whose 

 names I have given above, no notice is taken of theii- inventions. 



Drummond's apparatus, described in the Philosopliical Transactions for 1826, 

 consists of two telescopes and a mirror, the three so arranged and connected by 

 jointed bars, that when one telescope is dn-ected to the sun, and the other to 

 the distant point, the sun's light is then accurately reflected by the mm-or to 

 that point. 



Struve "s instrument is in principle the same as the second one I have de- 

 scribed above. 



Gauss invented two such instruments, and one of his contrivances is said to 

 enable the experimenter to use the sextant as a hehotrope. Let us suppose 

 that a third mnror were added to the sextant or octant, and firmly attached to 

 the index mirror, their reflecting surfaces forming with each other a suitable 

 fixed angle, easily determinable in the case of each instrument. This j)i'oper 

 fixed angle between the two index mirrors is equal to half the angle between 

 a ray, from the index mhror, incident on the horizon mii-ror and its reflected 

 ray going to the eye. It is not difiicult to see that if one now goes through the 

 well known operation of measuiing the angular distance between the centre of 

 the sun, and the given distant point, the third mirror T^ill reflect the sun's rays 

 directly to tha<. point, so long as we keep the image of the sun in apparent co- 

 incidence with that point seen in the centre of the field of view of the telescope 

 of the sextant. The range of appHcation of this form of hehotrope would be 

 limited hy the length of the arc of the octant or sextant ; a reflecting circle or 

 some similar instrument would give a greater range. Whether the device here 

 proposed be xDreciseiy the one adopted by Gauss, I am unable to say. This 

 sextant-heliotrope seems to be the first portable one that was invented. * 



* By a poi'tcible instrument Is here meant one wliicli does not require a fixed 

 stand or support, but may be put to use supported only by the bands of the experi- 

 menter. 



