ON THE CONSTRUCTION OP LARGE REFLECTING TELESCOPES. 81 



specula, being in a great measure dependent on manual dexterity, were un- 

 certain and not well-suited to large specula; accordingly, at an early period of 

 these expei'iments, in 1827, a machine was contrived for the purpose which 

 has subsequently been improved, and by means of it a close approximation 

 to the parabolic figure can be obtained with certainty : as it has been de- 

 scribed in the Philosophical Transactions for 1840, it is unnecessary to do 

 more than to point out the principle on which it acts ; the speculum is made 

 to revolve very sloM'ly, while the polishing tool is draAvn backwards and for- 

 wards by one excentric or crank, and from side to side slowly by another. 

 The polishing tool is connected with the excentrics by a ring which fits it 

 loosely, so as to permit it to revolve, deriving its rotatory motion from the 

 speculum, but revolving much more slowly. It is counterpoised so that it 

 may be made sufficiently stiff, and yet press lightly on the speculum, the 

 pressure being about one pound for every circular superficial foot. The 

 motions of this machine are relatively so adjusted, that the focal length of the 

 speculum during the polishing process, or towards the latter end of it, shall 

 be gradually becoming slightly longer ; and the figure will depend in a great 

 measure upon the rapidity with which this increase in the focal length takes 

 place. It will be evident that a surface spherical originally will cease to be 

 so if, while subjected to the action of the polisher, it is in a continual state of 

 transition from a shorter to a longer focus ; in fact during no instant of time 

 will it be actually spherical, but some curve differing a little from the sphere, 

 and which may be made to approach the parabola, provided it be possible in 

 practice to give effect to certain conditions. 



An immense number of experiments, where the results were carefully re- 

 gistered, eventually established an empirical formula, which affords at pre- 

 sent very good practical results, and may hereafter perhaps be considerably 

 improved. In fact, when the stroke of the first excentric is one third the 

 diameter of the speculum, and that of the second excentric is such as to pro- 

 duce a lateral motion of the bar which moves the polisher, measured on the 

 edge of the tank, equal to 0"27, the diameter of the speculum, (or referred to 

 the centre of the polisher to 0*17,) the figure will be nearly parabolic. The 

 velocity and direction of the motions which produce the necessary friction 

 being adjusted in due proportion by the arrangements of the machine, and 

 the temperature of the speculum being kept uniform by the water in which 

 it is immersed, there remain still other conditions which are essential to 

 the production of the required result. The process of polishing differs very 

 essentially from that of grinding ; in the latter, the powder employed runs 

 loose between two hard surfaces, and may produce scratches possibly equal 

 in depth to the size of the particles ; in the polishing process the case is very 

 different ; there the particles of the powder lodge in the comparatively soft 

 material of which the surface of the polishing tool is formed, and as the por- 

 tions projecting may bear a very small proportion to the size of the particles 

 themselves, the scratches necessarily will be diminished in the same propor- 

 tion. The particles are forced thus to imbed themselves, in consequence of 

 the extreme accuracy of contact between the surface of the polisher and the 

 speculum. But as soon as this accurate contact ceases, the polishing process 

 becomes but fine grinding. It is absolutely necessary therefore to secure 

 this accuracy of contact during the whole process ; if the surface of a polisher 

 of considerable dimensions is covered with a thin coat of pitch of sufficient 

 hardness to polish a true surface, however accurately it may fit the speculum, 

 it will very soon cease to do so, and the operation will fail. The reason is 

 this, that particles of the polishing powder and abraded matter will collect 

 in one place more than another, and as the pitch is not elastic, close contact 



1844. G 



