1886.] on Telescojjic Objectives and Mirrors. 425 



I have before mentioned that it is possible to measure with the 

 spherometer quantities not exceeding 5-77^0 o ^f an inch, or with special 

 precaution much less even than that ; but useful as this instrument is 

 for giving us information as to the general curves of the surface, it is 

 utterly useless in the figuring process, that is, an error which would be 

 beyond the po\ver of the spherometer to detect, would make all the 

 difference between a good and a bad objective. 



Take actual numbers and this will be evident. Take the case of 

 a 27-inch objective of 34 feet focus ; say there is an error in centre of 

 one surface of about 6 inches diameter, which causes the focus of that 

 part to be -^^ of an inch shorter than the rest. 



For simplicity sake, say that its surface is generally flat ; the 

 centre 6 inches of the surface therefore, instaad of being flat, must be 

 convex and of over 1,000,000 inches radius, about 17 miles. The versed 

 sine of this curve, as measured by spherometer, would be only about 

 2'5'uowo^ 4 millionths of an inch, a quantity mechanically unmeasu- 

 rable, in my opinion. 



If that error was spread over 3 inches only instead of 6 inches, 

 the versed sine would only be about iooooott- Probably the effect on 

 the image of this 3-inch portion of -^q inch shorter focus would not 

 be appreciable on account of the slight vergency of the rays, but a 

 similar error near edge of objective certainly would be appreciable. 

 Until therefore some means be devised of measuring with certainty 

 quantities of 1 millionth of an inch and less, it is useless to hope 

 for any help from mechanical measurement in this part of the process. 



If then no known mechanical arrangement be delicate enough to 

 measure these quantities, how, it may be asked, are these errors 

 detected ? 



The answer to this is, that certain optical arrangements enable us 

 to carry our investigations far beyond the limits of mechanical 

 accuracy. Trials of the objective or mirror as a telescope are really 

 the crucial test, but there are various devices by which defects are 

 detected and localised. 



The best object to employ is generally a star of the third or fourth 

 magnitude, when such is available, but as it frequently occurs that no 

 such object is visible, recourse is had to artificial objects. The 

 minute image of the sun reflected from little polished balls of 

 speculum metal, or even a thermometer bulb is a very good object ; 

 polished balls of black glass are also used with good effect ; but as 

 the sun also is of somewhat fickle disposition in this country, we have 

 frequently to have recourse to artificial light. Small electric lamps, 

 such as this, with their light condensed, and thrown on a polished ball 

 are very useful. In fact, I am never without one of them in working 

 order. 



For the detection and localisation of errors it is very useful to be 

 provided with sets of diaphrams which leave exposed various zones 

 of the surface, the foci of which can then be separately measured, but 

 a really experienced eye does not need them. 



