VOL. LXXII.] PHILOSOPHICAL TKANSACTIONS. 22Q 



XIII. Description of a Lamp-Micrometer, and the Method oj using it. By 

 Mr. William Herschel, F. R. S. p. 1 63. 



The great difficulty of measuring very small angles, such as hardly amount to 

 a few seconds, is well known to astronomers. Since I have been engaged in 

 observations on double stars, I have had so much occasion for micrometers that 

 would measure exceeding small distances exactly, that I have continually been 

 endeavouring to improve these instruments. 



The natural imperfections of the parallel wire micrometer, in taking the dis- 

 tance of very close double stars, are the following. When 2 stars are taken 

 between the parallels, the diameters must be included. I have in vain attempted 

 to find lines sufficiently thin to extend them across the centres of the stars, so 

 that their thickness might be neglected. The single threads of the silk-worm, 

 with such lenses as I use, are so much magnified, chat their diameter is more 

 than that of many of the stars. Besides, if they were much less than they are, 

 the power of deflection of light would make the attempt to measure the distance 

 of the centres this way fruitless: for I have always found the light of the stars to 

 play upon those lines, and separate their apparent diameters into 2 parts. Now 

 since the spurious diameters of the stars thus included, to my certain knowledge, 

 are continually changing according to the state of the air, and the length of 

 time we look at them, we are, in some respect, left at an uncertainty, and our 

 measures taken at different times, and with different degrees of attention, will 

 vary on that account. Nor can we come at the true distance of the centres of 

 any 2 stars, one from another, unless we could tell what to allow for the semi- 

 diameters of the stars themselves ; for different stars have different apparent 

 diameters, which, with a power of 227, may differ from each other, as I have 

 experienced, as far as 2 seconds. The next imperfection, is that which arises 

 from a deflection of light on the wires when they approach very near to each 

 other ; for if this be owing to a power of repulsion lodged at the surface, it is 

 easy to understand that such powers must interfere with each other, and give 

 the measures larger in proportion than they would have been, if the repulsive 

 power of one wire had not been opposed by a contrary power of the other. 

 Another very considerable imperfection of these micrometers is a continual un- 

 certainty of the real zero. I have found, that the least alteration in the situa- 

 tion and quantity of light will affect the zero, and that a change in the position 

 of the wires, when the light and other circumstances remain unaltered, will also 

 produce a difference. To obviate this difficulty, whenever I took a measure that 

 required the utmost accuracy, my zero was always taken immediately after, 

 while the apparatus remained in the same situation it was in when the measure 

 was taken ; but this enhances the difficulty, because it introduces an additional 

 observation. The next imperfection, which is none of the smallest, is that 



