344 



Messrs. J. C. McConnel and D. A. Kidd. [June 21, 



of the whole stand being slightly displaced when the telescope is slid 

 down to its lower position. In fact in our circumstances an ordinary 

 cathetometer would have been practically useless, owing to the bending 

 of the floor and table at the slightest movement of the observer. 

 Observations, even with our special form, required the utmost care. 

 The micrometer scale had twenty divisions, each 012 mm. in actual 

 size, and corresponding to about 0'3 mm. on the other scale. The 

 magnification of the telescope, as compared with the eye at 9 inches, 

 was about 5. This was scarcely great enough. We intended also to 

 have the micrometer divisions half the size, but the maker was not 

 able to graduate it so finely. Indeed, as it was, the lines were rather 

 too thick. 



By estimating tenths of the micrometer divisions we could read to 

 O03 mm., but the readings might easily be at least 0*06 mm. in error. 

 Each determination of the length between the needles depends on four 

 readings, the upper needle, and its corresponding scale division, and the 

 lower needle, and its scale division. If the four readings happened 

 to have each the maximum error 0'06 mm. with a suitable sign, the 

 total error might be 0"24 mm. Such a combination of chances is 

 highly improbable, but an error of 01 mm. is obviously not unlikely. 

 The cathetometer would have been a useful instrument for measuring 

 a large and regular extension with accuracy, but it was not adapted 

 to detect very small extensions, and a system of levers, which we 

 adopted as a rough mode of measurement in our second set of 

 apparatus, proved ;so much more satisfactory and suitable to our 

 purposes, that we almost entirely discarded the cathetometer. This 

 contrivance is shown in fig. 3, in the form finally adopted, a and b 

 are sections of the projecting ends of glass needles fixed in the ice, 

 cdef is a bent iron wire, " the indicator," booked to a wire loop m 

 securely fastened to a, h is a wooden lever suspended by a thread n, 

 which owing to the counterpoise pulls the indicator upwards with a 

 thread fastened to awire loop at e. The indicator is kept from rising 

 by the connecting fibre, a piece of stiff wire hooked at one end to the 

 loop g, fastened to &, and at the other to a bend d* in the indicator. 

 The lower end of the indicator gives the reading on a paper millimetre 

 scale Z, gummed on to the mirror^. The mirror, of course, enables the 

 observer to avoid errors of parallax. The stand of the mirror is glued 

 to the lower collar. To appreciate the action of the levers, regard a 

 for the moment as fixed, then lowering b through a small distance r will 

 move /"through a distance s = vr at right angles to mf, where v is the 

 ratio of the distance mf to the perpendicular let fall from m on the 

 line gd produced if necessary. If md be made perpendicular to gd, 

 when / is in the middle of the scale, the multiplier v remains 

 practically constant. This precaution was not always taken, but 

 * This was a deeper bend than is shown in the figure. 



