82 Mr. A. P. Trotter on a New Photometer. 



radius-bar or tube to which two needles are fastened. Fig. 3 

 is a full-size copy of a portion of the glass scale, on which, to 

 avoid fractions, the numbers are all multiplied by 10. The 

 inch unit was chosen instead of the centimetre, as the leading 

 screw had eight threads to the inch. 



It is evident that any curves in which simple relations exist 

 between the radius of curvature and the normal, the coordi- 

 nates, or other easily observed function of the curve, may be 

 readily drawn in the same way, but in general a scale of equal 

 parts is preferable to the reciprocal scale. The gain in accu- 

 racy and perfect evenness and smoothness of the curve over 

 what is obtainable by the use of compasses is the same as that 

 which was found in the case of the capillary curves of revolu- 

 tion, but the saving in time will of course, though still con- 

 siderable, be less. I am able to show as examples the cate- 



2 



nary p = — n, the undulating and the looped elastica p = + — 



the particular elastica p = ^n, the cycloid p = 2n with its iden- 



a 2 

 tical evolute, the tractrix p = — with its evolute the catenary 



and the evolute of the catenary, the parabola p = 2n with its 

 evolute, and all the conic sections (including the parabola) 



p=-p- 



It is, moreover, evident that the further use which Lord 

 Kelvin has made of the method of drawing curves from their 

 curvature in order to solve certain dynamical problems is one 

 to which the procedure described in this paper may be applied 

 with advantage. 



I must in conclusion express my obligation to Miss Ste- 

 venson, who has assisted me in the construction of these rules, 

 and who has spared no pains in setting out the beautifully 

 drawn curves which I am able to exhibit. 



VI. A New Photometer. By Alexander P. Trotter*. 



IN the course of my investigations on the distribution and 

 measurement of illumination f , which led to the exami- 

 nation of the lighting of several streets and public places in 

 London during the winter of 1891-92, I used illumination- 

 photometers of different kinds. The final form consisted of 



* Communicated by the Physical Society : read June 9, 1893. 

 t " The Distribution and Measurement of Illumination," Proc. Inst. 

 Civil Engineers, vol. ex. pt. iv. Paper No. 2619. 



