264 Life of the Duke de Chaulnes. 



The duke de Chaulnes, in 1 755, gave the world a me- 

 moir which contained the principles of this discovery. He 

 first thought to apply the motion of an endless screw, to 

 obtain these minute divisions. The screw made of steel 

 would itself iriark the widths of the worm on the edge of the 

 limb to be divided ; and these marks, which ought to be 

 perfectly equal, he thought might be regulated by means of 

 an index; and hence the smallest parts would become accu- 

 rately obtained by means of very fine and truly equal sub- 

 divisions. 



Who would not conceive, with him, but that a division 

 made in this manner was exact ? Could we suppose there 

 would be any inequalities in a small number of steps of 

 such a screw made with care, and in ihose of the same 

 species of screw all marked with the same worm ? The 

 duke dc Chaulnes, nevertheless, found by experience that no 

 confidence whatever is to be placed in this method : the un- 

 equal hardness and expansion of the particles of steel in the 

 screw, and of the brass in the instrument, renders the steps 

 of the one unequal to those of the other. Whence it fol- 

 lows that this method of dividing instruments cannot be 

 depended on, and that we must detern^iine bv observation 

 the value of each part of a micrometer, and not content our- 

 selves bv measuring the whole, or a large portion of its 

 conrse depending for the intermediate divisions on the 

 equality of the worm of the screw, as is commonly done. 

 This is a neiv source of error, for the discovery of which 

 we are indebted to the duke de Chaulnes, and which may 

 alter the most important and best made ob>ervations. 



It now became necessary to try other methods. The 

 duke de Chaulnes had found for a longtime, that /■?/ (ipply- 

 hig a micrometer to a microscope he could measure accu- 

 rately as far as the four thousandth part of a line. It was 

 on this truly ingenious principle, that he, first of any one, 

 imdertook to give the division of astronomical instrumentsj 

 a greater degree of accuracy than thev were hitherto thought 

 capable of receiving. We cannot- here follow him throuiih 

 the whole of his contrivances : ail we can say is, that never 

 was any principle applied with more address, and we are 



astonished, 



