from the water in which they have been plunged, as soon as the red- 

 ness in the centre of the drop ceases to he visible. 



Since the smallest portion of any polarizing crystal polarizes or 

 depolarizes light according to its position, the author expected to find 

 the same property in the fragments of a broken drop, but upon trial 

 they did not appear to possess this property. 



Of the many important conclusions to which the author thinks that 

 these experiments are calculated to conduct us, there is one which 

 he considers too palpable to be passed over, namely, that when the 

 particles of glass are separated to a certain distance by the expansive 

 agency of heat, they assume a crystalline arrangement, which would 

 not be discovered but by fixing them in this state by sudden cooling ; 

 since the gradual approximation of the particles, by slow cooling, en- 

 tirely destroys the crystalline structure thus produced. 



In a note the author remarks, that on more than one authority 

 steel is said to be less dense after being hardened by quenching than 

 before, which he ascribes, as in glass, to the sudden induration hav- 

 ing commenced at the surface. And he takes occasion to suggest 

 the possibility, that under these circumstances moderate changes of 

 temperature may not occasion any degree of expansion, and that we 

 may obtain, within certain limits, a substance of invariable length 

 that may be useful for pendulums. 



Description of a new Instrument for performing mechanically the Invo- 

 lution and Evolution of Numbers. By Peter M. Roget, M.D. Com- 

 municated by William Hyde Wollaston, M.D. Sec. R.S. Read 

 November 17, 1814. [Phil. Trans. 1815, p. 9.] 



The present instrument depends upon a new extension of the prin- 

 ciple of the common sliding-rule ; for as in that numbers themselves 

 are multiplied or divided by the mechanical addition of their loga- 

 rithms, so in this their logarithms are multiplied or divided by me- 

 chanical application of corresponding logometric spaces. 



In the common tables of logarithms, that of 10 is 1, and those of 

 its simple powers are 2, 3, 4, &c. ; so also the logarithm of the square 

 root of 10 is |, or 5 ; the fourth root is , or '25, being a decimal 

 index expressing a power of 10 less than unity. In the same manner 

 all other numbers are considered as powers of 10, and their logarithms 

 are integral or decimal indices of those powers. 



In the common sliding-rules the divisions are so placed as to mark 

 intervals that are proportional to these indices ; so that by simple 

 juxtaposition the sum or difference of any two indices, and conse- 

 quently the product or quotient of any two numbers, appears by in- 

 spection. 



In this manner, by addition of two equal logometric intervals, the 

 square of any number may be found ; but the instrument so con- 

 structed is not prepared to give the higher powers, without propor- 

 tionally frequent repetitions of the same process, which gives at length 

 a multiple of the index by the tedious operations of repeated addition. 



