482 M. Blot 071 certain Points of Mathematical Optics. 



generally the derivations of the effects produced by successive 

 surfaces. Following the path which that enlightened mind had 

 opened, and conducting it perhaps more practically through 

 the difficulties of physical circumstances, the peculiarities of 

 which were foreign to his genius, I have succeeded in ascer- 

 taining, as I have stated above, that, in the case of very small 

 inflexions which he had treated, and which is the only one with- 

 in our power, all the effects of any optical instruments whatso- 

 ever result in three independent coefficients, having each a 

 distinct physical meaning, which can be made use of, and ca- 

 pable of being derived by the simple differentiation of a single 

 one amongst them, whose general expression I have obtained 

 under an explicit form. All the details peculiar to each in- 

 strument are then presented as deductions from this general 

 form, with so much simplicity and evidence, that I could not 

 refrain from presenting them thus. Those geometricians who 

 will take the trouble to cast their eyes over the table of con- 

 tents, in which I have enumerated the series of questions which 

 this method has enabled me to solve, will perhaps excuse my 

 having brought it forward in a work which at least rendered 

 the results necessary. 



Having thus established the details of the optical instru- 

 ments which are constantly used in astronomy, I explain the 

 other means of accuracy which are not less necessary to it, 

 such as the processes which serve to subdivide the dimensions 

 of measures laid down upon material instruments, the levels, 

 and the plumb-lines, which serve to regulate the horizontality 

 or the verticality of the axes of rotation and of the planes of 

 divided limbs, the mechanical clocks which serve to measure 

 time. Having described the principles of these instruments, 

 and their application in the regulation of divided instruments, 

 fixed or moveable, which are used in astronomy, I make them 

 concur in the investigation of the diurnal motion of the hea- 

 vens, whose exact circularity and uniformity I demonstrate, 

 by observations strictly calculated. I thus succeed in intro- 

 ducing the use of this motion instead of that of mechanical 

 clocks, as giving a much more perfect unit of time and its sub- 

 divisions. To have proceeded further in following up the lo- 

 gical plan of deduction which I prescribed to myself, it would 

 have been necessary to enter on new questions which would 

 have extended this volume too much, and I have thrown them 

 into the succeeding one. Then, in order to complete this 

 volume by results the preparatory notions of which were al- 

 already comprised in it, I have annexed thereto, as an addi- 

 tion, the description of the measure of the seconds pendulum 

 by the process of Borda, and the discussion of the experiments 



