ASTRONOMY, ETC., OF SEVENTEENTH CENT. 213 



reader take a slip of cardboard, and, having marked upon it the exact 

 length of 9 inches, as from a to b, Fig. 99, let this length be divided 

 into ten equal parts, and let these be numbered from o to 10. The 

 slip of cardboard thus divided will form a vernier to a scale of inches, 

 such as a common foot-rule. Apply the. vernier to the foot-rule, so 

 that some one of the divisions on the cardboard shall exactly coincide 

 with one of the inch divisions on the rule. In the figure the sixth 

 vernier division is shown in a line with the nth inch; and now observe 

 that, going back on the vernier scale, each successive division is farther 

 to the right than the corresponding inch division by i, 2, 3, etc., 

 tenths of an inch successively, and when you come to o this is distant 

 from the 5th inch by T 6 oths of an inch. We can therefore determine the 

 position of a, with regard to the scale of inches, to be 5 T 6 o-, by merely 

 observing the coincidence of the sixth vernier division with one of 

 the marks on the inch-rule, and similarly of any other of the vernier 

 divisions. The thing to remark is that we can thus determine the posi- 

 tion of a to y^th of an inch, and yet employ a scale whose smallest 

 divisions are nine times as great as the length we measure. We have 

 here employed the inch merely as an illustration, for in practice the 

 vernier is applied only to scales which have divisions so small that 

 the vernier will in every place appear to have some one of its divisions 

 coinciding with some one of the scale. The observer pays no atten- 

 tion to the number of this mark on the scale, but notes the number 

 of the coinciding mark on the vernier ; this gives him at once the 

 number of tenths of a scale-division that the o point of the vernier is 

 past the division of the scale which precedes it. 



Continuing the account of the chief astronomical discoveries of the 

 seventeenth century, we have to mention the labours of J. D. CASSINI 

 (1625 1712), an Italian, who in 1669 was invited by Louis XIV. to 

 take charge of the lately-established Observatory of Paris. One of 

 the principal successes of Cassini was his discovery of the true theory 

 of the movements of Jupiter's satellites. These, as everybody knows, 

 are four in number, and they are eclipsed by the huge planet at almost 

 each revolution, so that these phenomena are of very frequent occur- 

 rence. Though these satellites are invisible to the unassisted eye, 

 they were attentively studied by astronomers, because, in the first 

 place, they presented to the view a system similar to the solar system 

 itself; and, secondly, because the frequent eclipses of the satellites 

 furnished a means of determining the longitudes of places on the 

 earth's surface. The eclipse of a satellite formed a signal, on seeing 

 which the observer noted the hour at his station, and this, when com- 

 pared with the hour at any other place where the same phenomenon 

 was observed, would indicate the difference of the longitudes. Cassini 

 was also the first who observed the rotation of Jupiter on his axis, and 

 he made the like observation with regard to the planet Mars. He com- 

 pleted the discoveries of Huyghens in the Saturnian system by find- 



